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Recover the square spiral example code. 

I hve no idea how this isn't in VCS.  I checked hg and git.  Is it in
an old branch that I deleted before merging or something?  I have
backups from which to restore, but it would be nice to know how I effed
it up in the first place, eh?
This commit is contained in:
Simon Forman 2021-11-27 09:04:25 -08:00
parent f96013d649
commit 1b193b1924
63 changed files with 17476 additions and 1013 deletions
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from notebook_preamble import J, V, define"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Square Spiral Example Joy Code"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"Here is the example of Joy code from the `README` file:\n",
"\n",
" [[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte\n",
"\n",
"It might seem unreadable but with a little familiarity it becomes just as\n",
"legible as any other notation. Some layout helps:\n",
"\n",
" [ [[abs] ii <=]\n",
" [\n",
" [<>] [pop !-] ||\n",
" ] &&\n",
" ]\n",
" [[ !-] [[++]] [[--]] ifte dip]\n",
" [[pop !-] [--] [++] ifte ]\n",
" ifte\n",
"\n",
"This function accepts two integers on the stack and increments or\n",
"decrements one of them such that the new pair of numbers is the next\n",
"coordinate pair in a square spiral (like the kind used to construct an\n",
"Ulam Spiral). \n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Original Form\n",
"\n",
"It's adapted from [the original code on StackOverflow](https://stackoverflow.com/questions/398299/looping-in-a-spiral/31864777#31864777):\n",
"\n",
"\n",
"> If all you're trying to do is generate the first N points in the spiral\n",
"> (without the original problem's constraint of masking to an N x M\n",
"> region), the code becomes very simple:\n",
"\n",
" void spiral(const int N)\n",
" {\n",
" int x = 0;\n",
" int y = 0;\n",
" for(int i = 0; i < N; ++i)\n",
" {\n",
" cout << x << '\\t' << y << '\\n';\n",
" if(abs(x) <= abs(y) && (x != y || x >= 0))\n",
" x += ((y >= 0) ? 1 : -1);\n",
" else\n",
" y += ((x >= 0) ? -1 : 1);\n",
" }\n",
" }"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Translation to Joy\n",
"\n",
"I'm going to make a function that take two ints (`x` and `y`) and\n",
"generates the next pair, we'll turn it into a generator later using the\n",
"`x` combinator."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### First Boolean Predicate\n",
"\n",
"We need a function that computes `abs(x) <= abs(y)`, we can use `ii` to\n",
"apply `abs` to both values and then compare them\n",
"with `<=`:\n",
"\n",
" [abs] ii <=\n",
"\n",
"I've defined two short-circuiting Boolean combinators `&&` and `||` that\n",
"each accept two quoted predicate programs, run the first, and\n",
"conditionally run the second only if required (to compute the final\n",
"Boolean value). They run their predicate arguments `nullary`."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"define('&& [nullary] cons [nullary [0]] dip branch')\n",
"define('|| [nullary] cons [nullary] dip [1] branch')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Given those, we can define `x != y || x >= 0` as:\n",
"\n",
" [<>] [pop 0 >=] ||\n",
"\n",
"And `(abs(x) <= abs(y) && (x != y || x >= 0))` as:\n",
"\n",
" [[abs] ii <=] [[<>] [pop 0 >=] ||] &&\n",
"\n",
"It's a little rough, but, as I say, with a little familiarity it becomes\n",
"legible."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The Increment / Decrement Branches\n",
"\n",
"Turning to the branches of the main `if` statement:\n",
"\n",
" x += ((y >= 0) ? 1 : -1);\n",
"\n",
"Rewrite as a hybrid (pseudo-code) `ifte` expression:\n",
"\n",
" [y >= 0] [x += 1] [X -= 1] ifte\n",
"\n",
"Change each C phrase to Joy code:\n",
"\n",
" [0 >=] [[++] dip] [[--] dip] ifte\n",
"\n",
"Factor out the dip from each branch:\n",
"\n",
" [0 >=] [[++]] [[--]] ifte dip\n",
"\n",
"Similar logic applies to the other branch:\n",
"\n",
" y += ((x >= 0) ? -1 : 1);\n",
"\n",
" [x >= 0] [y -= 1] [y += 1] ifte\n",
"\n",
" [pop 0 >=] [--] [++] ifte"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### \"Not Negative\""
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"define('!- 0 >=')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Putting the Pieces Together\n",
"\n",
"We can assemble the three functions we just defined in quotes and give\n",
"them them to the `ifte` combinator. With some arrangement to show off\n",
"the symmetry of the two branches, we have:\n",
"\n",
" [[[abs] ii <=] [[<>] [pop !-] ||] &&]\n",
" [[ !-] [[++]] [[--]] ifte dip]\n",
" [[pop !-] [--] [++] ifte ]\n",
" ifte\n",
"\n",
"As I was writing this up I realized that, since the `&&` combinator\n",
"doesn't consume the stack (below its quoted args), I can unquote the\n",
"predicate, swap the branches, and use the `branch` combinator instead of\n",
"`ifte`:\n",
"\n",
" [[abs] ii <=] [[<>] [pop !-] ||] &&\n",
" [[pop !-] [--] [++] ifte ]\n",
" [[ !-] [[++]] [[--]] ifte dip]\n",
" branch"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"define('spiral_next [[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's try it out:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 0\n"
]
}
],
"source": [
"J('0 0 spiral_next')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 -1\n"
]
}
],
"source": [
"J('1 0 spiral_next')"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 -1\n"
]
}
],
"source": [
"J('1 -1 spiral_next')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-1 -1\n"
]
}
],
"source": [
"J('0 -1 spiral_next')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Turning it into a Generator with `x`\n",
"\n",
"It can be used with the x combinator to make a kind of generator for\n",
"spiral square coordinates.\n",
"\n",
"\n",
"We can use `codireco` to make a generator\n",
"\n",
" codireco ::= cons dip rest cons\n",
"\n",
"It will look like this:\n",
"\n",
" [value [F] codireco]\n",
"\n",
"Here's a trace of how it works:\n",
"\n",
" [0 [dup ++] codireco] . x\n",
" [0 [dup ++] codireco] . 0 [dup ++] codireco\n",
" [0 [dup ++] codireco] 0 . [dup ++] codireco\n",
" [0 [dup ++] codireco] 0 [dup ++] . codireco\n",
" [0 [dup ++] codireco] 0 [dup ++] . cons dip rest cons\n",
" [0 [dup ++] codireco] [0 dup ++] . dip rest cons\n",
" . 0 dup ++ [0 [dup ++] codireco] rest cons\n",
" 0 . dup ++ [0 [dup ++] codireco] rest cons\n",
" 0 0 . ++ [0 [dup ++] codireco] rest cons\n",
" 0 1 . [0 [dup ++] codireco] rest cons\n",
" 0 1 [0 [dup ++] codireco] . rest cons\n",
" 0 1 [[dup ++] codireco] . cons\n",
" 0 [1 [dup ++] codireco] . "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But first we have to change the `spiral_next` function to work on a\n",
"quoted pair of integers, and leave a copy of the pair on the stack.\n",
"From:\n",
"\n",
" y x spiral_next\n",
" ---------------------\n",
" y' x'\n",
"\n",
"to:\n",
"\n",
" [x y] [spiral_next] infra\n",
" -------------------------------\n",
" [x' y']"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0 1]\n"
]
}
],
"source": [
"J('[0 0] [spiral_next] infra')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So our generator is:\n",
"\n",
" [[x y] [dup [spiral_next] infra] codireco]\n",
"\n",
"Or rather:\n",
"\n",
" [[0 0] [dup [spiral_next] infra] codireco]\n",
"\n",
"There is a function `make_generator` that will build the generator for us\n",
"out of the value and stepper function:\n",
"\n",
" [0 0] [dup [spiral_next] infra] make_generator\n",
" ----------------------------------------------------\n",
" [[0 0] [dup [spiral_next] infra] codireco]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here it is in action:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0 0] [0 1] [-1 1] [-1 0]\n"
]
}
],
"source": [
"J('[0 0] [dup [spiral_next] infra] make_generator x x x x pop')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Four `x` combinators, four pairs of coordinates."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Conclusion\n",
"\n",
"So that's an example of Joy code. It's a straightforward translation of\n",
"the original. It's a little long for a single definition, you might\n",
"break it up like so:\n",
"\n",
" _spn_P ::= [[abs] ii <=] [[<>] [pop !-] ||] &&\n",
"\n",
" _spn_T ::= [ !-] [[++]] [[--]] ifte dip\n",
" _spn_E ::= [pop !-] [--] [++] ifte\n",
"\n",
" spiral_next ::= _spn_P [_spn_E] [_spn_T] branch\n",
"\n",
"This way it's easy to see that the function is a branch with two\n",
"quasi-symmetrical paths.\n",
"\n",
"We then used this function to make a simple generator of coordinate\n",
"pairs, where the next pair in the series can be generated at any time by\n",
"using the `x` combinator on the generator (which is just a quoted\n",
"expression containing a copy of the current pair and the \"stepper\n",
"function\" to generate the next pair from that.)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"define('_spn_P [[abs] ii <=] [[<>] [pop !-] ||] &&')\n",
"define('_spn_T [!-] [[++]] [[--]] ifte dip')\n",
"define('_spn_E [pop !-] [--] [++] ifte')\n",
"define('spiral_next _spn_P [_spn_E] [_spn_T] branch')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" . 23 18 spiral_next\n",
" 23 . 18 spiral_next\n",
" 23 18 . spiral_next\n",
" 23 18 . _spn_P [_spn_E] [_spn_T] branch\n",
" 23 18 . [[abs] ii <=] [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch\n",
" 23 18 [[abs] ii <=] . [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch\n",
" 23 18 [[abs] ii <=] [[<>] [pop !-] ||] . && [_spn_E] [_spn_T] branch\n",
" 23 18 [[abs] ii <=] [[<>] [pop !-] ||] . [nullary] cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch\n",
" 23 18 [[abs] ii <=] [[<>] [pop !-] ||] [nullary] . cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch\n",
" 23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] . [nullary [0]] dip branch [_spn_E] [_spn_T] branch\n",
"23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] [nullary [0]] . dip branch [_spn_E] [_spn_T] branch\n",
" 23 18 [[abs] ii <=] . nullary [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [[abs] ii <=] . [stack] dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [[abs] ii <=] [stack] . dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [[abs] ii <=] [stack] . dip infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 . stack [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [18 23] . [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [18 23] [[abs] ii <=] . infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 . [abs] ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [abs] . ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [abs] . [dip] dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [abs] [dip] . dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [abs] . dip [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 . abs 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 . 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 . [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [abs] . i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 . abs <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 . <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" False . [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" False [18 23] . swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 [False] . first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 False . [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 False [0] . [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch\n",
" 23 18 False [0] [[[<>] [pop !-] ||] nullary] . branch [_spn_E] [_spn_T] branch\n",
" 23 18 . 0 [_spn_E] [_spn_T] branch\n",
" 23 18 0 . [_spn_E] [_spn_T] branch\n",
" 23 18 0 [_spn_E] . [_spn_T] branch\n",
" 23 18 0 [_spn_E] [_spn_T] . branch\n",
" 23 18 . _spn_E\n",
" 23 18 . [pop !-] [--] [++] ifte\n",
" 23 18 [pop !-] . [--] [++] ifte\n",
" 23 18 [pop !-] [--] . [++] ifte\n",
" 23 18 [pop !-] [--] [++] . ifte\n",
" 23 18 [pop !-] [--] [++] . [nullary not] dipd branch\n",
" 23 18 [pop !-] [--] [++] [nullary not] . dipd branch\n",
" 23 18 [pop !-] . nullary not [--] [++] branch\n",
" 23 18 [pop !-] . [stack] dinfrirst not [--] [++] branch\n",
" 23 18 [pop !-] [stack] . dinfrirst not [--] [++] branch\n",
" 23 18 [pop !-] [stack] . dip infra first not [--] [++] branch\n",
" 23 18 . stack [pop !-] infra first not [--] [++] branch\n",
" 23 18 [18 23] . [pop !-] infra first not [--] [++] branch\n",
" 23 18 [18 23] [pop !-] . infra first not [--] [++] branch\n",
" 23 18 . pop !- [18 23] swaack first not [--] [++] branch\n",
" 23 . !- [18 23] swaack first not [--] [++] branch\n",
" 23 . 0 >= [18 23] swaack first not [--] [++] branch\n",
" 23 0 . >= [18 23] swaack first not [--] [++] branch\n",
" True . [18 23] swaack first not [--] [++] branch\n",
" True [18 23] . swaack first not [--] [++] branch\n",
" 23 18 [True] . first not [--] [++] branch\n",
" 23 18 True . not [--] [++] branch\n",
" 23 18 False . [--] [++] branch\n",
" 23 18 False [--] . [++] branch\n",
" 23 18 False [--] [++] . branch\n",
" 23 18 . --\n",
" 23 17 . \n"
]
}
],
"source": [
"V('23 18 spiral_next')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
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```python
from notebook_preamble import J, V, define
```
# Square Spiral Example Joy Code
Here is the example of Joy code from the `README` file:
[[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
It might seem unreadable but with a little familiarity it becomes just as
legible as any other notation. Some layout helps:
[ [[abs] ii <=]
[
[<>] [pop !-] ||
] &&
]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
This function accepts two integers on the stack and increments or
decrements one of them such that the new pair of numbers is the next
coordinate pair in a square spiral (like the kind used to construct an
Ulam Spiral).
## Original Form
It's adapted from [the original code on StackOverflow](https://stackoverflow.com/questions/398299/looping-in-a-spiral/31864777#31864777):
> If all you're trying to do is generate the first N points in the spiral
> (without the original problem's constraint of masking to an N x M
> region), the code becomes very simple:
void spiral(const int N)
{
int x = 0;
int y = 0;
for(int i = 0; i < N; ++i)
{
cout << x << '\t' << y << '\n';
if(abs(x) <= abs(y) && (x != y || x >= 0))
x += ((y >= 0) ? 1 : -1);
else
y += ((x >= 0) ? -1 : 1);
}
}
## Translation to Joy
I'm going to make a function that take two ints (`x` and `y`) and
generates the next pair, we'll turn it into a generator later using the
`x` combinator.
### First Boolean Predicate
We need a function that computes `abs(x) <= abs(y)`, we can use `ii` to
apply `abs` to both values and then compare them
with `<=`:
[abs] ii <=
I've defined two short-circuiting Boolean combinators `&&` and `||` that
each accept two quoted predicate programs, run the first, and
conditionally run the second only if required (to compute the final
Boolean value). They run their predicate arguments `nullary`.
```python
define('&& [nullary] cons [nullary [0]] dip branch')
define('|| [nullary] cons [nullary] dip [1] branch')
```
Given those, we can define `x != y || x >= 0` as:
[<>] [pop 0 >=] ||
And `(abs(x) <= abs(y) && (x != y || x >= 0))` as:
[[abs] ii <=] [[<>] [pop 0 >=] ||] &&
It's a little rough, but, as I say, with a little familiarity it becomes
legible.
### The Increment / Decrement Branches
Turning to the branches of the main `if` statement:
x += ((y >= 0) ? 1 : -1);
Rewrite as a hybrid (pseudo-code) `ifte` expression:
[y >= 0] [x += 1] [X -= 1] ifte
Change each C phrase to Joy code:
[0 >=] [[++] dip] [[--] dip] ifte
Factor out the dip from each branch:
[0 >=] [[++]] [[--]] ifte dip
Similar logic applies to the other branch:
y += ((x >= 0) ? -1 : 1);
[x >= 0] [y -= 1] [y += 1] ifte
[pop 0 >=] [--] [++] ifte
### "Not Negative"
```python
define('!- 0 >=')
```
## Putting the Pieces Together
We can assemble the three functions we just defined in quotes and give
them them to the `ifte` combinator. With some arrangement to show off
the symmetry of the two branches, we have:
[[[abs] ii <=] [[<>] [pop !-] ||] &&]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
As I was writing this up I realized that, since the `&&` combinator
doesn't consume the stack (below its quoted args), I can unquote the
predicate, swap the branches, and use the `branch` combinator instead of
`ifte`:
[[abs] ii <=] [[<>] [pop !-] ||] &&
[[pop !-] [--] [++] ifte ]
[[ !-] [[++]] [[--]] ifte dip]
branch
```python
define('spiral_next [[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte')
```
Let's try it out:
```python
J('0 0 spiral_next')
```
1 0
```python
J('1 0 spiral_next')
```
1 -1
```python
J('1 -1 spiral_next')
```
0 -1
```python
J('0 -1 spiral_next')
```
-1 -1
## Turning it into a Generator with `x`
It can be used with the x combinator to make a kind of generator for
spiral square coordinates.
We can use `codireco` to make a generator
codireco ::= cons dip rest cons
It will look like this:
[value [F] codireco]
Here's a trace of how it works:
[0 [dup ++] codireco] . x
[0 [dup ++] codireco] . 0 [dup ++] codireco
[0 [dup ++] codireco] 0 . [dup ++] codireco
[0 [dup ++] codireco] 0 [dup ++] . codireco
[0 [dup ++] codireco] 0 [dup ++] . cons dip rest cons
[0 [dup ++] codireco] [0 dup ++] . dip rest cons
. 0 dup ++ [0 [dup ++] codireco] rest cons
0 . dup ++ [0 [dup ++] codireco] rest cons
0 0 . ++ [0 [dup ++] codireco] rest cons
0 1 . [0 [dup ++] codireco] rest cons
0 1 [0 [dup ++] codireco] . rest cons
0 1 [[dup ++] codireco] . cons
0 [1 [dup ++] codireco] .
But first we have to change the `spiral_next` function to work on a
quoted pair of integers, and leave a copy of the pair on the stack.
From:
y x spiral_next
---------------------
y' x'
to:
[x y] [spiral_next] infra
-------------------------------
[x' y']
```python
J('[0 0] [spiral_next] infra')
```
[0 1]
So our generator is:
[[x y] [dup [spiral_next] infra] codireco]
Or rather:
[[0 0] [dup [spiral_next] infra] codireco]
There is a function `make_generator` that will build the generator for us
out of the value and stepper function:
[0 0] [dup [spiral_next] infra] make_generator
----------------------------------------------------
[[0 0] [dup [spiral_next] infra] codireco]
Here it is in action:
```python
J('[0 0] [dup [spiral_next] infra] make_generator x x x x pop')
```
[0 0] [0 1] [-1 1] [-1 0]
Four `x` combinators, four pairs of coordinates.
## Conclusion
So that's an example of Joy code. It's a straightforward translation of
the original. It's a little long for a single definition, you might
break it up like so:
_spn_P ::= [[abs] ii <=] [[<>] [pop !-] ||] &&
_spn_T ::= [ !-] [[++]] [[--]] ifte dip
_spn_E ::= [pop !-] [--] [++] ifte
spiral_next ::= _spn_P [_spn_E] [_spn_T] branch
This way it's easy to see that the function is a branch with two
quasi-symmetrical paths.
We then used this function to make a simple generator of coordinate
pairs, where the next pair in the series can be generated at any time by
using the `x` combinator on the generator (which is just a quoted
expression containing a copy of the current pair and the "stepper
function" to generate the next pair from that.)
```python
define('_spn_P [[abs] ii <=] [[<>] [pop !-] ||] &&')
define('_spn_T [!-] [[++]] [[--]] ifte dip')
define('_spn_E [pop !-] [--] [++] ifte')
define('spiral_next _spn_P [_spn_E] [_spn_T] branch')
```
```python
V('23 18 spiral_next')
```
. 23 18 spiral_next
23 . 18 spiral_next
23 18 . spiral_next
23 18 . _spn_P [_spn_E] [_spn_T] branch
23 18 . [[abs] ii <=] [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . [nullary] cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] [nullary] . cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] . [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] [nullary [0]] . dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . nullary [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . [stack] dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [stack] . dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [stack] . dip infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . stack [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [18 23] . [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [18 23] [[abs] ii <=] . infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . [abs] ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . [dip] dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] [dip] . dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . dip [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 . abs 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 . 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . abs <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
False . [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
False [18 23] . swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [False] . first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False . [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False [0] . [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False [0] [[[<>] [pop !-] ||] nullary] . branch [_spn_E] [_spn_T] branch
23 18 . 0 [_spn_E] [_spn_T] branch
23 18 0 . [_spn_E] [_spn_T] branch
23 18 0 [_spn_E] . [_spn_T] branch
23 18 0 [_spn_E] [_spn_T] . branch
23 18 . _spn_E
23 18 . [pop !-] [--] [++] ifte
23 18 [pop !-] . [--] [++] ifte
23 18 [pop !-] [--] . [++] ifte
23 18 [pop !-] [--] [++] . ifte
23 18 [pop !-] [--] [++] . [nullary not] dipd branch
23 18 [pop !-] [--] [++] [nullary not] . dipd branch
23 18 [pop !-] . nullary not [--] [++] branch
23 18 [pop !-] . [stack] dinfrirst not [--] [++] branch
23 18 [pop !-] [stack] . dinfrirst not [--] [++] branch
23 18 [pop !-] [stack] . dip infra first not [--] [++] branch
23 18 . stack [pop !-] infra first not [--] [++] branch
23 18 [18 23] . [pop !-] infra first not [--] [++] branch
23 18 [18 23] [pop !-] . infra first not [--] [++] branch
23 18 . pop !- [18 23] swaack first not [--] [++] branch
23 . !- [18 23] swaack first not [--] [++] branch
23 . 0 >= [18 23] swaack first not [--] [++] branch
23 0 . >= [18 23] swaack first not [--] [++] branch
True . [18 23] swaack first not [--] [++] branch
True [18 23] . swaack first not [--] [++] branch
23 18 [True] . first not [--] [++] branch
23 18 True . not [--] [++] branch
23 18 False . [--] [++] branch
23 18 False [--] . [++] branch
23 18 False [--] [++] . branch
23 18 . --
23 17 .

421
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.. code:: ipython3
from notebook_preamble import J, V, define
Square Spiral Example Joy Code
==============================
Here is the example of Joy code from the ``README`` file:
::
[[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
It might seem unreadable but with a little familiarity it becomes just
as legible as any other notation. Some layout helps:
::
[ [[abs] ii <=]
[
[<>] [pop !-] ||
] &&
]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
This function accepts two integers on the stack and increments or
decrements one of them such that the new pair of numbers is the next
coordinate pair in a square spiral (like the kind used to construct an
Ulam Spiral).
Original Form
-------------
It's adapted from `the original code on
StackOverflow <https://stackoverflow.com/questions/398299/looping-in-a-spiral/31864777#31864777>`__:
If all you're trying to do is generate the first N points in the
spiral (without the original problem's constraint of masking to an N
x M region), the code becomes very simple:
::
void spiral(const int N)
{
int x = 0;
int y = 0;
for(int i = 0; i < N; ++i)
{
cout << x << '\t' << y << '\n';
if(abs(x) <= abs(y) && (x != y || x >= 0))
x += ((y >= 0) ? 1 : -1);
else
y += ((x >= 0) ? -1 : 1);
}
}
Translation to Joy
------------------
I'm going to make a function that take two ints (``x`` and ``y``) and
generates the next pair, we'll turn it into a generator later using the
``x`` combinator.
First Boolean Predicate
~~~~~~~~~~~~~~~~~~~~~~~
We need a function that computes ``abs(x) <= abs(y)``, we can use ``ii``
to apply ``abs`` to both values and then compare them with ``<=``:
::
[abs] ii <=
I've defined two short-circuiting Boolean combinators ``&&`` and ``||``
that each accept two quoted predicate programs, run the first, and
conditionally run the second only if required (to compute the final
Boolean value). They run their predicate arguments ``nullary``.
.. code:: ipython3
define('&& [nullary] cons [nullary [0]] dip branch')
define('|| [nullary] cons [nullary] dip [1] branch')
Given those, we can define ``x != y || x >= 0`` as:
::
[<>] [pop 0 >=] ||
And ``(abs(x) <= abs(y) && (x != y || x >= 0))`` as:
::
[[abs] ii <=] [[<>] [pop 0 >=] ||] &&
It's a little rough, but, as I say, with a little familiarity it becomes
legible.
The Increment / Decrement Branches
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Turning to the branches of the main ``if`` statement:
::
x += ((y >= 0) ? 1 : -1);
Rewrite as a hybrid (pseudo-code) ``ifte`` expression:
::
[y >= 0] [x += 1] [X -= 1] ifte
Change each C phrase to Joy code:
::
[0 >=] [[++] dip] [[--] dip] ifte
Factor out the dip from each branch:
::
[0 >=] [[++]] [[--]] ifte dip
Similar logic applies to the other branch:
::
y += ((x >= 0) ? -1 : 1);
[x >= 0] [y -= 1] [y += 1] ifte
[pop 0 >=] [--] [++] ifte
"Not Negative"
~~~~~~~~~~~~~~
.. code:: ipython3
define('!- 0 >=')
Putting the Pieces Together
---------------------------
We can assemble the three functions we just defined in quotes and give
them them to the ``ifte`` combinator. With some arrangement to show off
the symmetry of the two branches, we have:
::
[[[abs] ii <=] [[<>] [pop !-] ||] &&]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
As I was writing this up I realized that, since the ``&&`` combinator
doesn't consume the stack (below its quoted args), I can unquote the
predicate, swap the branches, and use the ``branch`` combinator instead
of ``ifte``:
::
[[abs] ii <=] [[<>] [pop !-] ||] &&
[[pop !-] [--] [++] ifte ]
[[ !-] [[++]] [[--]] ifte dip]
branch
.. code:: ipython3
define('spiral_next [[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte')
Let's try it out:
.. code:: ipython3
J('0 0 spiral_next')
.. parsed-literal::
1 0
.. code:: ipython3
J('1 0 spiral_next')
.. parsed-literal::
1 -1
.. code:: ipython3
J('1 -1 spiral_next')
.. parsed-literal::
0 -1
.. code:: ipython3
J('0 -1 spiral_next')
.. parsed-literal::
-1 -1
Turning it into a Generator with ``x``
--------------------------------------
It can be used with the x combinator to make a kind of generator for
spiral square coordinates.
We can use ``codireco`` to make a generator
::
codireco ::= cons dip rest cons
It will look like this:
::
[value [F] codireco]
Here's a trace of how it works:
::
[0 [dup ++] codireco] . x
[0 [dup ++] codireco] . 0 [dup ++] codireco
[0 [dup ++] codireco] 0 . [dup ++] codireco
[0 [dup ++] codireco] 0 [dup ++] . codireco
[0 [dup ++] codireco] 0 [dup ++] . cons dip rest cons
[0 [dup ++] codireco] [0 dup ++] . dip rest cons
. 0 dup ++ [0 [dup ++] codireco] rest cons
0 . dup ++ [0 [dup ++] codireco] rest cons
0 0 . ++ [0 [dup ++] codireco] rest cons
0 1 . [0 [dup ++] codireco] rest cons
0 1 [0 [dup ++] codireco] . rest cons
0 1 [[dup ++] codireco] . cons
0 [1 [dup ++] codireco] .
But first we have to change the ``spiral_next`` function to work on a
quoted pair of integers, and leave a copy of the pair on the stack.
From:
::
y x spiral_next
---------------------
y' x'
to:
::
[x y] [spiral_next] infra
-------------------------------
[x' y']
.. code:: ipython3
J('[0 0] [spiral_next] infra')
.. parsed-literal::
[0 1]
So our generator is:
::
[[x y] [dup [spiral_next] infra] codireco]
Or rather:
::
[[0 0] [dup [spiral_next] infra] codireco]
There is a function ``make_generator`` that will build the generator for
us out of the value and stepper function:
::
[0 0] [dup [spiral_next] infra] make_generator
----------------------------------------------------
[[0 0] [dup [spiral_next] infra] codireco]
Here it is in action:
.. code:: ipython3
J('[0 0] [dup [spiral_next] infra] make_generator x x x x pop')
.. parsed-literal::
[0 0] [0 1] [-1 1] [-1 0]
Four ``x`` combinators, four pairs of coordinates.
Conclusion
----------
So that's an example of Joy code. It's a straightforward translation of
the original. It's a little long for a single definition, you might
break it up like so:
::
_spn_P ::= [[abs] ii <=] [[<>] [pop !-] ||] &&
_spn_T ::= [ !-] [[++]] [[--]] ifte dip
_spn_E ::= [pop !-] [--] [++] ifte
spiral_next ::= _spn_P [_spn_E] [_spn_T] branch
This way it's easy to see that the function is a branch with two
quasi-symmetrical paths.
We then used this function to make a simple generator of coordinate
pairs, where the next pair in the series can be generated at any time by
using the ``x`` combinator on the generator (which is just a quoted
expression containing a copy of the current pair and the "stepper
function" to generate the next pair from that.)
.. code:: ipython3
define('_spn_P [[abs] ii <=] [[<>] [pop !-] ||] &&')
define('_spn_T [!-] [[++]] [[--]] ifte dip')
define('_spn_E [pop !-] [--] [++] ifte')
define('spiral_next _spn_P [_spn_E] [_spn_T] branch')
.. code:: ipython3
V('23 18 spiral_next')
.. parsed-literal::
. 23 18 spiral_next
23 . 18 spiral_next
23 18 . spiral_next
23 18 . _spn_P [_spn_E] [_spn_T] branch
23 18 . [[abs] ii <=] [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . [nullary] cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] [nullary] . cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] . [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] [nullary [0]] . dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . nullary [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . [stack] dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [stack] . dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [stack] . dip infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . stack [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [18 23] . [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [18 23] [[abs] ii <=] . infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . [abs] ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . [dip] dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] [dip] . dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . dip [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 . abs 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 . 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . abs <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
False . [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
False [18 23] . swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [False] . first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False . [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False [0] . [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False [0] [[[<>] [pop !-] ||] nullary] . branch [_spn_E] [_spn_T] branch
23 18 . 0 [_spn_E] [_spn_T] branch
23 18 0 . [_spn_E] [_spn_T] branch
23 18 0 [_spn_E] . [_spn_T] branch
23 18 0 [_spn_E] [_spn_T] . branch
23 18 . _spn_E
23 18 . [pop !-] [--] [++] ifte
23 18 [pop !-] . [--] [++] ifte
23 18 [pop !-] [--] . [++] ifte
23 18 [pop !-] [--] [++] . ifte
23 18 [pop !-] [--] [++] . [nullary not] dipd branch
23 18 [pop !-] [--] [++] [nullary not] . dipd branch
23 18 [pop !-] . nullary not [--] [++] branch
23 18 [pop !-] . [stack] dinfrirst not [--] [++] branch
23 18 [pop !-] [stack] . dinfrirst not [--] [++] branch
23 18 [pop !-] [stack] . dip infra first not [--] [++] branch
23 18 . stack [pop !-] infra first not [--] [++] branch
23 18 [18 23] . [pop !-] infra first not [--] [++] branch
23 18 [18 23] [pop !-] . infra first not [--] [++] branch
23 18 . pop !- [18 23] swaack first not [--] [++] branch
23 . !- [18 23] swaack first not [--] [++] branch
23 . 0 >= [18 23] swaack first not [--] [++] branch
23 0 . >= [18 23] swaack first not [--] [++] branch
True . [18 23] swaack first not [--] [++] branch
True [18 23] . swaack first not [--] [++] branch
23 18 [True] . first not [--] [++] branch
23 18 True . not [--] [++] branch
23 18 False . [--] [++] branch
23 18 False [--] . [++] branch
23 18 False [--] [++] . branch
23 18 . --
23 17 .

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@ -34,6 +34,31 @@ itself.
.. _Concatinative: https://en.wikipedia.org/wiki/Concatenative_programming_language .. _Concatinative: https://en.wikipedia.org/wiki/Concatenative_programming_language
Example Code
--------------------------------------------------
Here is an example of Joy code::
[[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
It might seem unreadable but with a little familiarity it becomes just as
legible as any other notation. Some layout helps::
[ [[abs] ii <=]
[
[<>] [pop !-] ||
] &&
]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
This function accepts two integers on the stack and increments or
decrements one of them such that the new pair of numbers is the next
coordinate pair in a square spiral (like the kind used to construct an
Ulam Spiral). For more information see :doc:`notebooks/Square_Spiral`
Quick Start Quick Start
-------------------------------------------------- --------------------------------------------------

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@ -76,7 +76,7 @@ E.g.:
Implementation Implementation
-------------- --------------
.. code:: python .. code:: ipython2
from functools import partial as curry from functools import partial as curry
from itertools import product from itertools import product
@ -86,7 +86,7 @@ Implementation
The empty set and the set of just the empty string. The empty set and the set of just the empty string.
.. code:: python .. code:: ipython2
phi = frozenset() # ϕ phi = frozenset() # ϕ
y = frozenset({''}) # λ y = frozenset({''}) # λ
@ -101,7 +101,7 @@ alphabet with two symbols (if you had to.)
I chose the names ``O`` and ``l`` (uppercase “o” and lowercase “L”) to I chose the names ``O`` and ``l`` (uppercase “o” and lowercase “L”) to
look like ``0`` and ``1`` (zero and one) respectively. look like ``0`` and ``1`` (zero and one) respectively.
.. code:: python .. code:: ipython2
syms = O, l = frozenset({'0'}), frozenset({'1'}) syms = O, l = frozenset({'0'}), frozenset({'1'})
@ -123,7 +123,7 @@ expression* is one of:
Where ``R`` and ``S`` stand for *regular expressions*. Where ``R`` and ``S`` stand for *regular expressions*.
.. code:: python .. code:: ipython2
AND, CONS, KSTAR, NOT, OR = 'and cons * not or'.split() # Tags are just strings. AND, CONS, KSTAR, NOT, OR = 'and cons * not or'.split() # Tags are just strings.
@ -133,7 +133,7 @@ only, these datastructures are immutable.
String Representation of RE Datastructures String Representation of RE Datastructures
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def stringy(re): def stringy(re):
''' '''
@ -175,11 +175,11 @@ Match anything. Often spelled “.”
I = (0|1)* I = (0|1)*
.. code:: python .. code:: ipython2
I = (KSTAR, (OR, O, l)) I = (KSTAR, (OR, O, l))
.. code:: python .. code:: ipython2
print stringy(I) print stringy(I)
@ -201,14 +201,14 @@ The example expression from Brzozowski:
Note that it contains one of everything. Note that it contains one of everything.
.. code:: python .. code:: ipython2
a = (CONS, I, (CONS, l, (CONS, l, (CONS, l, I)))) a = (CONS, I, (CONS, l, (CONS, l, (CONS, l, I))))
b = (CONS, I, (CONS, O, l)) b = (CONS, I, (CONS, O, l))
c = (CONS, l, (KSTAR, l)) c = (CONS, l, (KSTAR, l))
it = (AND, a, (NOT, (OR, b, c))) it = (AND, a, (NOT, (OR, b, c)))
.. code:: python .. code:: ipython2
print stringy(it) print stringy(it)
@ -223,7 +223,7 @@ Note that it contains one of everything.
Let’s get that auxiliary predicate function ``δ`` out of the way. Let’s get that auxiliary predicate function ``δ`` out of the way.
.. code:: python .. code:: ipython2
def nully(R): def nully(R):
''' '''
@ -263,7 +263,7 @@ This is the straightforward version with no “compaction”. It works fine,
but does waaaay too much work because the expressions grow each but does waaaay too much work because the expressions grow each
derivation. derivation.
.. code:: python .. code:: ipython2
def D(symbol): def D(symbol):
@ -308,7 +308,7 @@ derivation.
Compaction Rules Compaction Rules
~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def _compaction_rule(relation, one, zero, a, b): def _compaction_rule(relation, one, zero, a, b):
return ( return (
@ -320,7 +320,7 @@ Compaction Rules
An elegant symmetry. An elegant symmetry.
.. code:: python .. code:: ipython2
# R ∧ I = I ∧ R = R # R ∧ I = I ∧ R = R
# R ∧ ϕ = ϕ ∧ R = ϕ # R ∧ ϕ = ϕ ∧ R = ϕ
@ -341,7 +341,7 @@ We can save re-processing by remembering results we have already
computed. RE datastructures are immutable and the ``derv()`` functions computed. RE datastructures are immutable and the ``derv()`` functions
are *pure* so this is fine. are *pure* so this is fine.
.. code:: python .. code:: ipython2
class Memo(object): class Memo(object):
@ -365,7 +365,7 @@ With “Compaction”
This version uses the rules above to perform compaction. It keeps the This version uses the rules above to perform compaction. It keeps the
expressions from growing too large. expressions from growing too large.
.. code:: python .. code:: ipython2
def D_compaction(symbol): def D_compaction(symbol):
@ -414,7 +414,7 @@ Let’s try it out…
(FIXME: redo.) (FIXME: redo.)
.. code:: python .. code:: ipython2
o, z = D_compaction('0'), D_compaction('1') o, z = D_compaction('0'), D_compaction('1')
REs = set() REs = set()
@ -533,10 +533,10 @@ machine transition table.
Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.” Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”
.. figure:: omg.svg .. figure:: attachment:omg.svg
:alt: State Machine Graph :alt: omg.svg
State Machine Graph omg.svg
Start at ``a`` and follow the transition arrows according to their Start at ``a`` and follow the transition arrows according to their
labels. Accepting states have a double outline. (Graphic generated with labels. Accepting states have a double outline. (Graphic generated with
@ -605,20 +605,20 @@ You can see the one-way nature of the ``g`` state and the ``hij`` “trap”
in the way that the ``.111.`` on the left-hand side of the ``&`` in the way that the ``.111.`` on the left-hand side of the ``&``
disappears once it has been matched. disappears once it has been matched.
.. code:: python .. code:: ipython2
from collections import defaultdict from collections import defaultdict
from pprint import pprint from pprint import pprint
from string import ascii_lowercase from string import ascii_lowercase
.. code:: python .. code:: ipython2
d0, d1 = D_compaction('0'), D_compaction('1') d0, d1 = D_compaction('0'), D_compaction('1')
``explore()`` ``explore()``
~~~~~~~~~~~~~ ~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def explore(re): def explore(re):
@ -645,7 +645,7 @@ disappears once it has been matched.
return table, accepting return table, accepting
.. code:: python .. code:: ipython2
table, accepting = explore(it) table, accepting = explore(it)
table table
@ -678,7 +678,7 @@ disappears once it has been matched.
.. code:: python .. code:: ipython2
accepting accepting
@ -697,7 +697,7 @@ Generate Diagram
Once we have the FSM table and the set of accepting states we can Once we have the FSM table and the set of accepting states we can
generate the diagram above. generate the diagram above.
.. code:: python .. code:: ipython2
_template = '''\ _template = '''\
digraph finite_state_machine { digraph finite_state_machine {
@ -722,7 +722,7 @@ generate the diagram above.
) )
) )
.. code:: python .. code:: ipython2
print make_graph(table, accepting) print make_graph(table, accepting)
@ -776,7 +776,7 @@ Trampoline Function
Python has no GOTO statement but we can fake it with a “trampoline” Python has no GOTO statement but we can fake it with a “trampoline”
function. function.
.. code:: python .. code:: ipython2
def trampoline(input_, jump_from, accepting): def trampoline(input_, jump_from, accepting):
I = iter(input_) I = iter(input_)
@ -793,7 +793,7 @@ Stream Functions
Little helpers to process the iterator of our data (a “stream” of “1” Little helpers to process the iterator of our data (a “stream” of “1”
and “0” characters, not bits.) and “0” characters, not bits.)
.. code:: python .. code:: ipython2
getch = lambda I: int(next(I)) getch = lambda I: int(next(I))
@ -816,7 +816,7 @@ code. (You have to imagine that these are GOTO statements in C or
branches in assembly and that the state names are branch destination branches in assembly and that the state names are branch destination
labels.) labels.)
.. code:: python .. code:: ipython2
a = lambda I: c if getch(I) else b a = lambda I: c if getch(I) else b
b = lambda I: _0(I) or d b = lambda I: _0(I) or d
@ -833,12 +833,12 @@ Note that the implementations of ``h`` and ``g`` are identical ergo
``h = g`` and we could eliminate one in the code but ``h`` is an ``h = g`` and we could eliminate one in the code but ``h`` is an
accepting state and ``g`` isn’t. accepting state and ``g`` isn’t.
.. code:: python .. code:: ipython2
def acceptable(input_): def acceptable(input_):
return trampoline(input_, a, {h, i}) return trampoline(input_, a, {h, i})
.. code:: python .. code:: ipython2
for n in range(2**5): for n in range(2**5):
s = bin(n)[2:] s = bin(n)[2:]

76
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@ -3,7 +3,7 @@ Using ``x`` to Generate Values
Cf. jp-reprod.html Cf. jp-reprod.html
.. code:: python .. code:: ipython2
from notebook_preamble import J, V, define from notebook_preamble import J, V, define
@ -57,7 +57,7 @@ We can make a generator for the Natural numbers (0, 1, 2, …) by using
Let’s try it: Let’s try it:
.. code:: python .. code:: ipython2
V('[0 swap [dup ++] dip rest cons] x') V('[0 swap [dup ++] dip rest cons] x')
@ -81,7 +81,7 @@ Let’s try it:
After one application of ``x`` the quoted program contains ``1`` and After one application of ``x`` the quoted program contains ``1`` and
``0`` is below it on the stack. ``0`` is below it on the stack.
.. code:: python .. code:: ipython2
J('[0 swap [dup ++] dip rest cons] x x x x x pop') J('[0 swap [dup ++] dip rest cons] x x x x x pop')
@ -94,11 +94,11 @@ After one application of ``x`` the quoted program contains ``1`` and
``direco`` ``direco``
---------- ----------
.. code:: python .. code:: ipython2
define('direco == dip rest cons') define('direco == dip rest cons')
.. code:: python .. code:: ipython2
V('[0 swap [dup ++] direco] x') V('[0 swap [dup ++] direco] x')
@ -149,13 +149,13 @@ Reading from the bottom up:
G == [direco] cons [swap] swap concat cons G == [direco] cons [swap] swap concat cons
G == [direco] cons [swap] swoncat cons G == [direco] cons [swap] swoncat cons
.. code:: python .. code:: ipython2
define('G == [direco] cons [swap] swoncat cons') define('G == [direco] cons [swap] swoncat cons')
Let’s try it out: Let’s try it out:
.. code:: python .. code:: ipython2
J('0 [dup ++] G') J('0 [dup ++] G')
@ -165,7 +165,7 @@ Let’s try it out:
[0 swap [dup ++] direco] [0 swap [dup ++] direco]
.. code:: python .. code:: ipython2
J('0 [dup ++] G x x x pop') J('0 [dup ++] G x x x pop')
@ -178,7 +178,7 @@ Let’s try it out:
Powers of 2 Powers of 2
~~~~~~~~~~~ ~~~~~~~~~~~
.. code:: python .. code:: ipython2
J('1 [dup 1 <<] G x x x x x x x x x pop') J('1 [dup 1 <<] G x x x x x x x x x pop')
@ -194,7 +194,7 @@ Powers of 2
If we have one of these quoted programs we can drive it using ``times`` If we have one of these quoted programs we can drive it using ``times``
with the ``x`` combinator. with the ``x`` combinator.
.. code:: python .. code:: ipython2
J('23 [dup ++] G 5 [x] times') J('23 [dup ++] G 5 [x] times')
@ -226,11 +226,11 @@ int:
And pick them off by masking with 3 (binary 11) and then shifting the And pick them off by masking with 3 (binary 11) and then shifting the
int right two bits. int right two bits.
.. code:: python .. code:: ipython2
define('PE1.1 == dup [3 &] dip 2 >>') define('PE1.1 == dup [3 &] dip 2 >>')
.. code:: python .. code:: ipython2
V('14811 PE1.1') V('14811 PE1.1')
@ -252,7 +252,7 @@ int right two bits.
If we plug ``14811`` and ``[PE1.1]`` into our generator form… If we plug ``14811`` and ``[PE1.1]`` into our generator form…
.. code:: python .. code:: ipython2
J('14811 [PE1.1] G') J('14811 [PE1.1] G')
@ -264,7 +264,7 @@ If we plug ``14811`` and ``[PE1.1]`` into our generator form…
…we get a generator that works for seven cycles before it reaches zero: …we get a generator that works for seven cycles before it reaches zero:
.. code:: python .. code:: ipython2
J('[14811 swap [PE1.1] direco] 7 [x] times') J('[14811 swap [PE1.1] direco] 7 [x] times')
@ -280,11 +280,11 @@ Reset at Zero
We need a function that checks if the int has reached zero and resets it We need a function that checks if the int has reached zero and resets it
if so. if so.
.. code:: python .. code:: ipython2
define('PE1.1.check == dup [pop 14811] [] branch') define('PE1.1.check == dup [pop 14811] [] branch')
.. code:: python .. code:: ipython2
J('14811 [PE1.1.check PE1.1] G') J('14811 [PE1.1.check PE1.1] G')
@ -294,7 +294,7 @@ if so.
[14811 swap [PE1.1.check PE1.1] direco] [14811 swap [PE1.1.check PE1.1] direco]
.. code:: python .. code:: ipython2
J('[14811 swap [PE1.1.check PE1.1] direco] 21 [x] times') J('[14811 swap [PE1.1.check PE1.1] direco] 21 [x] times')
@ -316,7 +316,7 @@ In the PE1 problem we are asked to sum all the multiples of three and
five less than 1000. It’s worked out that we need to use all seven five less than 1000. It’s worked out that we need to use all seven
numbers sixty-six times and then four more. numbers sixty-six times and then four more.
.. code:: python .. code:: ipython2
J('7 66 * 4 +') J('7 66 * 4 +')
@ -328,7 +328,7 @@ numbers sixty-six times and then four more.
If we drive our generator 466 times and sum the stack we get 999. If we drive our generator 466 times and sum the stack we get 999.
.. code:: python .. code:: ipython2
J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times') J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times')
@ -338,7 +338,7 @@ If we drive our generator 466 times and sum the stack we get 999.
3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 [57 swap [PE1.1.check PE1.1] direco] 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 [57 swap [PE1.1.check PE1.1] direco]
.. code:: python .. code:: ipython2
J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum') J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum')
@ -351,13 +351,13 @@ If we drive our generator 466 times and sum the stack we get 999.
Project Euler Problem One Project Euler Problem One
------------------------- -------------------------
.. code:: python .. code:: ipython2
define('PE1.2 == + dup [+] dip') define('PE1.2 == + dup [+] dip')
Now we can add ``PE1.2`` to the quoted program given to ``G``. Now we can add ``PE1.2`` to the quoted program given to ``G``.
.. code:: python .. code:: ipython2
J('0 0 0 [PE1.1.check PE1.1] G 466 [x [PE1.2] dip] times popop') J('0 0 0 [PE1.1.check PE1.1] G 466 [x [PE1.2] dip] times popop')
@ -445,15 +445,15 @@ Putting it all together:
F == + [popdd over] cons infra uncons F == + [popdd over] cons infra uncons
fib_gen == [1 1 F] fib_gen == [1 1 F]
.. code:: python .. code:: ipython2
define('fib == + [popdd over] cons infra uncons') define('fib == + [popdd over] cons infra uncons')
.. code:: python .. code:: ipython2
define('fib_gen == [1 1 fib]') define('fib_gen == [1 1 fib]')
.. code:: python .. code:: ipython2
J('fib_gen 10 [x] times') J('fib_gen 10 [x] times')
@ -473,14 +473,14 @@ Now that we have a generator for the Fibonacci sequence, we need a
function that adds a term in the sequence to a sum if it is even, and function that adds a term in the sequence to a sum if it is even, and
``pop``\ s it otherwise. ``pop``\ s it otherwise.
.. code:: python .. code:: ipython2
define('PE2.1 == dup 2 % [+] [pop] branch') define('PE2.1 == dup 2 % [+] [pop] branch')
And a predicate function that detects when the terms in the series And a predicate function that detects when the terms in the series
“exceed four million”. “exceed four million”.
.. code:: python .. code:: ipython2
define('>4M == 4000000 >') define('>4M == 4000000 >')
@ -488,11 +488,11 @@ Now it’s straightforward to define ``PE2`` as a recursive function that
generates terms in the Fibonacci sequence until they exceed four million generates terms in the Fibonacci sequence until they exceed four million
and sums the even ones. and sums the even ones.
.. code:: python .. code:: ipython2
define('PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec') define('PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec')
.. code:: python .. code:: ipython2
J('PE2') J('PE2')
@ -535,7 +535,7 @@ So the Fibonacci sequence considered in terms of just parity would be:
Every third term is even. Every third term is even.
.. code:: python .. code:: ipython2
J('[1 0 fib] x x x') # To start the sequence with 1 1 2 3 instead of 1 2 3. J('[1 0 fib] x x x') # To start the sequence with 1 1 2 3 instead of 1 2 3.
@ -547,7 +547,7 @@ Every third term is even.
Drive the generator three times and ``popop`` the two odd terms. Drive the generator three times and ``popop`` the two odd terms.
.. code:: python .. code:: ipython2
J('[1 0 fib] x x x [popop] dipd') J('[1 0 fib] x x x [popop] dipd')
@ -557,11 +557,11 @@ Drive the generator three times and ``popop`` the two odd terms.
2 [3 2 fib] 2 [3 2 fib]
.. code:: python .. code:: ipython2
define('PE2.2 == x x x [popop] dipd') define('PE2.2 == x x x [popop] dipd')
.. code:: python .. code:: ipython2
J('[1 0 fib] 10 [PE2.2] times') J('[1 0 fib] 10 [PE2.2] times')
@ -574,7 +574,7 @@ Drive the generator three times and ``popop`` the two odd terms.
Replace ``x`` with our new driver function ``PE2.2`` and start our Replace ``x`` with our new driver function ``PE2.2`` and start our
``fib`` generator at ``1 0``. ``fib`` generator at ``1 0``.
.. code:: python .. code:: ipython2
J('0 [1 0 fib] PE2.2 [pop >4M] [popop] [[PE2.1] dip PE2.2] primrec') J('0 [1 0 fib] PE2.2 [pop >4M] [popop] [[PE2.1] dip PE2.2] primrec')
@ -593,11 +593,11 @@ modifications to the default ``x``?
An Interesting Variation An Interesting Variation
------------------------ ------------------------
.. code:: python .. code:: ipython2
define('codireco == cons dip rest cons') define('codireco == cons dip rest cons')
.. code:: python .. code:: ipython2
V('[0 [dup ++] codireco] x') V('[0 [dup ++] codireco] x')
@ -620,11 +620,11 @@ An Interesting Variation
0 [1 [dup ++] codireco] . 0 [1 [dup ++] codireco] .
.. code:: python .. code:: ipython2
define('G == [codireco] cons cons') define('G == [codireco] cons cons')
.. code:: python .. code:: ipython2
J('230 [dup ++] G 5 [x] times pop') J('230 [dup ++] G 5 [x] times pop')

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@ -7,7 +7,7 @@ to write a function that can compute the square root of a number.
Cf. `"Why Functional Programming Matters" by John Cf. `"Why Functional Programming Matters" by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__ Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
.. code:: python .. code:: ipython3
from notebook_preamble import J, V, define from notebook_preamble import J, V, define
@ -75,11 +75,11 @@ The generator can be written as:
1 [23 over / + 2 /] [dup] swoncat make_generator 1 [23 over / + 2 /] [dup] swoncat make_generator
1 [dup 23 over / + 2 /] make_generator 1 [dup 23 over / + 2 /] make_generator
.. code:: python .. code:: ipython3
define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator') define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
.. code:: python .. code:: ipython3
J('23 gsra') J('23 gsra')
@ -92,7 +92,7 @@ The generator can be written as:
Let's drive the generator a few time (with the ``x`` combinator) and Let's drive the generator a few time (with the ``x`` combinator) and
square the approximation to see how well it works... square the approximation to see how well it works...
.. code:: python .. code:: ipython3
J('23 gsra 6 [x popd] times first sqr') J('23 gsra 6 [x popd] times first sqr')
@ -142,7 +142,7 @@ Predicate
abs(a-b) ε <= abs(a-b) ε <=
(abs(a-b)<=ε) (abs(a-b)<=ε)
.. code:: python .. code:: ipython3
define('_within_P [first - abs] dip <=') define('_within_P [first - abs] dip <=')
@ -156,7 +156,7 @@ Base-Case
[b G] first [b G] first
b b
.. code:: python .. code:: ipython3
define('_within_B roll< popop first') define('_within_B roll< popop first')
@ -184,7 +184,7 @@ Pretty straightforward:
b [c G] ε within b [c G] ε within
.. code:: python .. code:: ipython3
define('_within_R [popd x] dip') define('_within_R [popd x] dip')
@ -199,14 +199,14 @@ The recursive function we have defined so far needs a slight preamble:
[a G] x ε ... [a G] x ε ...
a [b G] ε ... a [b G] ε ...
.. code:: python .. code:: ipython3
define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec') define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec')
define('sqrt gsra within') define('sqrt gsra within')
Try it out... Try it out...
.. code:: python .. code:: ipython3
J('36 sqrt') J('36 sqrt')
@ -216,7 +216,7 @@ Try it out...
6.0 6.0
.. code:: python .. code:: ipython3
J('23 sqrt') J('23 sqrt')
@ -228,7 +228,7 @@ Try it out...
Check it. Check it.
.. code:: python .. code:: ipython3
4.795831523312719**2 4.795831523312719**2
@ -241,7 +241,7 @@ Check it.
.. code:: python .. code:: ipython3
from math import sqrt from math import sqrt

98
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@ -36,7 +36,7 @@ implementation under the hood. (Where does the “type” come from? It has
a contingent existence predicated on the disciplined use of these a contingent existence predicated on the disciplined use of these
functions on otherwise undistinguished Joy datastructures.) functions on otherwise undistinguished Joy datastructures.)
.. code:: python .. code:: ipython2
from notebook_preamble import D, J, V, define, DefinitionWrapper from notebook_preamble import D, J, V, define, DefinitionWrapper
@ -87,11 +87,11 @@ Definition:
Tree-new == swap [[] []] cons cons Tree-new == swap [[] []] cons cons
.. code:: python .. code:: ipython2
define('Tree-new == swap [[] []] cons cons') define('Tree-new == swap [[] []] cons cons')
.. code:: python .. code:: ipython2
J('"v" "k" Tree-new') J('"v" "k" Tree-new')
@ -163,11 +163,11 @@ comparison operator:
P < == pop roll> pop first < P < == pop roll> pop first <
P == pop roll> pop first P == pop roll> pop first
.. code:: python .. code:: ipython2
define('P == pop roll> pop first') define('P == pop roll> pop first')
.. code:: python .. code:: ipython2
J('["old_key" 23 [] []] 17 "new_key" ["..."] P') J('["old_key" 23 [] []] 17 "new_key" ["..."] P')
@ -242,11 +242,11 @@ And so ``T`` is just:
T == cons cons [dipdd] cons infra T == cons cons [dipdd] cons infra
.. code:: python .. code:: ipython2
define('T == cons cons [dipdd] cons infra') define('T == cons cons [dipdd] cons infra')
.. code:: python .. code:: ipython2
J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] T') J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] T')
@ -266,7 +266,7 @@ This is very very similar to the above:
[key_n value_n left right] value key [Tree-add] E [key_n value_n left right] value key [Tree-add] E
[key_n value_n left right] value key [Tree-add] [P <] [Te] [Ee] ifte [key_n value_n left right] value key [Tree-add] [P <] [Te] [Ee] ifte
.. code:: python .. code:: ipython2
define('E == [P <] [Te] [Ee] ifte') define('E == [P <] [Te] [Ee] ifte')
@ -278,11 +278,11 @@ instead of the right, so the only difference is that it must use
Te == cons cons [dipd] cons infra Te == cons cons [dipd] cons infra
.. code:: python .. code:: ipython2
define('Te == cons cons [dipd] cons infra') define('Te == cons cons [dipd] cons infra')
.. code:: python .. code:: ipython2
J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] Te') J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] Te')
@ -320,11 +320,11 @@ Example:
key new_value [ left right] cons cons key new_value [ left right] cons cons
[key new_value left right] [key new_value left right]
.. code:: python .. code:: ipython2
define('Ee == pop swap roll< rest rest cons cons') define('Ee == pop swap roll< rest rest cons cons')
.. code:: python .. code:: ipython2
J('["k" "old_value" "left" "right"] "new_value" "k" ["Tree-add"] Ee') J('["k" "old_value" "left" "right"] "new_value" "k" ["Tree-add"] Ee')
@ -355,14 +355,14 @@ Putting it all together:
Tree-add == [popop not] [[pop] dipd Tree-new] [] [R] genrec Tree-add == [popop not] [[pop] dipd Tree-new] [] [R] genrec
.. code:: python .. code:: ipython2
define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P >] [T] [E] ifte] genrec') define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P >] [T] [E] ifte] genrec')
Examples Examples
~~~~~~~~ ~~~~~~~~
.. code:: python .. code:: ipython2
J('[] 23 "b" Tree-add') # Initial J('[] 23 "b" Tree-add') # Initial
@ -372,7 +372,7 @@ Examples
['b' 23 [] []] ['b' 23 [] []]
.. code:: python .. code:: ipython2
J('["b" 23 [] []] 88 "c" Tree-add') # Greater than J('["b" 23 [] []] 88 "c" Tree-add') # Greater than
@ -382,7 +382,7 @@ Examples
['b' 23 [] ['c' 88 [] []]] ['b' 23 [] ['c' 88 [] []]]
.. code:: python .. code:: ipython2
J('["b" 23 [] []] 88 "a" Tree-add') # Less than J('["b" 23 [] []] 88 "a" Tree-add') # Less than
@ -392,7 +392,7 @@ Examples
['b' 23 ['a' 88 [] []] []] ['b' 23 ['a' 88 [] []] []]
.. code:: python .. code:: ipython2
J('["b" 23 [] []] 88 "b" Tree-add') # Equal to J('["b" 23 [] []] 88 "b" Tree-add') # Equal to
@ -402,7 +402,7 @@ Examples
['b' 88 [] []] ['b' 88 [] []]
.. code:: python .. code:: ipython2
J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add') # Series. J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add') # Series.
@ -412,7 +412,7 @@ Examples
['b' 23 ['a' 88 [] []] ['c' 44 [] []]] ['b' 23 ['a' 88 [] []] ['c' 44 [] []]]
.. code:: python .. code:: ipython2
J('[] [[23 "b"] [88 "a"] [44 "c"]] [i Tree-add] step') J('[] [[23 "b"] [88 "a"] [44 "c"]] [i Tree-add] step')
@ -444,7 +444,7 @@ values:
------------------------- a < b ------------------------- a < b
L L
.. code:: python .. code:: ipython2
J("1 0 ['G'] ['E'] ['L'] cmp") J("1 0 ['G'] ['E'] ['L'] cmp")
@ -454,7 +454,7 @@ values:
'G' 'G'
.. code:: python .. code:: ipython2
J("1 1 ['G'] ['E'] ['L'] cmp") J("1 1 ['G'] ['E'] ['L'] cmp")
@ -464,7 +464,7 @@ values:
'E' 'E'
.. code:: python .. code:: ipython2
J("0 1 ['G'] ['E'] ['L'] cmp") J("0 1 ['G'] ['E'] ['L'] cmp")
@ -514,7 +514,7 @@ Or just:
P == over [popop popop first] nullary P == over [popop popop first] nullary
.. code:: python .. code:: ipython2
define('P == over [popop popop first] nullary') define('P == over [popop popop first] nullary')
@ -541,11 +541,11 @@ to understand:
Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec
.. code:: python .. code:: ipython2
define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec') define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec')
.. code:: python .. code:: ipython2
J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add') # Still works. J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add') # Still works.
@ -685,14 +685,14 @@ Working backward:
Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec
.. code:: python .. code:: ipython2
define('Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec') define('Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec')
Examples Examples
~~~~~~~~ ~~~~~~~~
.. code:: python .. code:: ipython2
J('[] [foo] Tree-iter') # It doesn't matter what F is as it won't be used. J('[] [foo] Tree-iter') # It doesn't matter what F is as it won't be used.
@ -702,7 +702,7 @@ Examples
.. code:: python .. code:: ipython2
J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [first] Tree-iter") J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [first] Tree-iter")
@ -712,7 +712,7 @@ Examples
'b' 'a' 'c' 'b' 'a' 'c'
.. code:: python .. code:: ipython2
J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [second] Tree-iter") J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [second] Tree-iter")
@ -731,7 +731,7 @@ to it will only occur once within it, and we can query it in
`:math:`O(\log_2 N)` <https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2>`__ `:math:`O(\log_2 N)` <https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2>`__
time. time.
.. code:: python .. code:: ipython2
J('[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step') J('[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step')
@ -741,11 +741,11 @@ time.
[3 0 [2 0 [] []] [9 0 [5 0 [4 0 [] []] [8 0 [6 0 [] [7 0 [] []]] []]] []]] [3 0 [2 0 [] []] [9 0 [5 0 [4 0 [] []] [8 0 [6 0 [] [7 0 [] []]] []]] []]]
.. code:: python .. code:: ipython2
define('to_set == [] swap [0 swap Tree-add] step') define('to_set == [] swap [0 swap Tree-add] step')
.. code:: python .. code:: ipython2
J('[3 9 5 2 8 6 7 8 4] to_set') J('[3 9 5 2 8 6 7 8 4] to_set')
@ -758,11 +758,11 @@ time.
And with that we can write a little program ``unique`` to remove And with that we can write a little program ``unique`` to remove
duplicate items from a list. duplicate items from a list.
.. code:: python .. code:: ipython2
define('unique == [to_set [first] Tree-iter] cons run') define('unique == [to_set [first] Tree-iter] cons run')
.. code:: python .. code:: ipython2
J('[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique') # Filter duplicate items. J('[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique') # Filter duplicate items.
@ -872,7 +872,7 @@ Let’s do a little semantic factoring:
Now we can sort sequences. Now we can sort sequences.
.. code:: python .. code:: ipython2
#define('Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec') #define('Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec')
@ -892,7 +892,7 @@ Now we can sort sequences.
.. code:: python .. code:: ipython2
J('[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order') J('[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order')
@ -1070,7 +1070,7 @@ So:
Tree-get == [pop not] swap [] [P [T>] [E] [T<] cmp] genrec Tree-get == [pop not] swap [] [P [T>] [E] [T<] cmp] genrec
.. code:: python .. code:: ipython2
# I don't want to deal with name conflicts with the above so I'm inlining everything here. # I don't want to deal with name conflicts with the above so I'm inlining everything here.
# The original Joy system has "hide" which is a meta-command which allows you to use named # The original Joy system has "hide" which is a meta-command which allows you to use named
@ -1088,7 +1088,7 @@ So:
] genrec ] genrec
''') ''')
.. code:: python .. code:: ipython2
J('["gary" 23 [] []] "mike" [popd " not in tree" +] Tree-get') J('["gary" 23 [] []] "mike" [popd " not in tree" +] Tree-get')
@ -1098,7 +1098,7 @@ So:
'mike not in tree' 'mike not in tree'
.. code:: python .. code:: ipython2
J('["gary" 23 [] []] "gary" [popop "err"] Tree-get') J('["gary" 23 [] []] "gary" [popop "err"] Tree-get')
@ -1108,7 +1108,7 @@ So:
23 23
.. code:: python .. code:: ipython2
J(''' J('''
@ -1124,7 +1124,7 @@ So:
2 2
.. code:: python .. code:: ipython2
J(''' J('''
@ -1500,7 +1500,7 @@ Refactoring
By the standards of the code I’ve written so far, this is a *huge* Joy By the standards of the code I’ve written so far, this is a *huge* Joy
program. program.
.. code:: python .. code:: ipython2
DefinitionWrapper.add_definitions(''' DefinitionWrapper.add_definitions('''
first_two == uncons uncons pop first_two == uncons uncons pop
@ -1519,7 +1519,7 @@ program.
Tree-Delete == [pop not] [pop] [R0] [R1] genrec Tree-Delete == [pop not] [pop] [R0] [R1] genrec
''', D) ''', D)
.. code:: python .. code:: ipython2
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'c' Tree-Delete ") J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'c' Tree-Delete ")
@ -1529,7 +1529,7 @@ program.
['a' 23 [] ['b' 88 [] []]] ['a' 23 [] ['b' 88 [] []]]
.. code:: python .. code:: ipython2
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'b' Tree-Delete ") J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'b' Tree-Delete ")
@ -1539,7 +1539,7 @@ program.
['a' 23 [] ['c' 44 [] []]] ['a' 23 [] ['c' 44 [] []]]
.. code:: python .. code:: ipython2
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'a' Tree-Delete ") J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'a' Tree-Delete ")
@ -1549,7 +1549,7 @@ program.
['b' 88 [] ['c' 44 [] []]] ['b' 88 [] ['c' 44 [] []]]
.. code:: python .. code:: ipython2
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' Tree-Delete ") J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' Tree-Delete ")
@ -1559,7 +1559,7 @@ program.
['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] ['a' 23 [] ['b' 88 [] ['c' 44 [] []]]]
.. code:: python .. code:: ipython2
J('[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step') J('[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step')
@ -1569,7 +1569,7 @@ program.
[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] [4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]]
.. code:: python .. code:: ipython2
J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete ") J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete ")
@ -1579,7 +1579,7 @@ program.
[4 0 [2 0 [1 0 [] []] []] [6 0 [5 0 [] []] [7 0 [] []]]] [4 0 [2 0 [1 0 [] []] []] [6 0 [5 0 [] []] [7 0 [] []]]]
.. code:: python .. code:: ipython2
J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete ") J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete ")

8
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@ -1,4 +1,4 @@
.. code:: python .. code:: ipython2
from notebook_preamble import J, V, define from notebook_preamble import J, V, define
@ -81,13 +81,13 @@ the variables:
The three arguments are to the left, so we can “chop off” everything to The three arguments are to the left, so we can “chop off” everything to
the right and say it’s the definition of the ``quadratic`` function: the right and say it’s the definition of the ``quadratic`` function:
.. code:: python .. code:: ipython2
define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2') define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2')
Let’s try it out: Let’s try it out:
.. code:: python .. code:: ipython2
J('3 1 1 quadratic') J('3 1 1 quadratic')
@ -102,7 +102,7 @@ lines are the ``dip`` and ``dipd`` combinators building the main program
by incorporating the values on the stack. Then that program runs and you by incorporating the values on the stack. Then that program runs and you
get the results. This is pretty typical of Joy code. get the results. This is pretty typical of Joy code.
.. code:: python .. code:: ipython2
V('-5 1 4 quadratic') V('-5 1 4 quadratic')

54
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@ -1,4 +1,4 @@
.. code:: python .. code:: ipython2
from notebook_preamble import D, DefinitionWrapper, J, V, define from notebook_preamble import D, DefinitionWrapper, J, V, define
@ -80,7 +80,7 @@ is a recursive function ``H :: A -> C`` that converts a value of type
It may be helpful to see this function implemented in imperative Python It may be helpful to see this function implemented in imperative Python
code. code.
.. code:: python .. code:: ipython2
def hylomorphism(c, F, P, G): def hylomorphism(c, F, P, G):
'''Return a hylomorphism function H.''' '''Return a hylomorphism function H.'''
@ -185,7 +185,7 @@ the left so we have a definition for ``hylomorphism``:
hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec
.. code:: python .. code:: ipython2
define('hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec') define('hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec')
@ -203,13 +203,13 @@ To sum a range of integers from 0 to *n* - 1:
- ``[G]`` is ``[-- dup]`` - ``[G]`` is ``[-- dup]``
- ``[F]`` is ``[+]`` - ``[F]`` is ``[+]``
.. code:: python .. code:: ipython2
define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism') define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism')
Let’s try it: Let’s try it:
.. code:: python .. code:: ipython2
J('5 triangular_number') J('5 triangular_number')
@ -219,7 +219,7 @@ Let’s try it:
10 10
.. code:: python .. code:: ipython2
J('[0 1 2 3 4 5 6] [triangular_number] map') J('[0 1 2 3 4 5 6] [triangular_number] map')
@ -391,10 +391,8 @@ values.
A == [P] [] [G] [swons] hylomorphism A == [P] [] [G] [swons] hylomorphism
``range`` et. al. ``range`` et. al. An example of an anamorphism is the ``range`` function which generates the list of integers from 0 to *n* - 1 given *n*.
~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
An example of an anamorphism is the ``range`` function which generates the list of integers from 0 to *n* - 1 given *n*.
Each of the above variations can be used to make four slightly different Each of the above variations can be used to make four slightly different
``range`` functions. ``range`` functions.
@ -407,11 +405,11 @@ Each of the above variations can be used to make four slightly different
H1 == [P] [pop c] [G] [dip F] genrec H1 == [P] [pop c] [G] [dip F] genrec
== [0 <=] [pop []] [-- dup] [dip swons] genrec == [0 <=] [pop []] [-- dup] [dip swons] genrec
.. code:: python .. code:: ipython2
define('range == [0 <=] [] [-- dup] [swons] hylomorphism') define('range == [0 <=] [] [-- dup] [swons] hylomorphism')
.. code:: python .. code:: ipython2
J('5 range') J('5 range')
@ -429,11 +427,11 @@ Each of the above variations can be used to make four slightly different
H2 == c swap [P] [pop] [G [F] dip] primrec H2 == c swap [P] [pop] [G [F] dip] primrec
== [] swap [0 <=] [pop] [-- dup [swons] dip] primrec == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec
.. code:: python .. code:: ipython2
define('range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec') define('range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec')
.. code:: python .. code:: ipython2
J('5 range_reverse') J('5 range_reverse')
@ -451,11 +449,11 @@ Each of the above variations can be used to make four slightly different
H3 == [P] [pop c] [[G] dupdip] [dip F] genrec H3 == [P] [pop c] [[G] dupdip] [dip F] genrec
== [0 <=] [pop []] [[--] dupdip] [dip swons] genrec == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec
.. code:: python .. code:: ipython2
define('ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec') define('ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec')
.. code:: python .. code:: ipython2
J('5 ranger') J('5 ranger')
@ -473,11 +471,11 @@ Each of the above variations can be used to make four slightly different
H4 == c swap [P] [pop] [[F] dupdip G ] primrec H4 == c swap [P] [pop] [[F] dupdip G ] primrec
== [] swap [0 <=] [pop] [[swons] dupdip --] primrec == [] swap [0 <=] [pop] [[swons] dupdip --] primrec
.. code:: python .. code:: ipython2
define('ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec') define('ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec')
.. code:: python .. code:: ipython2
J('5 ranger_reverse') J('5 ranger_reverse')
@ -503,7 +501,7 @@ and makes some new value.
C == [not] c [uncons swap] [F] hylomorphism C == [not] c [uncons swap] [F] hylomorphism
.. code:: python .. code:: ipython2
define('swuncons == uncons swap') # Awkward name. define('swuncons == uncons swap') # Awkward name.
@ -513,11 +511,11 @@ An example of a catamorphism is the sum function.
sum == [not] 0 [swuncons] [+] hylomorphism sum == [not] 0 [swuncons] [+] hylomorphism
.. code:: python .. code:: ipython2
define('sum == [not] 0 [swuncons] [+] hylomorphism') define('sum == [not] 0 [swuncons] [+] hylomorphism')
.. code:: python .. code:: ipython2
J('[5 4 3 2 1] sum') J('[5 4 3 2 1] sum')
@ -533,7 +531,7 @@ The ``step`` combinator
The ``step`` combinator will usually be better to use than The ``step`` combinator will usually be better to use than
``catamorphism``. ``catamorphism``.
.. code:: python .. code:: ipython2
J('[step] help') J('[step] help')
@ -562,11 +560,11 @@ The ``step`` combinator will usually be better to use than
.. code:: python .. code:: ipython2
define('sum == 0 swap [+] step') define('sum == 0 swap [+] step')
.. code:: python .. code:: ipython2
J('[5 4 3 2 1] sum') J('[5 4 3 2 1] sum')
@ -594,11 +592,11 @@ With:
G == -- G == --
P == 1 <= P == 1 <=
.. code:: python .. code:: ipython2
define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec') define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec')
.. code:: python .. code:: ipython2
J('5 factorial') J('5 factorial')
@ -637,11 +635,11 @@ We would use:
G == rest dup G == rest dup
P == not P == not
.. code:: python .. code:: ipython2
define('tails == [] swap [not] [pop] [rest dup [swons] dip] primrec') define('tails == [] swap [not] [pop] [rest dup [swons] dip] primrec')
.. code:: python .. code:: ipython2
J('[1 2 3] tails') J('[1 2 3] tails')

10
docs/sphinx_docs/_build/html/_sources/notebooks/Replacing.rst.txt
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@ -9,14 +9,14 @@ dictionary. However, there’s no function that does that. Adding a new
function to the dictionary is a meta-interpreter action, you have to do function to the dictionary is a meta-interpreter action, you have to do
it in Python, not Joy. it in Python, not Joy.
.. code:: python .. code:: ipython2
from notebook_preamble import D, J, V from notebook_preamble import D, J, V
A long trace A long trace
------------ ------------
.. code:: python .. code:: ipython2
V('[23 18] average') V('[23 18] average')
@ -81,7 +81,7 @@ An efficient ``sum`` function is already in the library. But for
``size`` we can use a “compiled” version hand-written in Python to speed ``size`` we can use a “compiled” version hand-written in Python to speed
up evaluation and make the trace more readable. up evaluation and make the trace more readable.
.. code:: python .. code:: ipython2
from joy.library import SimpleFunctionWrapper from joy.library import SimpleFunctionWrapper
from joy.utils.stack import iter_stack from joy.utils.stack import iter_stack
@ -99,7 +99,7 @@ up evaluation and make the trace more readable.
Now we replace the old version in the dictionary with the new version, Now we replace the old version in the dictionary with the new version,
and re-evaluate the expression. and re-evaluate the expression.
.. code:: python .. code:: ipython2
D['size'] = size D['size'] = size
@ -108,7 +108,7 @@ A shorter trace
You can see that ``size`` now executes in a single step. You can see that ``size`` now executes in a single step.
.. code:: python .. code:: ipython2
V('[23 18] average') V('[23 18] average')

421
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@ -0,0 +1,421 @@
.. code:: ipython3
from notebook_preamble import J, V, define
Square Spiral Example Joy Code
==============================
Here is the example of Joy code from the ``README`` file:
::
[[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
It might seem unreadable but with a little familiarity it becomes just
as legible as any other notation. Some layout helps:
::
[ [[abs] ii <=]
[
[<>] [pop !-] ||
] &&
]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
This function accepts two integers on the stack and increments or
decrements one of them such that the new pair of numbers is the next
coordinate pair in a square spiral (like the kind used to construct an
Ulam Spiral).
Original Form
-------------
It's adapted from `the original code on
StackOverflow <https://stackoverflow.com/questions/398299/looping-in-a-spiral/31864777#31864777>`__:
If all you're trying to do is generate the first N points in the
spiral (without the original problem's constraint of masking to an N
x M region), the code becomes very simple:
::
void spiral(const int N)
{
int x = 0;
int y = 0;
for(int i = 0; i < N; ++i)
{
cout << x << '\t' << y << '\n';
if(abs(x) <= abs(y) && (x != y || x >= 0))
x += ((y >= 0) ? 1 : -1);
else
y += ((x >= 0) ? -1 : 1);
}
}
Translation to Joy
------------------
I'm going to make a function that take two ints (``x`` and ``y``) and
generates the next pair, we'll turn it into a generator later using the
``x`` combinator.
First Boolean Predicate
~~~~~~~~~~~~~~~~~~~~~~~
We need a function that computes ``abs(x) <= abs(y)``, we can use ``ii``
to apply ``abs`` to both values and then compare them with ``<=``:
::
[abs] ii <=
I've defined two short-circuiting Boolean combinators ``&&`` and ``||``
that each accept two quoted predicate programs, run the first, and
conditionally run the second only if required (to compute the final
Boolean value). They run their predicate arguments ``nullary``.
.. code:: ipython3
define('&& [nullary] cons [nullary [0]] dip branch')
define('|| [nullary] cons [nullary] dip [1] branch')
Given those, we can define ``x != y || x >= 0`` as:
::
[<>] [pop 0 >=] ||
And ``(abs(x) <= abs(y) && (x != y || x >= 0))`` as:
::
[[abs] ii <=] [[<>] [pop 0 >=] ||] &&
It's a little rough, but, as I say, with a little familiarity it becomes
legible.
The Increment / Decrement Branches
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Turning to the branches of the main ``if`` statement:
::
x += ((y >= 0) ? 1 : -1);
Rewrite as a hybrid (pseudo-code) ``ifte`` expression:
::
[y >= 0] [x += 1] [X -= 1] ifte
Change each C phrase to Joy code:
::
[0 >=] [[++] dip] [[--] dip] ifte
Factor out the dip from each branch:
::
[0 >=] [[++]] [[--]] ifte dip
Similar logic applies to the other branch:
::
y += ((x >= 0) ? -1 : 1);
[x >= 0] [y -= 1] [y += 1] ifte
[pop 0 >=] [--] [++] ifte
"Not Negative"
~~~~~~~~~~~~~~
.. code:: ipython3
define('!- 0 >=')
Putting the Pieces Together
---------------------------
We can assemble the three functions we just defined in quotes and give
them them to the ``ifte`` combinator. With some arrangement to show off
the symmetry of the two branches, we have:
::
[[[abs] ii <=] [[<>] [pop !-] ||] &&]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
As I was writing this up I realized that, since the ``&&`` combinator
doesn't consume the stack (below its quoted args), I can unquote the
predicate, swap the branches, and use the ``branch`` combinator instead
of ``ifte``:
::
[[abs] ii <=] [[<>] [pop !-] ||] &&
[[pop !-] [--] [++] ifte ]
[[ !-] [[++]] [[--]] ifte dip]
branch
.. code:: ipython3
define('spiral_next [[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte')
Let's try it out:
.. code:: ipython3
J('0 0 spiral_next')
.. parsed-literal::
1 0
.. code:: ipython3
J('1 0 spiral_next')
.. parsed-literal::
1 -1
.. code:: ipython3
J('1 -1 spiral_next')
.. parsed-literal::
0 -1
.. code:: ipython3
J('0 -1 spiral_next')
.. parsed-literal::
-1 -1
Turning it into a Generator with ``x``
--------------------------------------
It can be used with the x combinator to make a kind of generator for
spiral square coordinates.
We can use ``codireco`` to make a generator
::
codireco ::= cons dip rest cons
It will look like this:
::
[value [F] codireco]
Here's a trace of how it works:
::
[0 [dup ++] codireco] . x
[0 [dup ++] codireco] . 0 [dup ++] codireco
[0 [dup ++] codireco] 0 . [dup ++] codireco
[0 [dup ++] codireco] 0 [dup ++] . codireco
[0 [dup ++] codireco] 0 [dup ++] . cons dip rest cons
[0 [dup ++] codireco] [0 dup ++] . dip rest cons
. 0 dup ++ [0 [dup ++] codireco] rest cons
0 . dup ++ [0 [dup ++] codireco] rest cons
0 0 . ++ [0 [dup ++] codireco] rest cons
0 1 . [0 [dup ++] codireco] rest cons
0 1 [0 [dup ++] codireco] . rest cons
0 1 [[dup ++] codireco] . cons
0 [1 [dup ++] codireco] .
But first we have to change the ``spiral_next`` function to work on a
quoted pair of integers, and leave a copy of the pair on the stack.
From:
::
y x spiral_next
---------------------
y' x'
to:
::
[x y] [spiral_next] infra
-------------------------------
[x' y']
.. code:: ipython3
J('[0 0] [spiral_next] infra')
.. parsed-literal::
[0 1]
So our generator is:
::
[[x y] [dup [spiral_next] infra] codireco]
Or rather:
::
[[0 0] [dup [spiral_next] infra] codireco]
There is a function ``make_generator`` that will build the generator for
us out of the value and stepper function:
::
[0 0] [dup [spiral_next] infra] make_generator
----------------------------------------------------
[[0 0] [dup [spiral_next] infra] codireco]
Here it is in action:
.. code:: ipython3
J('[0 0] [dup [spiral_next] infra] make_generator x x x x pop')
.. parsed-literal::
[0 0] [0 1] [-1 1] [-1 0]
Four ``x`` combinators, four pairs of coordinates.
Conclusion
----------
So that's an example of Joy code. It's a straightforward translation of
the original. It's a little long for a single definition, you might
break it up like so:
::
_spn_P ::= [[abs] ii <=] [[<>] [pop !-] ||] &&
_spn_T ::= [ !-] [[++]] [[--]] ifte dip
_spn_E ::= [pop !-] [--] [++] ifte
spiral_next ::= _spn_P [_spn_E] [_spn_T] branch
This way it's easy to see that the function is a branch with two
quasi-symmetrical paths.
We then used this function to make a simple generator of coordinate
pairs, where the next pair in the series can be generated at any time by
using the ``x`` combinator on the generator (which is just a quoted
expression containing a copy of the current pair and the "stepper
function" to generate the next pair from that.)
.. code:: ipython3
define('_spn_P [[abs] ii <=] [[<>] [pop !-] ||] &&')
define('_spn_T [!-] [[++]] [[--]] ifte dip')
define('_spn_E [pop !-] [--] [++] ifte')
define('spiral_next _spn_P [_spn_E] [_spn_T] branch')
.. code:: ipython3
V('23 18 spiral_next')
.. parsed-literal::
. 23 18 spiral_next
23 . 18 spiral_next
23 18 . spiral_next
23 18 . _spn_P [_spn_E] [_spn_T] branch
23 18 . [[abs] ii <=] [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . [nullary] cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] [nullary] . cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] . [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] [nullary [0]] . dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . nullary [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . [stack] dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [stack] . dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [stack] . dip infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . stack [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [18 23] . [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [18 23] [[abs] ii <=] . infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . [abs] ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . [dip] dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] [dip] . dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . dip [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 . abs 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 . 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . abs <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
False . [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
False [18 23] . swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [False] . first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False . [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False [0] . [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False [0] [[[<>] [pop !-] ||] nullary] . branch [_spn_E] [_spn_T] branch
23 18 . 0 [_spn_E] [_spn_T] branch
23 18 0 . [_spn_E] [_spn_T] branch
23 18 0 [_spn_E] . [_spn_T] branch
23 18 0 [_spn_E] [_spn_T] . branch
23 18 . _spn_E
23 18 . [pop !-] [--] [++] ifte
23 18 [pop !-] . [--] [++] ifte
23 18 [pop !-] [--] . [++] ifte
23 18 [pop !-] [--] [++] . ifte
23 18 [pop !-] [--] [++] . [nullary not] dipd branch
23 18 [pop !-] [--] [++] [nullary not] . dipd branch
23 18 [pop !-] . nullary not [--] [++] branch
23 18 [pop !-] . [stack] dinfrirst not [--] [++] branch
23 18 [pop !-] [stack] . dinfrirst not [--] [++] branch
23 18 [pop !-] [stack] . dip infra first not [--] [++] branch
23 18 . stack [pop !-] infra first not [--] [++] branch
23 18 [18 23] . [pop !-] infra first not [--] [++] branch
23 18 [18 23] [pop !-] . infra first not [--] [++] branch
23 18 . pop !- [18 23] swaack first not [--] [++] branch
23 . !- [18 23] swaack first not [--] [++] branch
23 . 0 >= [18 23] swaack first not [--] [++] branch
23 0 . >= [18 23] swaack first not [--] [++] branch
True . [18 23] swaack first not [--] [++] branch
True [18 23] . swaack first not [--] [++] branch
23 18 [True] . first not [--] [++] branch
23 18 True . not [--] [++] branch
23 18 False . [--] [++] branch
23 18 False [--] . [++] branch
23 18 False [--] [++] . branch
23 18 . --
23 17 .

48
docs/sphinx_docs/_build/html/_sources/notebooks/Treestep.rst.txt
View File

@ -148,11 +148,11 @@ Working backwards:
Define ``treestep`` Define ``treestep``
------------------- -------------------
.. code:: python .. code:: ipython2
from notebook_preamble import D, J, V, define, DefinitionWrapper from notebook_preamble import D, J, V, define, DefinitionWrapper
.. code:: python .. code:: ipython2
DefinitionWrapper.add_definitions(''' DefinitionWrapper.add_definitions('''
@ -173,7 +173,7 @@ all nodes in a tree with this function:
sumtree == [pop 0] [] [sum +] treestep sumtree == [pop 0] [] [sum +] treestep
.. code:: python .. code:: ipython2
define('sumtree == [pop 0] [] [sum +] treestep') define('sumtree == [pop 0] [] [sum +] treestep')
@ -185,7 +185,7 @@ Running this function on an empty tree value gives zero:
------------------------------------ ------------------------------------
0 0
.. code:: python .. code:: ipython2
J('[] sumtree') # Empty tree. J('[] sumtree') # Empty tree.
@ -205,7 +205,7 @@ Running it on a non-empty node:
n m + n m +
n+m n+m
.. code:: python .. code:: ipython2
J('[23] sumtree') # No child trees. J('[23] sumtree') # No child trees.
@ -215,7 +215,7 @@ Running it on a non-empty node:
23 23
.. code:: python .. code:: ipython2
J('[23 []] sumtree') # Child tree, empty. J('[23 []] sumtree') # Child tree, empty.
@ -225,7 +225,7 @@ Running it on a non-empty node:
23 23
.. code:: python .. code:: ipython2
J('[23 [2 [4]] [3]] sumtree') # Non-empty child trees. J('[23 [2 [4]] [3]] sumtree') # Non-empty child trees.
@ -235,7 +235,7 @@ Running it on a non-empty node:
32 32
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] sumtree') # Etc... J('[23 [2 [8] [9]] [3] [4 []]] sumtree') # Etc...
@ -245,7 +245,7 @@ Running it on a non-empty node:
49 49
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep') # Alternate "spelling". J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep') # Alternate "spelling".
@ -255,7 +255,7 @@ Running it on a non-empty node:
49 49
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep') # Replace each node. J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep') # Replace each node.
@ -265,7 +265,7 @@ Running it on a non-empty node:
[23 [23 [23] [23]] [23] [23 []]] [23 [23 [23] [23]] [23] [23 []]]
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep') J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep')
@ -275,7 +275,7 @@ Running it on a non-empty node:
[1 [1 [1] [1]] [1] [1 []]] [1 [1 [1] [1]] [1] [1 []]]
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree') J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree')
@ -285,7 +285,7 @@ Running it on a non-empty node:
6 6
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function. J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function.
@ -295,7 +295,7 @@ Running it on a non-empty node:
6 6
.. code:: python .. code:: ipython2
J('[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function. J('[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function.
@ -339,7 +339,7 @@ Traversal
This doesn’t quite work: This doesn’t quite work:
.. code:: python .. code:: ipython2
J('[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep') J('[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep')
@ -369,7 +369,7 @@ So:
[] [first] [flatten cons] treestep [] [first] [flatten cons] treestep
.. code:: python .. code:: ipython2
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep') J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep')
@ -401,7 +401,7 @@ So:
[] [i roll< swons concat] [first] treestep [] [i roll< swons concat] [first] treestep
.. code:: python .. code:: ipython2
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll< swons concat] treestep') J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll< swons concat] treestep')
@ -429,7 +429,7 @@ Plugging in our BTree structure:
[key value] N [left right] [K] C [key value] N [left right] [K] C
.. code:: python .. code:: ipython2
J('[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind') J('[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind')
@ -444,7 +444,7 @@ Plugging in our BTree structure:
Iteration through the nodes Iteration through the nodes
.. code:: python .. code:: ipython2
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] ["N"] [step] treegrind') J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] ["N"] [step] treegrind')
@ -456,7 +456,7 @@ Iteration through the nodes
Sum the nodes’ keys. Sum the nodes’ keys.
.. code:: python .. code:: ipython2
J('0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind') J('0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind')
@ -468,7 +468,7 @@ Sum the nodes’ keys.
Rebuild the tree using ``map`` (imitating ``treestep``.) Rebuild the tree using ``map`` (imitating ``treestep``.)
.. code:: python .. code:: ipython2
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind') J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind')
@ -574,7 +574,7 @@ Putting it together
To me, that seems simpler than the ``genrec`` version. To me, that seems simpler than the ``genrec`` version.
.. code:: python .. code:: ipython2
DefinitionWrapper.add_definitions(''' DefinitionWrapper.add_definitions('''
@ -587,7 +587,7 @@ To me, that seems simpler than the ``genrec`` version.
''', D) ''', D)
.. code:: python .. code:: ipython2
J('''\ J('''\
@ -603,7 +603,7 @@ To me, that seems simpler than the ``genrec`` version.
15 15
.. code:: python .. code:: ipython2
J('''\ J('''\

30
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@ -1,7 +1,7 @@
Type Checking Type Checking
============= =============
.. code:: python .. code:: ipython2
import logging, sys import logging, sys
@ -11,7 +11,7 @@ Type Checking
level=logging.INFO, level=logging.INFO,
) )
.. code:: python .. code:: ipython2
from joy.utils.types import ( from joy.utils.types import (
doc_from_stack_effect, doc_from_stack_effect,
@ -22,7 +22,7 @@ Type Checking
JoyTypeError, JoyTypeError,
) )
.. code:: python .. code:: ipython2
D = FUNCTIONS.copy() D = FUNCTIONS.copy()
del D['product'] del D['product']
@ -31,7 +31,7 @@ Type Checking
An Example An Example
---------- ----------
.. code:: python .. code:: ipython2
fi, fo = infer(pop, swap, rolldown, rrest, ccons)[0] fi, fo = infer(pop, swap, rolldown, rrest, ccons)[0]
@ -46,7 +46,7 @@ An Example
40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘ 40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
.. code:: python .. code:: ipython2
print doc_from_stack_effect(fi, fo) print doc_from_stack_effect(fi, fo)
@ -56,13 +56,13 @@ An Example
([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1])
.. code:: python .. code:: ipython2
from joy.parser import text_to_expression from joy.parser import text_to_expression
from joy.utils.stack import stack_to_string from joy.utils.stack import stack_to_string
.. code:: python .. code:: ipython2
e = text_to_expression('0 1 2 [3 4]') # reverse order e = text_to_expression('0 1 2 [3 4]') # reverse order
print stack_to_string(e) print stack_to_string(e)
@ -73,7 +73,7 @@ An Example
[3 4] 2 1 0 [3 4] 2 1 0
.. code:: python .. code:: ipython2
u = unify(e, fi)[0] u = unify(e, fi)[0]
u u
@ -87,7 +87,7 @@ An Example
.. code:: python .. code:: ipython2
g = reify(u, (fi, fo)) g = reify(u, (fi, fo))
print doc_from_stack_effect(*g) print doc_from_stack_effect(*g)
@ -101,11 +101,11 @@ An Example
Unification Works “in Reverse” Unification Works “in Reverse”
------------------------------ ------------------------------
.. code:: python .. code:: ipython2
e = text_to_expression('[2 3]') e = text_to_expression('[2 3]')
.. code:: python .. code:: ipython2
u = unify(e, fo)[0] # output side, not input side u = unify(e, fo)[0] # output side, not input side
u u
@ -119,7 +119,7 @@ Unification Works “in Reverse”
.. code:: python .. code:: ipython2
g = reify(u, (fi, fo)) g = reify(u, (fi, fo))
print doc_from_stack_effect(*g) print doc_from_stack_effect(*g)
@ -133,7 +133,7 @@ Unification Works “in Reverse”
Failing a Check Failing a Check
--------------- ---------------
.. code:: python .. code:: ipython2
fi, fo = infer(dup, mul)[0] fi, fo = infer(dup, mul)[0]
@ -146,7 +146,7 @@ Failing a Check
31 (i1 -- i2) ∘ 31 (i1 -- i2) ∘
.. code:: python .. code:: ipython2
e = text_to_expression('"two"') e = text_to_expression('"two"')
print stack_to_string(e) print stack_to_string(e)
@ -157,7 +157,7 @@ Failing a Check
'two' 'two'
.. code:: python .. code:: ipython2
try: try:
unify(e, fi) unify(e, fi)

228
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@ -184,7 +184,7 @@ Compiling ``pop∘swap∘roll<``
The simplest way to “compile” this function would be something like: The simplest way to “compile” this function would be something like:
.. code:: python .. code:: ipython2
def poswrd(s, e, d): def poswrd(s, e, d):
return rolldown(*swap(*pop(s, e, d))) return rolldown(*swap(*pop(s, e, d)))
@ -200,7 +200,7 @@ Looking ahead for a moment, from the stack effect comment:
We should be able to directly write out a Python function like: We should be able to directly write out a Python function like:
.. code:: python .. code:: ipython2
def poswrd(stack): def poswrd(stack):
(_, (a, (b, (c, stack)))) = stack (_, (a, (b, (c, stack)))) = stack
@ -393,7 +393,7 @@ And there you have it, the stack effect for
From this stack effect comment it should be possible to construct the From this stack effect comment it should be possible to construct the
following Python code: following Python code:
.. code:: python .. code:: ipython2
def F(stack): def F(stack):
(_, (d, (c, ((a, (b, S0)), stack)))) = stack (_, (d, (c, ((a, (b, S0)), stack)))) = stack
@ -408,7 +408,7 @@ Representing Stack Effect Comments in Python
I’m going to use pairs of tuples of type descriptors, which will be I’m going to use pairs of tuples of type descriptors, which will be
integers or tuples of type descriptors: integers or tuples of type descriptors:
.. code:: python .. code:: ipython2
roll_dn = (1, 2, 3), (2, 3, 1) roll_dn = (1, 2, 3), (2, 3, 1)
@ -419,7 +419,7 @@ integers or tuples of type descriptors:
``compose()`` ``compose()``
~~~~~~~~~~~~~ ~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def compose(f, g): def compose(f, g):
@ -465,7 +465,7 @@ integers or tuples of type descriptors:
``unify()`` ``unify()``
~~~~~~~~~~~ ~~~~~~~~~~~
.. code:: python .. code:: ipython2
def unify(u, v, s=None): def unify(u, v, s=None):
if s is None: if s is None:
@ -483,7 +483,7 @@ integers or tuples of type descriptors:
``update()`` ``update()``
~~~~~~~~~~~~ ~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def update(s, term): def update(s, term):
if not isinstance(term, tuple): if not isinstance(term, tuple):
@ -493,7 +493,7 @@ integers or tuples of type descriptors:
``relabel()`` ``relabel()``
~~~~~~~~~~~~~ ~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def relabel(left, right): def relabel(left, right):
return left, _1000(right) return left, _1000(right)
@ -517,7 +517,7 @@ integers or tuples of type descriptors:
``delabel()`` ``delabel()``
~~~~~~~~~~~~~ ~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def delabel(f): def delabel(f):
s = {u: i for i, u in enumerate(sorted(_unique(f)))} s = {u: i for i, u in enumerate(sorted(_unique(f)))}
@ -551,7 +551,7 @@ At last we put it all together in a function ``C()`` that accepts two
stack effect comments and returns their composition (or raises and stack effect comments and returns their composition (or raises and
exception if they can’t be composed due to type conflicts.) exception if they can’t be composed due to type conflicts.)
.. code:: python .. code:: ipython2
def C(f, g): def C(f, g):
f, g = relabel(f, g) f, g = relabel(f, g)
@ -560,7 +560,7 @@ exception if they can’t be composed due to type conflicts.)
Let’s try it out. Let’s try it out.
.. code:: python .. code:: ipython2
C(pop, swap) C(pop, swap)
@ -573,7 +573,7 @@ Let’s try it out.
.. code:: python .. code:: ipython2
C(C(pop, swap), roll_dn) C(C(pop, swap), roll_dn)
@ -586,7 +586,7 @@ Let’s try it out.
.. code:: python .. code:: ipython2
C(swap, roll_dn) C(swap, roll_dn)
@ -599,7 +599,7 @@ Let’s try it out.
.. code:: python .. code:: ipython2
C(pop, C(swap, roll_dn)) C(pop, C(swap, roll_dn))
@ -612,7 +612,7 @@ Let’s try it out.
.. code:: python .. code:: ipython2
poswrd = reduce(C, (pop, swap, roll_dn)) poswrd = reduce(C, (pop, swap, roll_dn))
poswrd poswrd
@ -633,13 +633,13 @@ Here’s that trick to represent functions like ``rest`` and ``cons`` that
manipulate stacks. We use a cons-list of tuples and give the tails their manipulate stacks. We use a cons-list of tuples and give the tails their
own numbers. Then everything above already works. own numbers. Then everything above already works.
.. code:: python .. code:: ipython2
rest = ((1, 2),), (2,) rest = ((1, 2),), (2,)
cons = (1, 2), ((1, 2),) cons = (1, 2), ((1, 2),)
.. code:: python .. code:: ipython2
C(poswrd, rest) C(poswrd, rest)
@ -671,7 +671,7 @@ The translation table, if you will, would be:
0: 0, 0: 0,
} }
.. code:: python .. code:: ipython2
F = reduce(C, (pop, swap, roll_dn, rest, rest, cons, cons)) F = reduce(C, (pop, swap, roll_dn, rest, rest, cons, cons))
@ -699,11 +699,11 @@ Dealing with ``cons`` and ``uncons``
However, if we try to compose e.g. ``cons`` and ``uncons`` it won’t However, if we try to compose e.g. ``cons`` and ``uncons`` it won’t
work: work:
.. code:: python .. code:: ipython2
uncons = ((1, 2),), (1, 2) uncons = ((1, 2),), (1, 2)
.. code:: python .. code:: ipython2
try: try:
C(cons, uncons) C(cons, uncons)
@ -723,7 +723,7 @@ The problem is that the ``unify()`` function as written doesn’t handle
the case when both terms are tuples. We just have to add a clause to the case when both terms are tuples. We just have to add a clause to
deal with this recursively: deal with this recursively:
.. code:: python .. code:: ipython2
def unify(u, v, s=None): def unify(u, v, s=None):
if s is None: if s is None:
@ -753,7 +753,7 @@ deal with this recursively:
return s return s
.. code:: python .. code:: ipython2
C(cons, uncons) C(cons, uncons)
@ -771,7 +771,7 @@ Part III: Compiling Yin Functions
Now consider the Python function we would like to derive: Now consider the Python function we would like to derive:
.. code:: python .. code:: ipython2
def F_python(stack): def F_python(stack):
(_, (d, (c, ((a, (b, S0)), stack)))) = stack (_, (d, (c, ((a, (b, S0)), stack)))) = stack
@ -779,7 +779,7 @@ Now consider the Python function we would like to derive:
And compare it to the input stack effect comment tuple we just computed: And compare it to the input stack effect comment tuple we just computed:
.. code:: python .. code:: ipython2
F[0] F[0]
@ -816,7 +816,7 @@ Eh?
And the return tuple And the return tuple
.. code:: python .. code:: ipython2
F[1] F[1]
@ -848,7 +848,7 @@ Python Identifiers
We want to substitute Python identifiers for the integers. I’m going to We want to substitute Python identifiers for the integers. I’m going to
repurpose ``joy.parser.Symbol`` class for this: repurpose ``joy.parser.Symbol`` class for this:
.. code:: python .. code:: ipython2
from collections import defaultdict from collections import defaultdict
from joy.parser import Symbol from joy.parser import Symbol
@ -874,7 +874,7 @@ effect comment tuples to reasonable text format. There are some details
in how this code works that related to stuff later in the notebook, so in how this code works that related to stuff later in the notebook, so
you should skip it for now and read it later if you’re interested. you should skip it for now and read it later if you’re interested.
.. code:: python .. code:: ipython2
def doc_from_stack_effect(inputs, outputs): def doc_from_stack_effect(inputs, outputs):
return '(%s--%s)' % ( return '(%s--%s)' % (
@ -914,7 +914,7 @@ Now we can write a compiler function to emit Python source code. (The
underscore suffix distiguishes it from the built-in ``compile()`` underscore suffix distiguishes it from the built-in ``compile()``
function.) function.)
.. code:: python .. code:: ipython2
def compile_(name, f, doc=None): def compile_(name, f, doc=None):
if doc is None: if doc is None:
@ -932,7 +932,7 @@ function.)
Here it is in action: Here it is in action:
.. code:: python .. code:: ipython2
source = compile_('F', F) source = compile_('F', F)
@ -949,7 +949,7 @@ Here it is in action:
Compare: Compare:
.. code:: python .. code:: ipython2
def F_python(stack): def F_python(stack):
(_, (d, (c, ((a, (b, S0)), stack)))) = stack (_, (d, (c, ((a, (b, S0)), stack)))) = stack
@ -957,7 +957,7 @@ Compare:
Next steps: Next steps:
.. code:: python .. code:: ipython2
L = {} L = {}
@ -976,16 +976,16 @@ Next steps:
Let’s try it out: Let’s try it out:
.. code:: python .. code:: ipython2
from notebook_preamble import D, J, V from notebook_preamble import D, J, V
from joy.library import SimpleFunctionWrapper from joy.library import SimpleFunctionWrapper
.. code:: python .. code:: ipython2
D['F'] = SimpleFunctionWrapper(L['F']) D['F'] = SimpleFunctionWrapper(L['F'])
.. code:: python .. code:: ipython2
J('[4 5 ...] 2 3 1 F') J('[4 5 ...] 2 3 1 F')
@ -1012,7 +1012,7 @@ Compiling Library Functions
We can use ``compile_()`` to generate many primitives in the library We can use ``compile_()`` to generate many primitives in the library
from their stack effect comments: from their stack effect comments:
.. code:: python .. code:: ipython2
def defs(): def defs():
@ -1036,7 +1036,7 @@ from their stack effect comments:
return locals() return locals()
.. code:: python .. code:: ipython2
for name, stack_effect_comment in sorted(defs().items()): for name, stack_effect_comment in sorted(defs().items()):
print print
@ -1205,7 +1205,7 @@ Python class hierarchy of Joy types and use the ``issubclass()`` method
to establish domain ordering, as well as other handy behaviour that will to establish domain ordering, as well as other handy behaviour that will
make it fairly easy to reuse most of the code above. make it fairly easy to reuse most of the code above.
.. code:: python .. code:: ipython2
class AnyJoyType(object): class AnyJoyType(object):
@ -1251,14 +1251,14 @@ make it fairly easy to reuse most of the code above.
Mess with it a little: Mess with it a little:
.. code:: python .. code:: ipython2
from itertools import permutations from itertools import permutations
“Any” types can be specialized to numbers and stacks, but not vice “Any” types can be specialized to numbers and stacks, but not vice
versa: versa:
.. code:: python .. code:: ipython2
for a, b in permutations((A[0], N[0], S[0]), 2): for a, b in permutations((A[0], N[0], S[0]), 2):
print a, '>=', b, '->', a >= b print a, '>=', b, '->', a >= b
@ -1278,7 +1278,7 @@ Our crude `Numerical
Tower <https://en.wikipedia.org/wiki/Numerical_tower>`__ of *numbers* > Tower <https://en.wikipedia.org/wiki/Numerical_tower>`__ of *numbers* >
*floats* > *integers* works as well (but we’re not going to use it yet): *floats* > *integers* works as well (but we’re not going to use it yet):
.. code:: python .. code:: ipython2
for a, b in permutations((A[0], N[0], FloatJoyType(0), IntJoyType(0)), 2): for a, b in permutations((A[0], N[0], FloatJoyType(0), IntJoyType(0)), 2):
print a, '>=', b, '->', a >= b print a, '>=', b, '->', a >= b
@ -1303,13 +1303,13 @@ Tower <https://en.wikipedia.org/wiki/Numerical_tower>`__ of *numbers* >
Typing ``sqr`` Typing ``sqr``
~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
dup = (A[1],), (A[1], A[1]) dup = (A[1],), (A[1], A[1])
mul = (N[1], N[2]), (N[3],) mul = (N[1], N[2]), (N[3],)
.. code:: python .. code:: ipython2
dup dup
@ -1322,7 +1322,7 @@ Typing ``sqr``
.. code:: python .. code:: ipython2
mul mul
@ -1340,7 +1340,7 @@ Modifying the Inferencer
Re-labeling still works fine: Re-labeling still works fine:
.. code:: python .. code:: ipython2
foo = relabel(dup, mul) foo = relabel(dup, mul)
@ -1361,7 +1361,7 @@ Re-labeling still works fine:
The ``delabel()`` function needs an overhaul. It now has to keep track The ``delabel()`` function needs an overhaul. It now has to keep track
of how many labels of each domain it has “seen”. of how many labels of each domain it has “seen”.
.. code:: python .. code:: ipython2
from collections import Counter from collections import Counter
@ -1383,7 +1383,7 @@ of how many labels of each domain it has “seen”.
return tuple(delabel(inner, seen, c) for inner in f) return tuple(delabel(inner, seen, c) for inner in f)
.. code:: python .. code:: ipython2
delabel(foo) delabel(foo)
@ -1399,7 +1399,7 @@ of how many labels of each domain it has “seen”.
``unify()`` version 3 ``unify()`` version 3
^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^
.. code:: python .. code:: ipython2
def unify(u, v, s=None): def unify(u, v, s=None):
if s is None: if s is None:
@ -1449,7 +1449,7 @@ of how many labels of each domain it has “seen”.
Rewrite the stack effect comments: Rewrite the stack effect comments:
.. code:: python .. code:: ipython2
def defs(): def defs():
@ -1503,11 +1503,11 @@ Rewrite the stack effect comments:
return locals() return locals()
.. code:: python .. code:: ipython2
DEFS = defs() DEFS = defs()
.. code:: python .. code:: ipython2
for name, stack_effect_comment in sorted(DEFS.items()): for name, stack_effect_comment in sorted(DEFS.items()):
print name, '=', doc_from_stack_effect(*stack_effect_comment) print name, '=', doc_from_stack_effect(*stack_effect_comment)
@ -1543,14 +1543,14 @@ Rewrite the stack effect comments:
uncons = ([a1 .1.] -- a1 [.1.]) uncons = ([a1 .1.] -- a1 [.1.])
.. code:: python .. code:: ipython2
globals().update(DEFS) globals().update(DEFS)
Compose ``dup`` and ``mul`` Compose ``dup`` and ``mul``
^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. code:: python .. code:: ipython2
C(dup, mul) C(dup, mul)
@ -1565,7 +1565,7 @@ Compose ``dup`` and ``mul``
Revisit the ``F`` function, works fine. Revisit the ``F`` function, works fine.
.. code:: python .. code:: ipython2
F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons)) F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons))
F F
@ -1579,7 +1579,7 @@ Revisit the ``F`` function, works fine.
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*F) print doc_from_stack_effect(*F)
@ -1592,12 +1592,12 @@ Revisit the ``F`` function, works fine.
Some otherwise inefficient functions are no longer to be feared. We can Some otherwise inefficient functions are no longer to be feared. We can
also get the effect of combinators in some limited cases. also get the effect of combinators in some limited cases.
.. code:: python .. code:: ipython2
def neato(*funcs): def neato(*funcs):
print doc_from_stack_effect(*reduce(C, funcs)) print doc_from_stack_effect(*reduce(C, funcs))
.. code:: python .. code:: ipython2
# e.g. [swap] dip # e.g. [swap] dip
neato(rollup, swap, rolldown) neato(rollup, swap, rolldown)
@ -1608,7 +1608,7 @@ also get the effect of combinators in some limited cases.
(a1 a2 a3 -- a2 a1 a3) (a1 a2 a3 -- a2 a1 a3)
.. code:: python .. code:: ipython2
# e.g. [popop] dipd # e.g. [popop] dipd
neato(popdd, rolldown, pop) neato(popdd, rolldown, pop)
@ -1619,7 +1619,7 @@ also get the effect of combinators in some limited cases.
(a1 a2 a3 a4 -- a3 a4) (a1 a2 a3 a4 -- a3 a4)
.. code:: python .. code:: ipython2
# Reverse the order of the top three items. # Reverse the order of the top three items.
neato(rollup, swap) neato(rollup, swap)
@ -1636,7 +1636,7 @@ also get the effect of combinators in some limited cases.
Because the type labels represent themselves as valid Python identifiers Because the type labels represent themselves as valid Python identifiers
the ``compile_()`` function doesn’t need to generate them anymore: the ``compile_()`` function doesn’t need to generate them anymore:
.. code:: python .. code:: ipython2
def compile_(name, f, doc=None): def compile_(name, f, doc=None):
inputs, outputs = f inputs, outputs = f
@ -1652,7 +1652,7 @@ the ``compile_()`` function doesn’t need to generate them anymore:
%s = stack %s = stack
return %s''' % (name, doc, i, o) return %s''' % (name, doc, i, o)
.. code:: python .. code:: ipython2
print compile_('F', F) print compile_('F', F)
@ -1668,7 +1668,7 @@ the ``compile_()`` function doesn’t need to generate them anymore:
But it cannot magically create new functions that involve e.g. math and But it cannot magically create new functions that involve e.g. math and
such. Note that this is *not* a ``sqr`` function implementation: such. Note that this is *not* a ``sqr`` function implementation:
.. code:: python .. code:: ipython2
print compile_('sqr', C(dup, mul)) print compile_('sqr', C(dup, mul))
@ -1696,7 +1696,7 @@ The functions that *can* be compiled are the ones that have only
``AnyJoyType`` and ``StackJoyType`` labels in their stack effect ``AnyJoyType`` and ``StackJoyType`` labels in their stack effect
comments. We can write a function to check that: comments. We can write a function to check that:
.. code:: python .. code:: ipython2
from itertools import imap from itertools import imap
@ -1704,7 +1704,7 @@ comments. We can write a function to check that:
def compilable(f): def compilable(f):
return isinstance(f, tuple) and all(imap(compilable, f)) or stacky(f) return isinstance(f, tuple) and all(imap(compilable, f)) or stacky(f)
.. code:: python .. code:: ipython2
for name, stack_effect_comment in sorted(defs().items()): for name, stack_effect_comment in sorted(defs().items()):
if compilable(stack_effect_comment): if compilable(stack_effect_comment):
@ -1828,7 +1828,7 @@ the “truthiness” of ``StackJoyType`` to false to let e.g.
``joy.utils.stack.concat`` work with our stack effect comment cons-list ``joy.utils.stack.concat`` work with our stack effect comment cons-list
tuples.) tuples.)
.. code:: python .. code:: ipython2
def compose(f, g): def compose(f, g):
(f_in, f_out), (g_in, g_out) = f, g (f_in, f_out), (g_in, g_out) = f, g
@ -1840,7 +1840,7 @@ tuples.)
I don’t want to rewrite all the defs myself, so I’ll write a little I don’t want to rewrite all the defs myself, so I’ll write a little
conversion function instead. This is programmer’s laziness. conversion function instead. This is programmer’s laziness.
.. code:: python .. code:: ipython2
def sequence_to_stack(seq, stack=StackJoyType(23)): def sequence_to_stack(seq, stack=StackJoyType(23)):
for item in seq: stack = item, stack for item in seq: stack = item, stack
@ -1854,7 +1854,7 @@ conversion function instead. This is programmer’s laziness.
NEW_DEFS['swaack'] = (S[1], S[0]), (S[0], S[1]) NEW_DEFS['swaack'] = (S[1], S[0]), (S[0], S[1])
globals().update(NEW_DEFS) globals().update(NEW_DEFS)
.. code:: python .. code:: ipython2
C(stack, uncons) C(stack, uncons)
@ -1867,7 +1867,7 @@ conversion function instead. This is programmer’s laziness.
.. code:: python .. code:: ipython2
reduce(C, (stack, uncons, uncons)) reduce(C, (stack, uncons, uncons))
@ -1887,7 +1887,7 @@ The display function should be changed too.
Clunky junk, but it will suffice for now. Clunky junk, but it will suffice for now.
.. code:: python .. code:: ipython2
def doc_from_stack_effect(inputs, outputs): def doc_from_stack_effect(inputs, outputs):
switch = [False] # Do we need to display the '...' for the rest of the main stack? switch = [False] # Do we need to display the '...' for the rest of the main stack?
@ -1935,7 +1935,7 @@ Clunky junk, but it will suffice for now.
a.append(end) a.append(end)
return '[%s]' % ' '.join(a) return '[%s]' % ' '.join(a)
.. code:: python .. code:: ipython2
for name, stack_effect_comment in sorted(NEW_DEFS.items()): for name, stack_effect_comment in sorted(NEW_DEFS.items()):
print name, '=', doc_from_stack_effect(*stack_effect_comment) print name, '=', doc_from_stack_effect(*stack_effect_comment)
@ -1973,7 +1973,7 @@ Clunky junk, but it will suffice for now.
uncons = ([a1 .1.] -- a1 [.1.]) uncons = ([a1 .1.] -- a1 [.1.])
.. code:: python .. code:: ipython2
print ; print doc_from_stack_effect(*stack) print ; print doc_from_stack_effect(*stack)
print ; print doc_from_stack_effect(*C(stack, uncons)) print ; print doc_from_stack_effect(*C(stack, uncons))
@ -1993,7 +1993,7 @@ Clunky junk, but it will suffice for now.
(... a1 -- ... a1 [a1 ...]) (... a1 -- ... a1 [a1 ...])
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*C(ccons, stack)) print doc_from_stack_effect(*C(ccons, stack))
@ -2003,7 +2003,7 @@ Clunky junk, but it will suffice for now.
(... a2 a1 [.1.] -- ... [a2 a1 .1.] [[a2 a1 .1.] ...]) (... a2 a1 [.1.] -- ... [a2 a1 .1.] [[a2 a1 .1.] ...])
.. code:: python .. code:: ipython2
Q = C(ccons, stack) Q = C(ccons, stack)
@ -2024,7 +2024,7 @@ Clunky junk, but it will suffice for now.
This makes the ``compile_()`` function pretty simple as the stack effect This makes the ``compile_()`` function pretty simple as the stack effect
comments are now already in the form needed for the Python code: comments are now already in the form needed for the Python code:
.. code:: python .. code:: ipython2
def compile_(name, f, doc=None): def compile_(name, f, doc=None):
i, o = f i, o = f
@ -2035,7 +2035,7 @@ comments are now already in the form needed for the Python code:
%s = stack %s = stack
return %s''' % (name, doc, i, o) return %s''' % (name, doc, i, o)
.. code:: python .. code:: ipython2
print compile_('Q', Q) print compile_('Q', Q)
@ -2053,12 +2053,12 @@ comments are now already in the form needed for the Python code:
.. code:: python .. code:: ipython2
unstack = (S[1], S[0]), S[1] unstack = (S[1], S[0]), S[1]
enstacken = S[0], (S[0], S[1]) enstacken = S[0], (S[0], S[1])
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*unstack) print doc_from_stack_effect(*unstack)
@ -2068,7 +2068,7 @@ comments are now already in the form needed for the Python code:
([.1.] --) ([.1.] --)
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*enstacken) print doc_from_stack_effect(*enstacken)
@ -2078,7 +2078,7 @@ comments are now already in the form needed for the Python code:
(-- [.0.]) (-- [.0.])
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*C(cons, unstack)) print doc_from_stack_effect(*C(cons, unstack))
@ -2088,7 +2088,7 @@ comments are now already in the form needed for the Python code:
(a1 [.1.] -- a1) (a1 [.1.] -- a1)
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*C(cons, enstacken)) print doc_from_stack_effect(*C(cons, enstacken))
@ -2098,7 +2098,7 @@ comments are now already in the form needed for the Python code:
(a1 [.1.] -- [[a1 .1.] .2.]) (a1 [.1.] -- [[a1 .1.] .2.])
.. code:: python .. code:: ipython2
C(cons, unstack) C(cons, unstack)
@ -2117,7 +2117,7 @@ Part VI: Multiple Stack Effects
… …
.. code:: python .. code:: ipython2
class IntJoyType(NumberJoyType): prefix = 'i' class IntJoyType(NumberJoyType): prefix = 'i'
@ -2125,7 +2125,7 @@ Part VI: Multiple Stack Effects
F = map(FloatJoyType, _R) F = map(FloatJoyType, _R)
I = map(IntJoyType, _R) I = map(IntJoyType, _R)
.. code:: python .. code:: ipython2
muls = [ muls = [
((I[2], (I[1], S[0])), (I[3], S[0])), ((I[2], (I[1], S[0])), (I[3], S[0])),
@ -2134,7 +2134,7 @@ Part VI: Multiple Stack Effects
((F[2], (F[1], S[0])), (F[3], S[0])), ((F[2], (F[1], S[0])), (F[3], S[0])),
] ]
.. code:: python .. code:: ipython2
for f in muls: for f in muls:
print doc_from_stack_effect(*f) print doc_from_stack_effect(*f)
@ -2148,7 +2148,7 @@ Part VI: Multiple Stack Effects
(f1 f2 -- f3) (f1 f2 -- f3)
.. code:: python .. code:: ipython2
for f in muls: for f in muls:
try: try:
@ -2164,7 +2164,7 @@ Part VI: Multiple Stack Effects
(a1 -- a1 a1) (f1 f2 -- f3) (f1 -- f2) (a1 -- a1 a1) (f1 f2 -- f3) (f1 -- f2)
.. code:: python .. code:: ipython2
from itertools import product from itertools import product
@ -2180,7 +2180,7 @@ Part VI: Multiple Stack Effects
def MC(F, G): def MC(F, G):
return sorted(set(meta_compose(F, G))) return sorted(set(meta_compose(F, G)))
.. code:: python .. code:: ipython2
for f in MC([dup], [mul]): for f in MC([dup], [mul]):
print doc_from_stack_effect(*f) print doc_from_stack_effect(*f)
@ -2191,7 +2191,7 @@ Part VI: Multiple Stack Effects
(n1 -- n2) (n1 -- n2)
.. code:: python .. code:: ipython2
for f in MC([dup], muls): for f in MC([dup], muls):
print doc_from_stack_effect(*f) print doc_from_stack_effect(*f)
@ -2264,7 +2264,7 @@ Giving us two unifiers:
{c: a, d: b, .1.: .0.} {c: a, d: b, .1.: .0.}
{c: a, d: e, .1.: A* b .0.} {c: a, d: e, .1.: A* b .0.}
.. code:: python .. code:: ipython2
class KleeneStar(object): class KleeneStar(object):
@ -2314,7 +2314,7 @@ Giving us two unifiers:
Can now return multiple results… Can now return multiple results…
.. code:: python .. code:: ipython2
def unify(u, v, s=None): def unify(u, v, s=None):
if s is None: if s is None:
@ -2386,7 +2386,7 @@ Can now return multiple results…
def stacky(thing): def stacky(thing):
return thing.__class__ in {AnyJoyType, StackJoyType} return thing.__class__ in {AnyJoyType, StackJoyType}
.. code:: python .. code:: ipython2
a = (As[1], S[1]) a = (As[1], S[1])
a a
@ -2400,7 +2400,7 @@ Can now return multiple results…
.. code:: python .. code:: ipython2
b = (A[1], S[2]) b = (A[1], S[2])
b b
@ -2414,7 +2414,7 @@ Can now return multiple results…
.. code:: python .. code:: ipython2
for result in unify(b, a): for result in unify(b, a):
print result, '->', update(result, a), update(result, b) print result, '->', update(result, a), update(result, b)
@ -2426,7 +2426,7 @@ Can now return multiple results…
{a1: a10001, s2: (a1*, s1)} -> (a1*, s1) (a10001, (a1*, s1)) {a1: a10001, s2: (a1*, s1)} -> (a1*, s1) (a10001, (a1*, s1))
.. code:: python .. code:: ipython2
for result in unify(a, b): for result in unify(a, b):
print result, '->', update(result, a), update(result, b) print result, '->', update(result, a), update(result, b)
@ -2446,7 +2446,7 @@ Can now return multiple results…
(a1*, s1) [a1*] (a2, (a1*, s1)) [a2 a1*] (a1*, s1) [a1*] (a2, (a1*, s1)) [a2 a1*]
.. code:: python .. code:: ipython2
sum_ = ((Ns[1], S[1]), S[0]), (N[0], S[0]) sum_ = ((Ns[1], S[1]), S[0]), (N[0], S[0])
@ -2458,7 +2458,7 @@ Can now return multiple results…
([n1* .1.] -- n0) ([n1* .1.] -- n0)
.. code:: python .. code:: ipython2
f = (N[1], (N[2], (N[3], S[1]))), S[0] f = (N[1], (N[2], (N[3], S[1]))), S[0]
@ -2470,7 +2470,7 @@ Can now return multiple results…
(-- [n1 n2 n3 .1.]) (-- [n1 n2 n3 .1.])
.. code:: python .. code:: ipython2
for result in unify(sum_[0], f): for result in unify(sum_[0], f):
print result, '->', update(result, sum_[1]) print result, '->', update(result, sum_[1])
@ -2489,7 +2489,7 @@ Can now return multiple results…
This function has to be modified to yield multiple results. This function has to be modified to yield multiple results.
.. code:: python .. code:: ipython2
def compose(f, g): def compose(f, g):
(f_in, f_out), (g_in, g_out) = f, g (f_in, f_out), (g_in, g_out) = f, g
@ -2501,7 +2501,7 @@ This function has to be modified to yield multiple results.
.. code:: python .. code:: ipython2
def meta_compose(F, G): def meta_compose(F, G):
for f, g in product(F, G): for f, g in product(F, G):
@ -2517,7 +2517,7 @@ This function has to be modified to yield multiple results.
for fg in compose(f, g): for fg in compose(f, g):
yield delabel(fg) yield delabel(fg)
.. code:: python .. code:: ipython2
for f in MC([dup], muls): for f in MC([dup], muls):
print doc_from_stack_effect(*f) print doc_from_stack_effect(*f)
@ -2529,7 +2529,7 @@ This function has to be modified to yield multiple results.
(i1 -- i2) (i1 -- i2)
.. code:: python .. code:: ipython2
@ -2542,7 +2542,7 @@ This function has to be modified to yield multiple results.
([n1* .1.] -- [n1* .1.] n1) ([n1* .1.] -- [n1* .1.] n1)
.. code:: python .. code:: ipython2
@ -2556,7 +2556,7 @@ This function has to be modified to yield multiple results.
(n1 [n1* .1.] -- n2) (n1 [n1* .1.] -- n2)
.. code:: python .. code:: ipython2
sum_ = (((N[1], (Ns[1], S[1])), S[0]), (N[0], S[0])) sum_ = (((N[1], (Ns[1], S[1])), S[0]), (N[0], S[0]))
print doc_from_stack_effect(*cons), print doc_from_stack_effect(*cons),
@ -2571,7 +2571,7 @@ This function has to be modified to yield multiple results.
(a1 [.1.] -- [a1 .1.]) ([n1 n1* .1.] -- n0) (n1 [n1* .1.] -- n2) (a1 [.1.] -- [a1 .1.]) ([n1 n1* .1.] -- n0) (n1 [n1* .1.] -- n2)
.. code:: python .. code:: ipython2
a = (A[4], (As[1], (A[3], S[1]))) a = (A[4], (As[1], (A[3], S[1])))
a a
@ -2585,7 +2585,7 @@ This function has to be modified to yield multiple results.
.. code:: python .. code:: ipython2
b = (A[1], (A[2], S[2])) b = (A[1], (A[2], S[2]))
b b
@ -2599,7 +2599,7 @@ This function has to be modified to yield multiple results.
.. code:: python .. code:: ipython2
for result in unify(b, a): for result in unify(b, a):
print result print result
@ -2611,7 +2611,7 @@ This function has to be modified to yield multiple results.
{a1: a4, s2: (a1*, (a3, s1)), a2: a10003} {a1: a4, s2: (a1*, (a3, s1)), a2: a10003}
.. code:: python .. code:: ipython2
for result in unify(a, b): for result in unify(a, b):
print result print result
@ -2681,7 +2681,7 @@ We need a type variable for Joy functions that can go in our expressions
and be used by the hybrid inferencer/interpreter. They have to store a and be used by the hybrid inferencer/interpreter. They have to store a
name and a list of stack effects. name and a list of stack effects.
.. code:: python .. code:: ipython2
class FunctionJoyType(AnyJoyType): class FunctionJoyType(AnyJoyType):
@ -2703,14 +2703,14 @@ Specialized for Simple Functions and Combinators
For non-combinator functions the stack effects list contains stack For non-combinator functions the stack effects list contains stack
effect comments (represented by pairs of cons-lists as described above.) effect comments (represented by pairs of cons-lists as described above.)
.. code:: python .. code:: ipython2
class SymbolJoyType(FunctionJoyType): class SymbolJoyType(FunctionJoyType):
prefix = 'F' prefix = 'F'
For combinators the list contains Python functions. For combinators the list contains Python functions.
.. code:: python .. code:: ipython2
class CombinatorJoyType(FunctionJoyType): class CombinatorJoyType(FunctionJoyType):
@ -2731,7 +2731,7 @@ For combinators the list contains Python functions.
For simple combinators that have only one effect (like ``dip``) you only For simple combinators that have only one effect (like ``dip``) you only
need one function and it can be the combinator itself. need one function and it can be the combinator itself.
.. code:: python .. code:: ipython2
import joy.library import joy.library
@ -2741,7 +2741,7 @@ For combinators that can have more than one effect (like ``branch``) you
have to write functions that each implement the action of one of the have to write functions that each implement the action of one of the
effects. effects.
.. code:: python .. code:: ipython2
def branch_true(stack, expression, dictionary): def branch_true(stack, expression, dictionary):
(then, (else_, (flag, stack))) = stack (then, (else_, (flag, stack))) = stack
@ -2771,7 +2771,7 @@ updated along with the stack effects after doing unification or we risk
losing useful information. This was a straightforward, if awkward, losing useful information. This was a straightforward, if awkward,
modification to the call structure of ``meta_compose()`` et. al. modification to the call structure of ``meta_compose()`` et. al.
.. code:: python .. code:: ipython2
ID = S[0], S[0] # Identity function. ID = S[0], S[0] # Identity function.
@ -2833,7 +2833,7 @@ cruft to convert the definitions in ``DEFS`` to the new
``SymbolJoyType`` objects, and some combinators. Here is an example of ``SymbolJoyType`` objects, and some combinators. Here is an example of
output from the current code : output from the current code :
.. code:: python .. code:: ipython2
1/0 # (Don't try to run this cell! It's not going to work. This is "read only" code heh..) 1/0 # (Don't try to run this cell! It's not going to work. This is "read only" code heh..)
@ -2956,7 +2956,7 @@ module. But if you’re interested in all that you should just use Prolog!
Anyhow, type *checking* is a few easy steps away. Anyhow, type *checking* is a few easy steps away.
.. code:: python .. code:: ipython2
def _ge(self, other): def _ge(self, other):
return (issubclass(other.__class__, self.__class__) return (issubclass(other.__class__, self.__class__)

36
docs/sphinx_docs/_build/html/_sources/notebooks/Zipper.rst.txt
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@ -10,7 +10,7 @@ Huet <https://www.st.cs.uni-saarland.de/edu/seminare/2005/advanced-fp/docs/huet-
Given a datastructure on the stack we can navigate through it, modify Given a datastructure on the stack we can navigate through it, modify
it, and rebuild it using the “zipper” technique. it, and rebuild it using the “zipper” technique.
.. code:: python .. code:: ipython2
from notebook_preamble import J, V, define from notebook_preamble import J, V, define
@ -23,7 +23,7 @@ strings, Symbols (strings that are names of functions) and sequences
`trees <https://en.wikipedia.org/wiki/Tree_%28data_structure%29>`__ out `trees <https://en.wikipedia.org/wiki/Tree_%28data_structure%29>`__ out
of sequences. of sequences.
.. code:: python .. code:: ipython2
J('[1 [2 [3 4 25 6] 7] 8]') J('[1 [2 [3 4 25 6] 7] 8]')
@ -54,14 +54,14 @@ show the trace so you can see how it works. If we were going to use
these a lot it would make sense to write Python versions for efficiency, these a lot it would make sense to write Python versions for efficiency,
but see below. but see below.
.. code:: python .. code:: ipython2
define('z-down == [] swap uncons swap') define('z-down == [] swap uncons swap')
define('z-up == swons swap shunt') define('z-up == swons swap shunt')
define('z-right == [swons] cons dip uncons swap') define('z-right == [swons] cons dip uncons swap')
define('z-left == swons [uncons swap] dip swap') define('z-left == swons [uncons swap] dip swap')
.. code:: python .. code:: ipython2
V('[1 [2 [3 4 25 6] 7] 8] z-down') V('[1 [2 [3 4 25 6] 7] 8] z-down')
@ -77,7 +77,7 @@ but see below.
[] [[2 [3 4 25 6] 7] 8] 1 . [] [[2 [3 4 25 6] 7] 8] 1 .
.. code:: python .. code:: ipython2
V('[] [[2 [3 4 25 6] 7] 8] 1 z-right') V('[] [[2 [3 4 25 6] 7] 8] 1 z-right')
@ -101,7 +101,7 @@ but see below.
[1] [8] [2 [3 4 25 6] 7] . [1] [8] [2 [3 4 25 6] 7] .
.. code:: python .. code:: ipython2
J('[1] [8] [2 [3 4 25 6] 7] z-down') J('[1] [8] [2 [3 4 25 6] 7] z-down')
@ -111,7 +111,7 @@ but see below.
[1] [8] [] [[3 4 25 6] 7] 2 [1] [8] [] [[3 4 25 6] 7] 2
.. code:: python .. code:: ipython2
J('[1] [8] [] [[3 4 25 6] 7] 2 z-right') J('[1] [8] [] [[3 4 25 6] 7] 2 z-right')
@ -121,7 +121,7 @@ but see below.
[1] [8] [2] [7] [3 4 25 6] [1] [8] [2] [7] [3 4 25 6]
.. code:: python .. code:: ipython2
J('[1] [8] [2] [7] [3 4 25 6] z-down') J('[1] [8] [2] [7] [3 4 25 6] z-down')
@ -131,7 +131,7 @@ but see below.
[1] [8] [2] [7] [] [4 25 6] 3 [1] [8] [2] [7] [] [4 25 6] 3
.. code:: python .. code:: ipython2
J('[1] [8] [2] [7] [] [4 25 6] 3 z-right') J('[1] [8] [2] [7] [] [4 25 6] 3 z-right')
@ -141,7 +141,7 @@ but see below.
[1] [8] [2] [7] [3] [25 6] 4 [1] [8] [2] [7] [3] [25 6] 4
.. code:: python .. code:: ipython2
J('[1] [8] [2] [7] [3] [25 6] 4 z-right') J('[1] [8] [2] [7] [3] [25 6] 4 z-right')
@ -151,7 +151,7 @@ but see below.
[1] [8] [2] [7] [4 3] [6] 25 [1] [8] [2] [7] [4 3] [6] 25
.. code:: python .. code:: ipython2
J('[1] [8] [2] [7] [4 3] [6] 25 sqr') J('[1] [8] [2] [7] [4 3] [6] 25 sqr')
@ -161,7 +161,7 @@ but see below.
[1] [8] [2] [7] [4 3] [6] 625 [1] [8] [2] [7] [4 3] [6] 625
.. code:: python .. code:: ipython2
V('[1] [8] [2] [7] [4 3] [6] 625 z-up') V('[1] [8] [2] [7] [4 3] [6] 625 z-up')
@ -184,7 +184,7 @@ but see below.
[1] [8] [2] [7] [3 4 625 6] . [1] [8] [2] [7] [3 4 625 6] .
.. code:: python .. code:: ipython2
J('[1] [8] [2] [7] [3 4 625 6] z-up') J('[1] [8] [2] [7] [3 4 625 6] z-up')
@ -194,7 +194,7 @@ but see below.
[1] [8] [2 [3 4 625 6] 7] [1] [8] [2 [3 4 625 6] 7]
.. code:: python .. code:: ipython2
J('[1] [8] [2 [3 4 625 6] 7] z-up') J('[1] [8] [2 [3 4 625 6] 7] z-up')
@ -210,7 +210,7 @@ but see below.
In Joy we have the ``dip`` and ``infra`` combinators which can “target” In Joy we have the ``dip`` and ``infra`` combinators which can “target”
or “address” any particular item in a Joy tree structure. or “address” any particular item in a Joy tree structure.
.. code:: python .. code:: ipython2
V('[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra') V('[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra')
@ -270,13 +270,13 @@ been embedded in a nested series of quoted programs, e.g.:
The ``Z`` function isn’t hard to make. The ``Z`` function isn’t hard to make.
.. code:: python .. code:: ipython2
define('Z == [[] cons cons] step i') define('Z == [[] cons cons] step i')
Here it is in action in a simplified scenario. Here it is in action in a simplified scenario.
.. code:: python .. code:: ipython2
V('1 [2 3 4] Z') V('1 [2 3 4] Z')
@ -314,7 +314,7 @@ Here it is in action in a simplified scenario.
And here it is doing the main thing. And here it is doing the main thing.
.. code:: python .. code:: ipython2
J('[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z') J('[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z')

1
docs/sphinx_docs/_build/html/_sources/notebooks/index.rst.txt
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@ -16,6 +16,7 @@ These essays are adapted from Jupyter notebooks. I hope to have those hosted so
Treestep Treestep
Generator_Programs Generator_Programs
Newton-Raphson Newton-Raphson
Square_Spiral
Zipper Zipper
Types Types
TypeChecking TypeChecking

24
docs/sphinx_docs/_build/html/index.html
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@ -54,6 +54,29 @@ additional joy interpreter (the binary in the archive from La Trobe seems
to run just fine on my modern Linux machine!) But I also hope that you to run just fine on my modern Linux machine!) But I also hope that you
can read and understand the Python code and play with the implementation can read and understand the Python code and play with the implementation
itself.</p> itself.</p>
<section id="example-code">
<h2>Example Code<a class="headerlink" href="#example-code" title="Permalink to this headline"></a></h2>
<p>Here is an example of Joy code:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[[[abs]ii &lt;=][[&lt;&gt;][pop !-]||]&amp;&amp;][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
</pre></div>
</div>
<p>It might seem unreadable but with a little familiarity it becomes just as
legible as any other notation. Some layout helps:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[ [[abs] ii &lt;=]
[
[&lt;&gt;] [pop !-] ||
] &amp;&amp;
]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
</pre></div>
</div>
<p>This function accepts two integers on the stack and increments or
decrements one of them such that the new pair of numbers is the next
coordinate pair in a square spiral (like the kind used to construct an
Ulam Spiral). For more information see <a class="reference internal" href="notebooks/Square_Spiral.html"><span class="doc">Square Spiral Example Joy Code</span></a></p>
</section>
<section id="quick-start"> <section id="quick-start">
<h2>Quick Start<a class="headerlink" href="#quick-start" title="Permalink to this headline"></a></h2> <h2>Quick Start<a class="headerlink" href="#quick-start" title="Permalink to this headline"></a></h2>
<p>Install from <a class="reference external" href="https://pypi.org/project/Thun/">PyPI</a> in the usual way:</p> <p>Install from <a class="reference external" href="https://pypi.org/project/Thun/">PyPI</a> in the usual way:</p>
@ -145,6 +168,7 @@ interesting aspects. It’s quite a treasure trove.</p>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li> <li class="toctree-l2"><a class="reference internal" href="notebooks/Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li> <li class="toctree-l2"><a class="reference internal" href="notebooks/Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Newton-Raphson.html">Newton’s method</a></li> <li class="toctree-l2"><a class="reference internal" href="notebooks/Newton-Raphson.html">Newton’s method</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Square_Spiral.html">Square Spiral Example Joy Code</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Zipper.html">Traversing Datastructures with Zippers</a></li> <li class="toctree-l2"><a class="reference internal" href="notebooks/Zipper.html">Traversing Datastructures with Zippers</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Types.html">The Blissful Elegance of Typing Joy</a></li> <li class="toctree-l2"><a class="reference internal" href="notebooks/Types.html">The Blissful Elegance of Typing Joy</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/TypeChecking.html">Type Checking</a></li> <li class="toctree-l2"><a class="reference internal" href="notebooks/TypeChecking.html">Type Checking</a></li>

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@ -96,14 +96,14 @@ R∘λ = λ∘R = R
</section> </section>
<section id="implementation"> <section id="implementation">
<h2>Implementation<a class="headerlink" href="#implementation" title="Permalink to this headline"></a></h2> <h2>Implementation<a class="headerlink" href="#implementation" title="Permalink to this headline"></a></h2>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span> <span class="k">as</span> <span class="n">curry</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span> <span class="k">as</span> <span class="n">curry</span>
<span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span> <span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span>
</pre></div> </pre></div>
</div> </div>
<section id="and"> <section id="and">
<h3><code class="docutils literal notranslate"><span class="pre">ϕ</span></code> and <code class="docutils literal notranslate"><span class="pre">λ</span></code><a class="headerlink" href="#and" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">ϕ</span></code> and <code class="docutils literal notranslate"><span class="pre">λ</span></code><a class="headerlink" href="#and" title="Permalink to this headline"></a></h3>
<p>The empty set and the set of just the empty string.</p> <p>The empty set and the set of just the empty string.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">phi</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">()</span> <span class="c1"># ϕ</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">phi</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">()</span> <span class="c1"># ϕ</span>
<span class="n">y</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;&#39;</span><span class="p">})</span> <span class="c1"># λ</span> <span class="n">y</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;&#39;</span><span class="p">})</span> <span class="c1"># λ</span>
</pre></div> </pre></div>
</div> </div>
@ -115,7 +115,7 @@ illustrate the algorithm and because you can represent any other
alphabet with two symbols (if you had to.)</p> alphabet with two symbols (if you had to.)</p>
<p>I chose the names <code class="docutils literal notranslate"><span class="pre">O</span></code> and <code class="docutils literal notranslate"><span class="pre">l</span></code> (uppercase “o” and lowercase “L”) to <p>I chose the names <code class="docutils literal notranslate"><span class="pre">O</span></code> and <code class="docutils literal notranslate"><span class="pre">l</span></code> (uppercase “o” and lowercase “L”) to
look like <code class="docutils literal notranslate"><span class="pre">0</span></code> and <code class="docutils literal notranslate"><span class="pre">1</span></code> (zero and one) respectively.</p> look like <code class="docutils literal notranslate"><span class="pre">0</span></code> and <code class="docutils literal notranslate"><span class="pre">1</span></code> (zero and one) respectively.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">syms</span> <span class="o">=</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;0&#39;</span><span class="p">}),</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;1&#39;</span><span class="p">})</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">syms</span> <span class="o">=</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;0&#39;</span><span class="p">}),</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;1&#39;</span><span class="p">})</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -133,7 +133,7 @@ expression</em> is one of:</p>
</pre></div> </pre></div>
</div> </div>
<p>Where <code class="docutils literal notranslate"><span class="pre">R</span></code> and <code class="docutils literal notranslate"><span class="pre">S</span></code> stand for <em>regular expressions</em>.</p> <p>Where <code class="docutils literal notranslate"><span class="pre">R</span></code> and <code class="docutils literal notranslate"><span class="pre">S</span></code> stand for <em>regular expressions</em>.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">,</span> <span class="n">KSTAR</span><span class="p">,</span> <span class="n">NOT</span><span class="p">,</span> <span class="n">OR</span> <span class="o">=</span> <span class="s1">&#39;and cons * not or&#39;</span><span class="o">.</span><span class="n">split</span><span class="p">()</span> <span class="c1"># Tags are just strings.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">,</span> <span class="n">KSTAR</span><span class="p">,</span> <span class="n">NOT</span><span class="p">,</span> <span class="n">OR</span> <span class="o">=</span> <span class="s1">&#39;and cons * not or&#39;</span><span class="o">.</span><span class="n">split</span><span class="p">()</span> <span class="c1"># Tags are just strings.</span>
</pre></div> </pre></div>
</div> </div>
<p>Because they are formed of <code class="docutils literal notranslate"><span class="pre">frozenset</span></code>, <code class="docutils literal notranslate"><span class="pre">tuple</span></code> and <code class="docutils literal notranslate"><span class="pre">str</span></code> objects <p>Because they are formed of <code class="docutils literal notranslate"><span class="pre">frozenset</span></code>, <code class="docutils literal notranslate"><span class="pre">tuple</span></code> and <code class="docutils literal notranslate"><span class="pre">str</span></code> objects
@ -141,7 +141,7 @@ only, these datastructures are immutable.</p>
</section> </section>
<section id="string-representation-of-re-datastructures"> <section id="string-representation-of-re-datastructures">
<h3>String Representation of RE Datastructures<a class="headerlink" href="#string-representation-of-re-datastructures" title="Permalink to this headline"></a></h3> <h3>String Representation of RE Datastructures<a class="headerlink" href="#string-representation-of-re-datastructures" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
<span class="sd">&#39;&#39;&#39;</span> <span class="sd">&#39;&#39;&#39;</span>
<span class="sd"> Return a nice string repr for a regular expression datastructure.</span> <span class="sd"> Return a nice string repr for a regular expression datastructure.</span>
<span class="sd"> &#39;&#39;&#39;</span> <span class="sd"> &#39;&#39;&#39;</span>
@ -180,10 +180,10 @@ only, these datastructures are immutable.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="o">|</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="o">|</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">I</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">.</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">.</span>
@ -198,13 +198,13 @@ only, these datastructures are immutable.</p>
</pre></div> </pre></div>
</div> </div>
<p>Note that it contains one of everything.</p> <p>Note that it contains one of everything.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">I</span><span class="p">))))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">I</span><span class="p">))))</span>
<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span> <span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
<span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span> <span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
<span class="n">it</span> <span class="o">=</span> <span class="p">(</span><span class="n">AND</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">)))</span> <span class="n">it</span> <span class="o">=</span> <span class="p">(</span><span class="n">AND</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">)))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
@ -214,7 +214,7 @@ only, these datastructures are immutable.</p>
<section id="nully"> <section id="nully">
<h3><code class="docutils literal notranslate"><span class="pre">nully()</span></code><a class="headerlink" href="#nully" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">nully()</span></code><a class="headerlink" href="#nully" title="Permalink to this headline"></a></h3>
<p>Let’s get that auxiliary predicate function <code class="docutils literal notranslate"><span class="pre">δ</span></code> out of the way.</p> <p>Let’s get that auxiliary predicate function <code class="docutils literal notranslate"><span class="pre">δ</span></code> out of the way.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">nully</span><span class="p">(</span><span class="n">R</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">nully</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
<span class="sd">&#39;&#39;&#39;</span> <span class="sd">&#39;&#39;&#39;</span>
<span class="sd"> δ - Return λ if λ ⊆ R otherwise ϕ.</span> <span class="sd"> δ - Return λ if λ ⊆ R otherwise ϕ.</span>
<span class="sd"> &#39;&#39;&#39;</span> <span class="sd"> &#39;&#39;&#39;</span>
@ -252,7 +252,7 @@ only, these datastructures are immutable.</p>
<p>This is the straightforward version with no “compaction”. It works fine, <p>This is the straightforward version with no “compaction”. It works fine,
but does waaaay too much work because the expressions grow each but does waaaay too much work because the expressions grow each
derivation.</p> derivation.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span> <span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
@ -296,7 +296,7 @@ derivation.</p>
</section> </section>
<section id="compaction-rules"> <section id="compaction-rules">
<h3>Compaction Rules<a class="headerlink" href="#compaction-rules" title="Permalink to this headline"></a></h3> <h3>Compaction Rules<a class="headerlink" href="#compaction-rules" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_compaction_rule</span><span class="p">(</span><span class="n">relation</span><span class="p">,</span> <span class="n">one</span><span class="p">,</span> <span class="n">zero</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_compaction_rule</span><span class="p">(</span><span class="n">relation</span><span class="p">,</span> <span class="n">one</span><span class="p">,</span> <span class="n">zero</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span> <span class="k">return</span> <span class="p">(</span>
<span class="n">b</span> <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span> <span class="c1"># R*1 = 1*R = R</span> <span class="n">b</span> <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span> <span class="c1"># R*1 = 1*R = R</span>
<span class="n">a</span> <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span> <span class="n">a</span> <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span>
@ -306,7 +306,7 @@ derivation.</p>
</pre></div> </pre></div>
</div> </div>
<p>An elegant symmetry.</p> <p>An elegant symmetry.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># R ∧ I = I ∧ R = R</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># R ∧ I = I ∧ R = R</span>
<span class="c1"># R ∧ ϕ = ϕ ∧ R = ϕ</span> <span class="c1"># R ∧ ϕ = ϕ ∧ R = ϕ</span>
<span class="n">_and</span> <span class="o">=</span> <span class="n">curry</span><span class="p">(</span><span class="n">_compaction_rule</span><span class="p">,</span> <span class="n">AND</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span> <span class="n">_and</span> <span class="o">=</span> <span class="n">curry</span><span class="p">(</span><span class="n">_compaction_rule</span><span class="p">,</span> <span class="n">AND</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
@ -325,7 +325,7 @@ derivation.</p>
<p>We can save re-processing by remembering results we have already <p>We can save re-processing by remembering results we have already
computed. RE datastructures are immutable and the <code class="docutils literal notranslate"><span class="pre">derv()</span></code> functions computed. RE datastructures are immutable and the <code class="docutils literal notranslate"><span class="pre">derv()</span></code> functions
are <em>pure</em> so this is fine.</p> are <em>pure</em> so this is fine.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Memo</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Memo</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">f</span> <span class="o">=</span> <span class="n">f</span> <span class="bp">self</span><span class="o">.</span><span class="n">f</span> <span class="o">=</span> <span class="n">f</span>
@ -347,7 +347,7 @@ are <em>pure</em> so this is fine.</p>
<h3>With “Compaction”<a class="headerlink" href="#with-compaction" title="Permalink to this headline"></a></h3> <h3>With “Compaction”<a class="headerlink" href="#with-compaction" title="Permalink to this headline"></a></h3>
<p>This version uses the rules above to perform compaction. It keeps the <p>This version uses the rules above to perform compaction. It keeps the
expressions from growing too large.</p> expressions from growing too large.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D_compaction</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D_compaction</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
<span class="nd">@Memo</span> <span class="nd">@Memo</span>
<span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span> <span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
@ -395,7 +395,7 @@ expressions from growing too large.</p>
<section id="lets-try-it-out"> <section id="lets-try-it-out">
<h2>Let’s try it out…<a class="headerlink" href="#lets-try-it-out" title="Permalink to this headline"></a></h2> <h2>Let’s try it out…<a class="headerlink" href="#lets-try-it-out" title="Permalink to this headline"></a></h2>
<p>(FIXME: redo.)</p> <p>(FIXME: redo.)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">o</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">o</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span>
<span class="n">REs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span> <span class="n">REs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">5</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">names</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">product</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">N</span> <span class="o">*</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)])))</span> <span class="n">names</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">product</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">N</span> <span class="o">*</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)])))</span>
@ -500,8 +500,8 @@ machine transition table.</p>
</div> </div>
<p>Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”</p> <p>Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”</p>
<figure class="align-default" id="id2"> <figure class="align-default" id="id2">
<img alt="State Machine Graph" src="../_images/omg.svg" /><figcaption> <img alt="omg.svg" src="notebooks/attachment:omg.svg" /><figcaption>
<p><span class="caption-text">State Machine Graph</span><a class="headerlink" href="#id2" title="Permalink to this image"></a></p> <p><span class="caption-text">omg.svg</span><a class="headerlink" href="#id2" title="Permalink to this image"></a></p>
</figcaption> </figcaption>
</figure> </figure>
<p>Start at <code class="docutils literal notranslate"><span class="pre">a</span></code> and follow the transition arrows according to their <p>Start at <code class="docutils literal notranslate"><span class="pre">a</span></code> and follow the transition arrows according to their
@ -555,18 +555,18 @@ a --1--&gt; ∂1(a)
<p>You can see the one-way nature of the <code class="docutils literal notranslate"><span class="pre">g</span></code> state and the <code class="docutils literal notranslate"><span class="pre">hij</span></code> “trap” <p>You can see the one-way nature of the <code class="docutils literal notranslate"><span class="pre">g</span></code> state and the <code class="docutils literal notranslate"><span class="pre">hij</span></code> “trap”
in the way that the <code class="docutils literal notranslate"><span class="pre">.111.</span></code> on the left-hand side of the <code class="docutils literal notranslate"><span class="pre">&amp;</span></code> in the way that the <code class="docutils literal notranslate"><span class="pre">.111.</span></code> on the left-hand side of the <code class="docutils literal notranslate"><span class="pre">&amp;</span></code>
disappears once it has been matched.</p> disappears once it has been matched.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
<span class="kn">from</span> <span class="nn">pprint</span> <span class="kn">import</span> <span class="n">pprint</span> <span class="kn">from</span> <span class="nn">pprint</span> <span class="kn">import</span> <span class="n">pprint</span>
<span class="kn">from</span> <span class="nn">string</span> <span class="kn">import</span> <span class="n">ascii_lowercase</span> <span class="kn">from</span> <span class="nn">string</span> <span class="kn">import</span> <span class="n">ascii_lowercase</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">d0</span><span class="p">,</span> <span class="n">d1</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">d0</span><span class="p">,</span> <span class="n">d1</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
<section id="explore"> <section id="explore">
<h3><code class="docutils literal notranslate"><span class="pre">explore()</span></code><a class="headerlink" href="#explore" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">explore()</span></code><a class="headerlink" href="#explore" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">explore</span><span class="p">(</span><span class="n">re</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">explore</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
<span class="c1"># Don&#39;t have more than 26 states...</span> <span class="c1"># Don&#39;t have more than 26 states...</span>
<span class="n">names</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">ascii_lowercase</span><span class="p">)</span><span class="o">.</span><span class="n">next</span><span class="p">)</span> <span class="n">names</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">ascii_lowercase</span><span class="p">)</span><span class="o">.</span><span class="n">next</span><span class="p">)</span>
@ -592,7 +592,7 @@ disappears once it has been matched.</p>
<span class="k">return</span> <span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="k">return</span> <span class="n">table</span><span class="p">,</span> <span class="n">accepting</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="n">explore</span><span class="p">(</span><span class="n">it</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="n">explore</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
<span class="n">table</span> <span class="n">table</span>
</pre></div> </pre></div>
</div> </div>
@ -618,7 +618,7 @@ disappears once it has been matched.</p>
<span class="p">(</span><span class="s1">&#39;j&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">&#39;h&#39;</span><span class="p">}</span> <span class="p">(</span><span class="s1">&#39;j&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">&#39;h&#39;</span><span class="p">}</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">accepting</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">accepting</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="s1">&#39;h&#39;</span><span class="p">,</span> <span class="s1">&#39;i&#39;</span><span class="p">}</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="s1">&#39;h&#39;</span><span class="p">,</span> <span class="s1">&#39;i&#39;</span><span class="p">}</span>
@ -629,7 +629,7 @@ disappears once it has been matched.</p>
<h3>Generate Diagram<a class="headerlink" href="#generate-diagram" title="Permalink to this headline"></a></h3> <h3>Generate Diagram<a class="headerlink" href="#generate-diagram" title="Permalink to this headline"></a></h3>
<p>Once we have the FSM table and the set of accepting states we can <p>Once we have the FSM table and the set of accepting states we can
generate the diagram above.</p> generate the diagram above.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">_template</span> <span class="o">=</span> <span class="s1">&#39;&#39;&#39;</span><span class="se">\</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">_template</span> <span class="o">=</span> <span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
<span class="s1">digraph finite_state_machine {</span> <span class="s1">digraph finite_state_machine {</span>
<span class="s1"> rankdir=LR;</span> <span class="s1"> rankdir=LR;</span>
<span class="s1"> size=&quot;8,5&quot;</span> <span class="s1"> size=&quot;8,5&quot;</span>
@ -653,7 +653,7 @@ generate the diagram above.</p>
<span class="p">)</span> <span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">make_graph</span><span class="p">(</span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">make_graph</span><span class="p">(</span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">digraph</span> <span class="n">finite_state_machine</span> <span class="p">{</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">digraph</span> <span class="n">finite_state_machine</span> <span class="p">{</span>
@ -699,7 +699,7 @@ hard-code the information in the table into a little patch of branches.</p>
<h4>Trampoline Function<a class="headerlink" href="#trampoline-function" title="Permalink to this headline"></a></h4> <h4>Trampoline Function<a class="headerlink" href="#trampoline-function" title="Permalink to this headline"></a></h4>
<p>Python has no GOTO statement but we can fake it with a “trampoline” <p>Python has no GOTO statement but we can fake it with a “trampoline”
function.</p> function.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">jump_from</span><span class="p">,</span> <span class="n">accepting</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">jump_from</span><span class="p">,</span> <span class="n">accepting</span><span class="p">):</span>
<span class="n">I</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">input_</span><span class="p">)</span> <span class="n">I</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">input_</span><span class="p">)</span>
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<span class="k">try</span><span class="p">:</span> <span class="k">try</span><span class="p">:</span>
@ -714,7 +714,7 @@ function.</p>
<h4>Stream Functions<a class="headerlink" href="#stream-functions" title="Permalink to this headline"></a></h4> <h4>Stream Functions<a class="headerlink" href="#stream-functions" title="Permalink to this headline"></a></h4>
<p>Little helpers to process the iterator of our data (a “stream” of “1” <p>Little helpers to process the iterator of our data (a “stream” of “1”
and “0” characters, not bits.)</p> and “0” characters, not bits.)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">getch</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="nb">int</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">I</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">getch</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="nb">int</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">I</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">_1</span><span class="p">(</span><span class="n">I</span><span class="p">):</span> <span class="k">def</span> <span class="nf">_1</span><span class="p">(</span><span class="n">I</span><span class="p">):</span>
@ -735,7 +735,7 @@ and “0” characters, not bits.)</p>
code. (You have to imagine that these are GOTO statements in C or code. (You have to imagine that these are GOTO statements in C or
branches in assembly and that the state names are branch destination branches in assembly and that the state names are branch destination
labels.)</p> labels.)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">c</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">c</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
<span class="n">b</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_0</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">d</span> <span class="n">b</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_0</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">d</span>
<span class="n">c</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">e</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span> <span class="n">c</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">e</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
<span class="n">d</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">f</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span> <span class="n">d</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">f</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
@ -750,11 +750,11 @@ labels.)</p>
<p>Note that the implementations of <code class="docutils literal notranslate"><span class="pre">h</span></code> and <code class="docutils literal notranslate"><span class="pre">g</span></code> are identical ergo <p>Note that the implementations of <code class="docutils literal notranslate"><span class="pre">h</span></code> and <code class="docutils literal notranslate"><span class="pre">g</span></code> are identical ergo
<code class="docutils literal notranslate"><span class="pre">h</span> <span class="pre">=</span> <span class="pre">g</span></code> and we could eliminate one in the code but <code class="docutils literal notranslate"><span class="pre">h</span></code> is an <code class="docutils literal notranslate"><span class="pre">h</span> <span class="pre">=</span> <span class="pre">g</span></code> and we could eliminate one in the code but <code class="docutils literal notranslate"><span class="pre">h</span></code> is an
accepting state and <code class="docutils literal notranslate"><span class="pre">g</span></code> isn’t.</p> accepting state and <code class="docutils literal notranslate"><span class="pre">g</span></code> isn’t.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">acceptable</span><span class="p">(</span><span class="n">input_</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">acceptable</span><span class="p">(</span><span class="n">input_</span><span class="p">):</span>
<span class="k">return</span> <span class="n">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">{</span><span class="n">h</span><span class="p">,</span> <span class="n">i</span><span class="p">})</span> <span class="k">return</span> <span class="n">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">{</span><span class="n">h</span><span class="p">,</span> <span class="n">i</span><span class="p">})</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="mi">5</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="mi">5</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">bin</span><span class="p">(</span><span class="n">n</span><span class="p">)[</span><span class="mi">2</span><span class="p">:]</span> <span class="n">s</span> <span class="o">=</span> <span class="nb">bin</span><span class="p">(</span><span class="n">n</span><span class="p">)[</span><span class="mi">2</span><span class="p">:]</span>
<span class="nb">print</span> <span class="s1">&#39;</span><span class="si">%05s</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">s</span><span class="p">,</span> <span class="n">acceptable</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="nb">print</span> <span class="s1">&#39;</span><span class="si">%05s</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">s</span><span class="p">,</span> <span class="n">acceptable</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
</pre></div> </pre></div>
@ -878,6 +878,7 @@ derivative-with-respect-to-N of some other state/RE:</p>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li> <li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li> <li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li> <li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html">Square Spiral Example Joy Code</a></li>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li> <li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li> <li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li> <li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li>

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@ -40,7 +40,7 @@
to write a function that can compute the square root of a number.</p> to write a function that can compute the square root of a number.</p>
<p>Cf. <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John <p>Cf. <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
Hughes</a></p> Hughes</a></p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div> </pre></div>
</div> </div>
<section id="a-generator-for-approximations"> <section id="a-generator-for-approximations">
@ -92,10 +92,10 @@ function we’re writing. If we let 1 be the initial approximation:</p>
<span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">make_generator</span> <span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">make_generator</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator&#39;</span><span class="p">)</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra&#39;</span><span class="p">)</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
@ -103,7 +103,7 @@ function we’re writing. If we let 1 be the initial approximation:</p>
</div> </div>
<p>Let’s drive the generator a few time (with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator) and <p>Let’s drive the generator a few time (with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator) and
square the approximation to see how well it works…</p> square the approximation to see how well it works…</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra 6 [x popd] times first sqr&#39;</span><span class="p">)</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra 6 [x popd] times first sqr&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">23.0000000001585</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">23.0000000001585</span>
@ -145,7 +145,7 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span><span class="o">&lt;=</span><span class="n">ε</span><span class="p">)</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span><span class="o">&lt;=</span><span class="n">ε</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_P [first - abs] dip &lt;=&#39;</span><span class="p">)</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_P [first - abs] dip &lt;=&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -157,7 +157,7 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="n">b</span> <span class="n">b</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_B roll&lt; popop first&#39;</span><span class="p">)</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_B roll&lt; popop first&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -182,7 +182,7 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span> <span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_R [popd x] dip&#39;</span><span class="p">)</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_R [popd x] dip&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -194,31 +194,31 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span> <span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec&#39;</span><span class="p">)</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;sqrt gsra within&#39;</span><span class="p">)</span> <span class="n">define</span><span class="p">(</span><span class="s1">&#39;sqrt gsra within&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>Try it out…</p> <p>Try it out…</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;36 sqrt&#39;</span><span class="p">)</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;36 sqrt&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.0</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.0</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 sqrt&#39;</span><span class="p">)</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 sqrt&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
</pre></div> </pre></div>
</div> </div>
<p>Check it.</p> <p>Check it.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">22.999999999999996</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">22.999999999999996</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span> <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
<span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
</pre></div> </pre></div>

98
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@ -63,7 +63,7 @@ the Sufficiently Smart Compiler can be modified to use an optimized
implementation under the hood. (Where does the “type” come from? It has implementation under the hood. (Where does the “type” come from? It has
a contingent existence predicated on the disciplined use of these a contingent existence predicated on the disciplined use of these
functions on otherwise undistinguished Joy datastructures.)</p> functions on otherwise undistinguished Joy datastructures.)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
</pre></div> </pre></div>
</div> </div>
<section id="adding-nodes-to-the-tree"> <section id="adding-nodes-to-the-tree">
@ -100,10 +100,10 @@ functions on otherwise undistinguished Joy datastructures.)</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="n">new</span> <span class="o">==</span> <span class="n">swap</span> <span class="p">[[]</span> <span class="p">[]]</span> <span class="n">cons</span> <span class="n">cons</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="n">new</span> <span class="o">==</span> <span class="n">swap</span> <span class="p">[[]</span> <span class="p">[]]</span> <span class="n">cons</span> <span class="n">cons</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-new == swap [[] []] cons cons&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-new == swap [[] []] cons cons&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&quot;v&quot; &quot;k&quot; Tree-new&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&quot;v&quot; &quot;k&quot; Tree-new&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;k&#39;</span> <span class="s1">&#39;v&#39;</span> <span class="p">[]</span> <span class="p">[]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;k&#39;</span> <span class="s1">&#39;v&#39;</span> <span class="p">[]</span> <span class="p">[]]</span>
@ -159,10 +159,10 @@ comparison operator:</p>
<span class="n">P</span> <span class="o">==</span> <span class="n">pop</span> <span class="n">roll</span><span class="o">&gt;</span> <span class="n">pop</span> <span class="n">first</span> <span class="n">P</span> <span class="o">==</span> <span class="n">pop</span> <span class="n">roll</span><span class="o">&gt;</span> <span class="n">pop</span> <span class="n">first</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;P == pop roll&gt; pop first&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;P == pop roll&gt; pop first&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_key&quot; 23 [] []] 17 &quot;new_key&quot; [&quot;...&quot;] P&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_key&quot; 23 [] []] 17 &quot;new_key&quot; [&quot;...&quot;] P&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;old_key&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;old_key&#39;</span>
@ -217,10 +217,10 @@ stack:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">T</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dipdd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">T</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dipdd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;T == cons cons [dipdd] cons infra&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;T == cons cons [dipdd] cons infra&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] T&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] T&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;old_k&#39;</span> <span class="s1">&#39;old_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;Tree-add&#39;</span> <span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;old_k&#39;</span> <span class="s1">&#39;old_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;Tree-add&#39;</span> <span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span>
@ -234,7 +234,7 @@ stack:</p>
<span class="p">[</span><span class="n">key_n</span> <span class="n">value_n</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">value</span> <span class="n">key</span> <span class="p">[</span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span><span class="p">]</span> <span class="p">[</span><span class="n">P</span> <span class="o">&lt;</span><span class="p">]</span> <span class="p">[</span><span class="n">Te</span><span class="p">]</span> <span class="p">[</span><span class="n">Ee</span><span class="p">]</span> <span class="n">ifte</span> <span class="p">[</span><span class="n">key_n</span> <span class="n">value_n</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">value</span> <span class="n">key</span> <span class="p">[</span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span><span class="p">]</span> <span class="p">[</span><span class="n">P</span> <span class="o">&lt;</span><span class="p">]</span> <span class="p">[</span><span class="n">Te</span><span class="p">]</span> <span class="p">[</span><span class="n">Ee</span><span class="p">]</span> <span class="n">ifte</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;E == [P &lt;] [Te] [Ee] ifte&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;E == [P &lt;] [Te] [Ee] ifte&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>In this case <code class="docutils literal notranslate"><span class="pre">Te</span></code> works that same as <code class="docutils literal notranslate"><span class="pre">T</span></code> but on the left child tree <p>In this case <code class="docutils literal notranslate"><span class="pre">Te</span></code> works that same as <code class="docutils literal notranslate"><span class="pre">T</span></code> but on the left child tree
@ -243,10 +243,10 @@ instead of the right, so the only difference is that it must use
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Te</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dipd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Te</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dipd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Te == cons cons [dipd] cons infra&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Te == cons cons [dipd] cons infra&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] Te&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] Te&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;old_k&#39;</span> <span class="s1">&#39;old_value&#39;</span> <span class="s1">&#39;Tree-add&#39;</span> <span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;old_k&#39;</span> <span class="s1">&#39;old_value&#39;</span> <span class="s1">&#39;Tree-add&#39;</span> <span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span>
@ -274,10 +274,10 @@ instead of the right, so the only difference is that it must use
<span class="p">[</span><span class="n">key</span> <span class="n">new_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">key</span> <span class="n">new_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Ee == pop swap roll&lt; rest rest cons cons&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Ee == pop swap roll&lt; rest rest cons cons&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;k&quot; [&quot;Tree-add&quot;] Ee&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;k&quot; [&quot;Tree-add&quot;] Ee&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;k&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;k&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span>
@ -302,43 +302,43 @@ instead of the right, so the only difference is that it must use
<span class="n">Tree</span><span class="o">-</span><span class="n">add</span> <span class="o">==</span> <span class="p">[</span><span class="n">popop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[[</span><span class="n">pop</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">Tree</span><span class="o">-</span><span class="n">new</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">R</span><span class="p">]</span> <span class="n">genrec</span> <span class="n">Tree</span><span class="o">-</span><span class="n">add</span> <span class="o">==</span> <span class="p">[</span><span class="n">popop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[[</span><span class="n">pop</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">Tree</span><span class="o">-</span><span class="n">new</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">R</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P &gt;] [T] [E] ifte] genrec&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P &gt;] [T] [E] ifte] genrec&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
<section id="examples"> <section id="examples">
<h3>Examples<a class="headerlink" href="#examples" title="Permalink to this headline"></a></h3> <h3>Examples<a class="headerlink" href="#examples" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Initial</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Initial</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Greater than</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Greater than</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;a&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Less than</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;a&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Less than</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;b&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Equal to</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;b&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Equal to</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Series.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Series.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [[23 &quot;b&quot;] [88 &quot;a&quot;] [44 &quot;c&quot;]] [i Tree-add] step&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [[23 &quot;b&quot;] [88 &quot;a&quot;] [44 &quot;c&quot;]] [i Tree-add] step&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
@ -365,19 +365,19 @@ values:</p>
<span class="n">L</span> <span class="n">L</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;1 0 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;1 0 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;G&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;G&#39;</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;1 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;1 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;E&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;E&#39;</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;0 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;0 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;L&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;L&#39;</span>
@ -414,7 +414,7 @@ node key (by throwing everything else away):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">P</span> <span class="o">==</span> <span class="n">over</span> <span class="p">[</span><span class="n">popop</span> <span class="n">popop</span> <span class="n">first</span><span class="p">]</span> <span class="n">nullary</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">P</span> <span class="o">==</span> <span class="n">over</span> <span class="p">[</span><span class="n">popop</span> <span class="n">popop</span> <span class="n">first</span><span class="p">]</span> <span class="n">nullary</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;P == over [popop popop first] nullary&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;P == over [popop popop first] nullary&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>Using <code class="docutils literal notranslate"><span class="pre">cmp</span></code> to simplify <cite>our code above at <p>Using <code class="docutils literal notranslate"><span class="pre">cmp</span></code> to simplify <cite>our code above at
@ -434,10 +434,10 @@ to understand:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span> <span class="o">==</span> <span class="p">[</span><span class="n">popop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[[</span><span class="n">pop</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">Tree</span><span class="o">-</span><span class="n">new</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">Ee</span><span class="p">]</span> <span class="p">[</span><span class="n">Te</span><span class="p">]</span> <span class="n">cmp</span><span class="p">]</span> <span class="n">genrec</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span> <span class="o">==</span> <span class="p">[</span><span class="n">popop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[[</span><span class="n">pop</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">Tree</span><span class="o">-</span><span class="n">new</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">Ee</span><span class="p">]</span> <span class="p">[</span><span class="n">Te</span><span class="p">]</span> <span class="n">cmp</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Still works.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Still works.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
@ -545,22 +545,22 @@ with an interesting situation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="nb">iter</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="p">[</span><span class="n">dupdip</span> <span class="n">rest</span> <span class="n">rest</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">step</span><span class="p">]</span> <span class="n">genrec</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="nb">iter</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="p">[</span><span class="n">dupdip</span> <span class="n">rest</span> <span class="n">rest</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">step</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-iter == [not] [pop] roll&lt; [dupdip rest rest] cons [step] genrec&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-iter == [not] [pop] roll&lt; [dupdip rest rest] cons [step] genrec&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
<section id="id1"> <section id="id1">
<h3>Examples<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h3> <h3>Examples<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [foo] Tree-iter&#39;</span><span class="p">)</span> <span class="c1"># It doesn&#39;t matter what F is as it won&#39;t be used.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [foo] Tree-iter&#39;</span><span class="p">)</span> <span class="c1"># It doesn&#39;t matter what F is as it won&#39;t be used.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [first] Tree-iter&quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [first] Tree-iter&quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;b&#39;</span> <span class="s1">&#39;a&#39;</span> <span class="s1">&#39;c&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;b&#39;</span> <span class="s1">&#39;a&#39;</span> <span class="s1">&#39;c&#39;</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [second] Tree-iter&quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [second] Tree-iter&quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span> <span class="mi">88</span> <span class="mi">44</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span> <span class="mi">88</span> <span class="mi">44</span>
@ -575,16 +575,16 @@ to e.g. 0 and ignoring them. It’s set-like in that duplicate items added
to it will only occur once within it, and we can query it in to it will only occur once within it, and we can query it in
<cite>:math:`O(log_2 N)</cite> &lt;<a class="reference external" href="https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2">https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2</a>&gt;`__ <cite>:math:`O(log_2 N)</cite> &lt;<a class="reference external" href="https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2">https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2</a>&gt;`__
time.</p> time.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;to_set == [] swap [0 swap Tree-add] step&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;to_set == [] swap [0 swap Tree-add] step&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 5 2 8 6 7 8 4] to_set&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 5 2 8 6 7 8 4] to_set&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
@ -592,10 +592,10 @@ time.</p>
</div> </div>
<p>And with that we can write a little program <code class="docutils literal notranslate"><span class="pre">unique</span></code> to remove <p>And with that we can write a little program <code class="docutils literal notranslate"><span class="pre">unique</span></code> to remove
duplicate items from a list.</p> duplicate items from a list.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;unique == [to_set [first] Tree-iter] cons run&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;unique == [to_set [first] Tree-iter] cons run&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique&#39;</span><span class="p">)</span> <span class="c1"># Filter duplicate items.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique&#39;</span><span class="p">)</span> <span class="c1"># Filter duplicate items.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">7</span> <span class="mi">6</span> <span class="mi">8</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">9</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">7</span> <span class="mi">6</span> <span class="mi">8</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">9</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span>
@ -679,7 +679,7 @@ right side:</p>
</pre></div> </pre></div>
</div> </div>
<p>Now we can sort sequences.</p> <p>Now we can sort sequences.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1">#define(&#39;Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec&#39;)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1">#define(&#39;Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec&#39;)</span>
<span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span> <span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
@ -695,7 +695,7 @@ right side:</p>
<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span> <span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span>
@ -835,7 +835,7 @@ because there’s no value to discard.</p>
<span class="n">Tree</span><span class="o">-</span><span class="n">get</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="ow">not</span><span class="p">]</span> <span class="n">swap</span> <span class="p">[]</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o">&lt;</span><span class="p">]</span> <span class="n">cmp</span><span class="p">]</span> <span class="n">genrec</span> <span class="n">Tree</span><span class="o">-</span><span class="n">get</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="ow">not</span><span class="p">]</span> <span class="n">swap</span> <span class="p">[]</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o">&lt;</span><span class="p">]</span> <span class="n">cmp</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># I don&#39;t want to deal with name conflicts with the above so I&#39;m inlining everything here.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># I don&#39;t want to deal with name conflicts with the above so I&#39;m inlining everything here.</span>
<span class="c1"># The original Joy system has &quot;hide&quot; which is a meta-command which allows you to use named</span> <span class="c1"># The original Joy system has &quot;hide&quot; which is a meta-command which allows you to use named</span>
<span class="c1"># definitions that are only in scope for a given definition. I don&#39;t want to implement</span> <span class="c1"># definitions that are only in scope for a given definition. I don&#39;t want to implement</span>
<span class="c1"># that (yet) so...</span> <span class="c1"># that (yet) so...</span>
@ -852,19 +852,19 @@ because there’s no value to discard.</p>
<span class="s1">&#39;&#39;&#39;</span><span class="p">)</span> <span class="s1">&#39;&#39;&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;gary&quot; 23 [] []] &quot;mike&quot; [popd &quot; not in tree&quot; +] Tree-get&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;gary&quot; 23 [] []] &quot;mike&quot; [popd &quot; not in tree&quot; +] Tree-get&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;mike not in tree&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;mike not in tree&#39;</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;gary&quot; 23 [] []] &quot;gary&quot; [popop &quot;err&quot;] Tree-get&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;gary&quot; 23 [] []] &quot;gary&quot; [popop &quot;err&quot;] Tree-get&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1"> [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step</span> <span class="s1"> [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step</span>
@ -876,7 +876,7 @@ because there’s no value to discard.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1"> [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step</span> <span class="s1"> [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step</span>
@ -1175,7 +1175,7 @@ E == [
</div> </div>
<p>By the standards of the code I’ve written so far, this is a <em>huge</em> Joy <p>By the standards of the code I’ve written so far, this is a <em>huge</em> Joy
program.</p> program.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1">first_two == uncons uncons pop</span> <span class="s1">first_two == uncons uncons pop</span>
<span class="s1">fourth == rest rest rest first</span> <span class="s1">fourth == rest rest rest first</span>
<span class="s1">?fourth == [] [fourth] [] ifte</span> <span class="s1">?fourth == [] [fourth] [] ifte</span>
@ -1193,43 +1193,43 @@ program.</p>
<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span> <span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;c&#39; Tree-Delete &quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;c&#39; Tree-Delete &quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;b&#39; Tree-Delete &quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;b&#39; Tree-Delete &quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;a&#39; Tree-Delete &quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;a&#39; Tree-Delete &quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;der&#39; Tree-Delete &quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;der&#39; Tree-Delete &quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete &quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete &quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete &quot;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete &quot;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>

8
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@ -34,7 +34,7 @@
<div class="body" role="main"> <div class="body" role="main">
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div> </pre></div>
</div> </div>
<section id="quadratic-formula"> <section id="quadratic-formula">
@ -100,11 +100,11 @@ the variables:</p>
</div> </div>
<p>The three arguments are to the left, so we can “chop off” everything to <p>The three arguments are to the left, so we can “chop off” everything to
the right and say it’s the definition of the <code class="docutils literal notranslate"><span class="pre">quadratic</span></code> function:</p> the right and say it’s the definition of the <code class="docutils literal notranslate"><span class="pre">quadratic</span></code> function:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>Let’s try it out:</p> <p>Let’s try it out:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;3 1 1 quadratic&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;3 1 1 quadratic&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="o">-</span><span class="mf">2.618033988749895</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="o">-</span><span class="mf">2.618033988749895</span>
@ -114,7 +114,7 @@ the right and say it’s the definition of the <code class="docutils literal not
lines are the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">dipd</span></code> combinators building the main program lines are the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">dipd</span></code> combinators building the main program
by incorporating the values on the stack. Then that program runs and you by incorporating the values on the stack. Then that program runs and you
get the results. This is pretty typical of Joy code.</p> get the results. This is pretty typical of Joy code.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;-5 1 4 quadratic&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;-5 1 4 quadratic&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="o">-</span><span class="mi">5</span> <span class="mi">1</span> <span class="mi">4</span> <span class="n">quadratic</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="o">-</span><span class="mi">5</span> <span class="mi">1</span> <span class="mi">4</span> <span class="n">quadratic</span>

53
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@ -33,7 +33,7 @@
<div class="body" role="main"> <div class="body" role="main">
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">DefinitionWrapper</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">DefinitionWrapper</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div> </pre></div>
</div> </div>
<section id="recursion-combinators"> <section id="recursion-combinators">
@ -101,7 +101,7 @@ cons list”.</p></li>
</ul> </ul>
<p>It may be helpful to see this function implemented in imperative Python <p>It may be helpful to see this function implemented in imperative Python
code.</p> code.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hylomorphism</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hylomorphism</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
<span class="sd">&#39;&#39;&#39;Return a hylomorphism function H.&#39;&#39;&#39;</span> <span class="sd">&#39;&#39;&#39;Return a hylomorphism function H.&#39;&#39;&#39;</span>
<span class="k">def</span> <span class="nf">H</span><span class="p">(</span><span class="n">a</span><span class="p">):</span> <span class="k">def</span> <span class="nf">H</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
@ -185,7 +185,7 @@ the left so we have a definition for <code class="docutils literal notranslate">
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hylomorphism</span> <span class="o">==</span> <span class="p">[</span><span class="n">unit</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">swoncat</span><span class="p">]</span> <span class="n">dipd</span> <span class="p">[</span><span class="n">dip</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">genrec</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hylomorphism</span> <span class="o">==</span> <span class="p">[</span><span class="n">unit</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">swoncat</span><span class="p">]</span> <span class="n">dipd</span> <span class="p">[</span><span class="n">dip</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">genrec</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<section id="example-finding-triangular-numbers"> <section id="example-finding-triangular-numbers">
@ -200,17 +200,17 @@ of all positive integers less than that one. (In this case the types
<li><p><code class="docutils literal notranslate"><span class="pre">[G]</span></code> is <code class="docutils literal notranslate"><span class="pre">[--</span> <span class="pre">dup]</span></code></p></li> <li><p><code class="docutils literal notranslate"><span class="pre">[G]</span></code> is <code class="docutils literal notranslate"><span class="pre">[--</span> <span class="pre">dup]</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">[F]</span></code> is <code class="docutils literal notranslate"><span class="pre">[+]</span></code></p></li> <li><p><code class="docutils literal notranslate"><span class="pre">[F]</span></code> is <code class="docutils literal notranslate"><span class="pre">[+]</span></code></p></li>
</ul> </ul>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;triangular_number == [1 &lt;=] 0 [-- dup] [+] hylomorphism&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;triangular_number == [1 &lt;=] 0 [-- dup] [+] hylomorphism&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>Let’s try it:</p> <p>Let’s try it:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 triangular_number&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 triangular_number&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[0 1 2 3 4 5 6] [triangular_number] map&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[0 1 2 3 4 5 6] [triangular_number] map&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">6</span> <span class="mi">10</span> <span class="mi">15</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">6</span> <span class="mi">10</span> <span class="mi">15</span><span class="p">]</span>
@ -362,9 +362,8 @@ values.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">hylomorphism</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">hylomorphism</span>
</pre></div> </pre></div>
</div> </div>
<section id="range-et-al"> <section id="range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n">
<h3><code class="docutils literal notranslate"><span class="pre">range</span></code> et. al.<a class="headerlink" href="#range-et-al" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">range</span></code> et. al. An example of an anamorphism is the <code class="docutils literal notranslate"><span class="pre">range</span></code> function which generates the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.<a class="headerlink" href="#range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n" title="Permalink to this headline"></a></h3>
<p>An example of an anamorphism is the <code class="docutils literal notranslate"><span class="pre">range</span></code> function which generates the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.</p>
<p>Each of the above variations can be used to make four slightly different <p>Each of the above variations can be used to make four slightly different
<code class="docutils literal notranslate"><span class="pre">range</span></code> functions.</p> <code class="docutils literal notranslate"><span class="pre">range</span></code> functions.</p>
<section id="range-with-h1"> <section id="range-with-h1">
@ -373,10 +372,10 @@ values.</p>
<span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="p">[]]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</span> <span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="p">[]]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;range == [0 &lt;=] [] [-- dup] [swons] hylomorphism&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;range == [0 &lt;=] [] [-- dup] [swons] hylomorphism&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 range&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 range&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span><span class="p">]</span>
@ -389,10 +388,10 @@ values.</p>
<span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">primrec</span> <span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">primrec</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;range_reverse == [] swap [0 &lt;=] [pop] [-- dup [swons] dip] primrec&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;range_reverse == [] swap [0 &lt;=] [pop] [-- dup [swons] dip] primrec&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 range_reverse&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 range_reverse&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span>
@ -405,10 +404,10 @@ values.</p>
<span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="p">[]]</span> <span class="p">[[</span><span class="o">--</span><span class="p">]</span> <span class="n">dupdip</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</span> <span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="p">[]]</span> <span class="p">[[</span><span class="o">--</span><span class="p">]</span> <span class="n">dupdip</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;ranger == [0 &lt;=] [pop []] [[--] dupdip] [dip swons] genrec&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;ranger == [0 &lt;=] [pop []] [[--] dupdip] [dip swons] genrec&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 ranger&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 ranger&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">5</span> <span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">5</span> <span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span><span class="p">]</span>
@ -421,10 +420,10 @@ values.</p>
<span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">--</span><span class="p">]</span> <span class="n">primrec</span> <span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">--</span><span class="p">]</span> <span class="n">primrec</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;ranger_reverse == [] swap [0 &lt;=] [pop] [[swons] dupdip --] primrec&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;ranger_reverse == [] swap [0 &lt;=] [pop] [[swons] dupdip --] primrec&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 ranger_reverse&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 ranger_reverse&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span><span class="p">]</span>
@ -445,17 +444,17 @@ and makes some new value.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">C</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="n">c</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">hylomorphism</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">C</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="n">c</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">hylomorphism</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;swuncons == uncons swap&#39;</span><span class="p">)</span> <span class="c1"># Awkward name.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;swuncons == uncons swap&#39;</span><span class="p">)</span> <span class="c1"># Awkward name.</span>
</pre></div> </pre></div>
</div> </div>
<p>An example of a catamorphism is the sum function.</p> <p>An example of a catamorphism is the sum function.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">sum</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="mi">0</span> <span class="p">[</span><span class="n">swuncons</span><span class="p">]</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">hylomorphism</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">sum</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="mi">0</span> <span class="p">[</span><span class="n">swuncons</span><span class="p">]</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">hylomorphism</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sum == [not] 0 [swuncons] [+] hylomorphism&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sum == [not] 0 [swuncons] [+] hylomorphism&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[5 4 3 2 1] sum&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[5 4 3 2 1] sum&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
@ -465,7 +464,7 @@ and makes some new value.</p>
<h3>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator<a class="headerlink" href="#the-step-combinator" title="Permalink to this headline"></a></h3> <h3>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator<a class="headerlink" href="#the-step-combinator" title="Permalink to this headline"></a></h3>
<p>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator will usually be better to use than <p>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator will usually be better to use than
<code class="docutils literal notranslate"><span class="pre">catamorphism</span></code>.</p> <code class="docutils literal notranslate"><span class="pre">catamorphism</span></code>.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[step] help&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[step] help&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Run</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">program</span> <span class="n">on</span> <span class="n">each</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">a</span> <span class="n">sequence</span><span class="o">.</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Run</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">program</span> <span class="n">on</span> <span class="n">each</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">a</span> <span class="n">sequence</span><span class="o">.</span>
@ -489,10 +488,10 @@ and makes some new value.</p>
<span class="n">on</span> <span class="n">top</span> <span class="n">of</span> <span class="n">the</span> <span class="n">stack</span><span class="o">.</span> <span class="n">on</span> <span class="n">top</span> <span class="n">of</span> <span class="n">the</span> <span class="n">stack</span><span class="o">.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sum == 0 swap [+] step&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sum == 0 swap [+] step&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[5 4 3 2 1] sum&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[5 4 3 2 1] sum&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
@ -513,10 +512,10 @@ and makes some new value.</p>
<span class="n">P</span> <span class="o">==</span> <span class="mi">1</span> <span class="o">&lt;=</span> <span class="n">P</span> <span class="o">==</span> <span class="mi">1</span> <span class="o">&lt;=</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;factorial == 1 swap [1 &lt;=] [pop] [[*] dupdip --] primrec&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;factorial == 1 swap [1 &lt;=] [pop] [[*] dupdip --] primrec&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 factorial&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 factorial&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">120</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">120</span>
@ -545,10 +544,10 @@ pattern <code class="docutils literal notranslate"><span class="pre">H2</span></
<span class="n">P</span> <span class="o">==</span> <span class="ow">not</span> <span class="n">P</span> <span class="o">==</span> <span class="ow">not</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;tails == [] swap [not] [pop] [rest dup [swons] dip] primrec&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;tails == [] swap [not] [pop] [rest dup [swons] dip] primrec&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 2 3] tails&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 2 3] tails&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]]</span>

10
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@ -42,12 +42,12 @@ we can implement e.g. a function that adds new functions to the
dictionary. However, there’s no function that does that. Adding a new dictionary. However, there’s no function that does that. Adding a new
function to the dictionary is a meta-interpreter action, you have to do function to the dictionary is a meta-interpreter action, you have to do
it in Python, not Joy.</p> it in Python, not Joy.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
</pre></div> </pre></div>
</div> </div>
<section id="a-long-trace"> <section id="a-long-trace">
<h2>A long trace<a class="headerlink" href="#a-long-trace" title="Permalink to this headline"></a></h2> <h2>A long trace<a class="headerlink" href="#a-long-trace" title="Permalink to this headline"></a></h2>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
@ -105,7 +105,7 @@ it in Python, not Joy.</p>
<p>An efficient <code class="docutils literal notranslate"><span class="pre">sum</span></code> function is already in the library. But for <p>An efficient <code class="docutils literal notranslate"><span class="pre">sum</span></code> function is already in the library. But for
<code class="docutils literal notranslate"><span class="pre">size</span></code> we can use a “compiled” version hand-written in Python to speed <code class="docutils literal notranslate"><span class="pre">size</span></code> we can use a “compiled” version hand-written in Python to speed
up evaluation and make the trace more readable.</p> up evaluation and make the trace more readable.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">iter_stack</span> <span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">iter_stack</span>
@ -121,14 +121,14 @@ up evaluation and make the trace more readable.</p>
</div> </div>
<p>Now we replace the old version in the dictionary with the new version, <p>Now we replace the old version in the dictionary with the new version,
and re-evaluate the expression.</p> and re-evaluate the expression.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">&#39;size&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">size</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">&#39;size&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">size</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
<section id="a-shorter-trace"> <section id="a-shorter-trace">
<h2>A shorter trace<a class="headerlink" href="#a-shorter-trace" title="Permalink to this headline"></a></h2> <h2>A shorter trace<a class="headerlink" href="#a-shorter-trace" title="Permalink to this headline"></a></h2>
<p>You can see that <code class="docutils literal notranslate"><span class="pre">size</span></code> now executes in a single step.</p> <p>You can see that <code class="docutils literal notranslate"><span class="pre">size</span></code> now executes in a single step.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>

463
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@ -0,0 +1,463 @@
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
<title>Square Spiral Example Joy Code &#8212; Thun 0.4.1 documentation</title>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div>
</div>
<section id="square-spiral-example-joy-code">
<h1>Square Spiral Example Joy Code<a class="headerlink" href="#square-spiral-example-joy-code" title="Permalink to this headline"></a></h1>
<p>Here is the example of Joy code from the <code class="docutils literal notranslate"><span class="pre">README</span></code> file:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[[[abs]ii &lt;=][[&lt;&gt;][pop !-]||]&amp;&amp;][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
</pre></div>
</div>
<p>It might seem unreadable but with a little familiarity it becomes just
as legible as any other notation. Some layout helps:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[ [[abs] ii &lt;=]
[
[&lt;&gt;] [pop !-] ||
] &amp;&amp;
]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
</pre></div>
</div>
<p>This function accepts two integers on the stack and increments or
decrements one of them such that the new pair of numbers is the next
coordinate pair in a square spiral (like the kind used to construct an
Ulam Spiral).</p>
<section id="original-form">
<h2>Original Form<a class="headerlink" href="#original-form" title="Permalink to this headline"></a></h2>
<p>It’s adapted from <a class="reference external" href="https://stackoverflow.com/questions/398299/looping-in-a-spiral/31864777#31864777">the original code on
StackOverflow</a>:</p>
<blockquote>
<div><p>If all you’re trying to do is generate the first N points in the
spiral (without the original problem’s constraint of masking to an N
x M region), the code becomes very simple:</p>
</div></blockquote>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>void spiral(const int N)
{
int x = 0;
int y = 0;
for(int i = 0; i &lt; N; ++i)
{
cout &lt;&lt; x &lt;&lt; &#39;\t&#39; &lt;&lt; y &lt;&lt; &#39;\n&#39;;
if(abs(x) &lt;= abs(y) &amp;&amp; (x != y || x &gt;= 0))
x += ((y &gt;= 0) ? 1 : -1);
else
y += ((x &gt;= 0) ? -1 : 1);
}
}
</pre></div>
</div>
</section>
<section id="translation-to-joy">
<h2>Translation to Joy<a class="headerlink" href="#translation-to-joy" title="Permalink to this headline"></a></h2>
<p>I’m going to make a function that take two ints (<code class="docutils literal notranslate"><span class="pre">x</span></code> and <code class="docutils literal notranslate"><span class="pre">y</span></code>) and
generates the next pair, we’ll turn it into a generator later using the
<code class="docutils literal notranslate"><span class="pre">x</span></code> combinator.</p>
<section id="first-boolean-predicate">
<h3>First Boolean Predicate<a class="headerlink" href="#first-boolean-predicate" title="Permalink to this headline"></a></h3>
<p>We need a function that computes <code class="docutils literal notranslate"><span class="pre">abs(x)</span> <span class="pre">&lt;=</span> <span class="pre">abs(y)</span></code>, we can use <code class="docutils literal notranslate"><span class="pre">ii</span></code>
to apply <code class="docutils literal notranslate"><span class="pre">abs</span></code> to both values and then compare them with <code class="docutils literal notranslate"><span class="pre">&lt;=</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="nb">abs</span><span class="p">]</span> <span class="n">ii</span> <span class="o">&lt;=</span>
</pre></div>
</div>
<p>I’ve defined two short-circuiting Boolean combinators <code class="docutils literal notranslate"><span class="pre">&amp;&amp;</span></code> and <code class="docutils literal notranslate"><span class="pre">||</span></code>
that each accept two quoted predicate programs, run the first, and
conditionally run the second only if required (to compute the final
Boolean value). They run their predicate arguments <code class="docutils literal notranslate"><span class="pre">nullary</span></code>.</p>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;&amp;&amp; [nullary] cons [nullary [0]] dip branch&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;|| [nullary] cons [nullary] dip [1] branch&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Given those, we can define <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">!=</span> <span class="pre">y</span> <span class="pre">||</span> <span class="pre">x</span> <span class="pre">&gt;=</span> <span class="pre">0</span></code> as:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="o">&lt;&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="mi">0</span> <span class="o">&gt;=</span><span class="p">]</span> <span class="o">||</span>
</pre></div>
</div>
<p>And <code class="docutils literal notranslate"><span class="pre">(abs(x)</span> <span class="pre">&lt;=</span> <span class="pre">abs(y)</span> <span class="pre">&amp;&amp;</span> <span class="pre">(x</span> <span class="pre">!=</span> <span class="pre">y</span> <span class="pre">||</span> <span class="pre">x</span> <span class="pre">&gt;=</span> <span class="pre">0))</span></code> as:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="nb">abs</span><span class="p">]</span> <span class="n">ii</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[[</span><span class="o">&lt;&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="mi">0</span> <span class="o">&gt;=</span><span class="p">]</span> <span class="o">||</span><span class="p">]</span> <span class="o">&amp;&amp;</span>
</pre></div>
</div>
<p>It’s a little rough, but, as I say, with a little familiarity it becomes
legible.</p>
</section>
<section id="the-increment-decrement-branches">
<h3>The Increment / Decrement Branches<a class="headerlink" href="#the-increment-decrement-branches" title="Permalink to this headline"></a></h3>
<p>Turning to the branches of the main <code class="docutils literal notranslate"><span class="pre">if</span></code> statement:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>x += ((y &gt;= 0) ? 1 : -1);
</pre></div>
</div>
<p>Rewrite as a hybrid (pseudo-code) <code class="docutils literal notranslate"><span class="pre">ifte</span></code> expression:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">y</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">x</span> <span class="o">+=</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="n">X</span> <span class="o">-=</span> <span class="mi">1</span><span class="p">]</span> <span class="n">ifte</span>
</pre></div>
</div>
<p>Change each C phrase to Joy code:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="o">&gt;=</span><span class="p">]</span> <span class="p">[[</span><span class="o">++</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[[</span><span class="o">--</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">ifte</span>
</pre></div>
</div>
<p>Factor out the dip from each branch:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="o">&gt;=</span><span class="p">]</span> <span class="p">[[</span><span class="o">++</span><span class="p">]]</span> <span class="p">[[</span><span class="o">--</span><span class="p">]]</span> <span class="n">ifte</span> <span class="n">dip</span>
</pre></div>
</div>
<p>Similar logic applies to the other branch:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>y += ((x &gt;= 0) ? -1 : 1);
[x &gt;= 0] [y -= 1] [y += 1] ifte
[pop 0 &gt;=] [--] [++] ifte
</pre></div>
</div>
</section>
<section id="not-negative">
<h3>“Not Negative”<a class="headerlink" href="#not-negative" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;!- 0 &gt;=&#39;</span><span class="p">)</span>
</pre></div>
</div>
</section>
</section>
<section id="putting-the-pieces-together">
<h2>Putting the Pieces Together<a class="headerlink" href="#putting-the-pieces-together" title="Permalink to this headline"></a></h2>
<p>We can assemble the three functions we just defined in quotes and give
them them to the <code class="docutils literal notranslate"><span class="pre">ifte</span></code> combinator. With some arrangement to show off
the symmetry of the two branches, we have:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[[[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] &amp;&amp;]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
</pre></div>
</div>
<p>As I was writing this up I realized that, since the <code class="docutils literal notranslate"><span class="pre">&amp;&amp;</span></code> combinator
doesn’t consume the stack (below its quoted args), I can unquote the
predicate, swap the branches, and use the <code class="docutils literal notranslate"><span class="pre">branch</span></code> combinator instead
of <code class="docutils literal notranslate"><span class="pre">ifte</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] &amp;&amp;
[[pop !-] [--] [++] ifte ]
[[ !-] [[++]] [[--]] ifte dip]
branch
</pre></div>
</div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;spiral_next [[[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] &amp;&amp;] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Let’s try it out:</p>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 0 spiral_next&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">0</span>
</pre></div>
</div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;1 0 spiral_next&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="o">-</span><span class="mi">1</span>
</pre></div>
</div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;1 -1 spiral_next&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="o">-</span><span class="mi">1</span>
</pre></div>
</div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 -1 spiral_next&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mi">1</span> <span class="o">-</span><span class="mi">1</span>
</pre></div>
</div>
</section>
<section id="turning-it-into-a-generator-with-x">
<h2>Turning it into a Generator with <code class="docutils literal notranslate"><span class="pre">x</span></code><a class="headerlink" href="#turning-it-into-a-generator-with-x" title="Permalink to this headline"></a></h2>
<p>It can be used with the x combinator to make a kind of generator for
spiral square coordinates.</p>
<p>We can use <code class="docutils literal notranslate"><span class="pre">codireco</span></code> to make a generator</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">codireco</span> <span class="p">:</span><span class="o">:=</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
</pre></div>
</div>
<p>It will look like this:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">value</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
</pre></div>
</div>
<p>Here’s a trace of how it works:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span> <span class="n">x</span>
<span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span> <span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span>
<span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="mi">0</span> <span class="o">.</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span>
<span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">codireco</span>
<span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
<span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="p">[</span><span class="mi">0</span> <span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
<span class="o">.</span> <span class="mi">0</span> <span class="n">dup</span> <span class="o">++</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
<span class="mi">0</span> <span class="o">.</span> <span class="n">dup</span> <span class="o">++</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
<span class="mi">0</span> <span class="mi">0</span> <span class="o">.</span> <span class="o">++</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
<span class="mi">0</span> <span class="mi">1</span> <span class="o">.</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
<span class="mi">0</span> <span class="mi">1</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span> <span class="n">rest</span> <span class="n">cons</span>
<span class="mi">0</span> <span class="mi">1</span> <span class="p">[[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span>
<span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span>
</pre></div>
</div>
<p>But first we have to change the <code class="docutils literal notranslate"><span class="pre">spiral_next</span></code> function to work on a
quoted pair of integers, and leave a copy of the pair on the stack.
From:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">y</span> <span class="n">x</span> <span class="n">spiral_next</span>
<span class="o">---------------------</span>
<span class="n">y</span><span class="s1">&#39; x&#39;</span>
</pre></div>
</div>
<p>to:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">x</span> <span class="n">y</span><span class="p">]</span> <span class="p">[</span><span class="n">spiral_next</span><span class="p">]</span> <span class="n">infra</span>
<span class="o">-------------------------------</span>
<span class="p">[</span><span class="n">x</span><span class="s1">&#39; y&#39;</span><span class="p">]</span>
</pre></div>
</div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[0 0] [spiral_next] infra&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">1</span><span class="p">]</span>
</pre></div>
</div>
<p>So our generator is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="n">x</span> <span class="n">y</span><span class="p">]</span> <span class="p">[</span><span class="n">dup</span> <span class="p">[</span><span class="n">spiral_next</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
</pre></div>
</div>
<p>Or rather:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">0</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">dup</span> <span class="p">[</span><span class="n">spiral_next</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
</pre></div>
</div>
<p>There is a function <code class="docutils literal notranslate"><span class="pre">make_generator</span></code> that will build the generator for
us out of the value and stepper function:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="mi">0</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">dup</span> <span class="p">[</span><span class="n">spiral_next</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">make_generator</span>
<span class="o">----------------------------------------------------</span>
<span class="p">[[</span><span class="mi">0</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">dup</span> <span class="p">[</span><span class="n">spiral_next</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
</pre></div>
</div>
<p>Here it is in action:</p>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[0 0] [dup [spiral_next] infra] make_generator x x x x pop&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span> <span class="mi">0</span><span class="p">]</span>
</pre></div>
</div>
<p>Four <code class="docutils literal notranslate"><span class="pre">x</span></code> combinators, four pairs of coordinates.</p>
</section>
<section id="conclusion">
<h2>Conclusion<a class="headerlink" href="#conclusion" title="Permalink to this headline"></a></h2>
<p>So that’s an example of Joy code. It’s a straightforward translation of
the original. It’s a little long for a single definition, you might
break it up like so:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> _spn_P ::= [[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] &amp;&amp;
_spn_T ::= [ !-] [[++]] [[--]] ifte dip
_spn_E ::= [pop !-] [--] [++] ifte
spiral_next ::= _spn_P [_spn_E] [_spn_T] branch
</pre></div>
</div>
<p>This way it’s easy to see that the function is a branch with two
quasi-symmetrical paths.</p>
<p>We then used this function to make a simple generator of coordinate
pairs, where the next pair in the series can be generated at any time by
using the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator on the generator (which is just a quoted
expression containing a copy of the current pair and the “stepper
function” to generate the next pair from that.)</p>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_spn_P [[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] &amp;&amp;&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;_spn_T [!-] [[++]] [[--]] ifte dip&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;_spn_E [pop !-] [--] [++] ifte&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;spiral_next _spn_P [_spn_E] [_spn_T] branch&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;23 18 spiral_next&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> . 23 18 spiral_next
23 . 18 spiral_next
23 18 . spiral_next
23 18 . _spn_P [_spn_E] [_spn_T] branch
23 18 . [[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] &amp;&amp; [_spn_E] [_spn_T] branch
23 18 [[abs] ii &lt;=] . [[&lt;&gt;] [pop !-] ||] &amp;&amp; [_spn_E] [_spn_T] branch
23 18 [[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] . &amp;&amp; [_spn_E] [_spn_T] branch
23 18 [[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] . [nullary] cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] [nullary] . cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii &lt;=] [[[&lt;&gt;] [pop !-] ||] nullary] . [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii &lt;=] [[[&lt;&gt;] [pop !-] ||] nullary] [nullary [0]] . dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii &lt;=] . nullary [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii &lt;=] . [stack] dinfrirst [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii &lt;=] [stack] . dinfrirst [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii &lt;=] [stack] . dip infra first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . stack [[abs] ii &lt;=] infra first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [18 23] . [[abs] ii &lt;=] infra first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [18 23] [[abs] ii &lt;=] . infra first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . [abs] ii &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . ii &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . [dip] dupdip i &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] [dip] . dupdip i &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . dip [abs] i &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 . abs 18 [abs] i &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 . 18 [abs] i &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . [abs] i &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . i &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . abs &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . &lt;= [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
False . [18 23] swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
False [18 23] . swaack first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [False] . first [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False . [0] [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False [0] . [[[&lt;&gt;] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False [0] [[[&lt;&gt;] [pop !-] ||] nullary] . branch [_spn_E] [_spn_T] branch
23 18 . 0 [_spn_E] [_spn_T] branch
23 18 0 . [_spn_E] [_spn_T] branch
23 18 0 [_spn_E] . [_spn_T] branch
23 18 0 [_spn_E] [_spn_T] . branch
23 18 . _spn_E
23 18 . [pop !-] [--] [++] ifte
23 18 [pop !-] . [--] [++] ifte
23 18 [pop !-] [--] . [++] ifte
23 18 [pop !-] [--] [++] . ifte
23 18 [pop !-] [--] [++] . [nullary not] dipd branch
23 18 [pop !-] [--] [++] [nullary not] . dipd branch
23 18 [pop !-] . nullary not [--] [++] branch
23 18 [pop !-] . [stack] dinfrirst not [--] [++] branch
23 18 [pop !-] [stack] . dinfrirst not [--] [++] branch
23 18 [pop !-] [stack] . dip infra first not [--] [++] branch
23 18 . stack [pop !-] infra first not [--] [++] branch
23 18 [18 23] . [pop !-] infra first not [--] [++] branch
23 18 [18 23] [pop !-] . infra first not [--] [++] branch
23 18 . pop !- [18 23] swaack first not [--] [++] branch
23 . !- [18 23] swaack first not [--] [++] branch
23 . 0 &gt;= [18 23] swaack first not [--] [++] branch
23 0 . &gt;= [18 23] swaack first not [--] [++] branch
True . [18 23] swaack first not [--] [++] branch
True [18 23] . swaack first not [--] [++] branch
23 18 [True] . first not [--] [++] branch
23 18 True . not [--] [++] branch
23 18 False . [--] [++] branch
23 18 False [--] . [++] branch
23 18 False [--] [++] . branch
23 18 . --
23 17 .
</pre></div>
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@ -148,10 +148,10 @@ the desired outcome.</p>
</section> </section>
<section id="define-treestep"> <section id="define-treestep">
<h2>Define <code class="docutils literal notranslate"><span class="pre">treestep</span></code><a class="headerlink" href="#define-treestep" title="Permalink to this headline"></a></h2> <h2>Define <code class="docutils literal notranslate"><span class="pre">treestep</span></code><a class="headerlink" href="#define-treestep" title="Permalink to this headline"></a></h2>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1"> _treestep_0 == [[not] swap] dip</span> <span class="s1"> _treestep_0 == [[not] swap] dip</span>
<span class="s1"> _treestep_1 == [dip] cons [uncons] swoncat</span> <span class="s1"> _treestep_1 == [dip] cons [uncons] swoncat</span>
@ -169,7 +169,7 @@ all nodes in a tree with this function:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sumtree</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="nb">sum</span> <span class="o">+</span><span class="p">]</span> <span class="n">treestep</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sumtree</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="nb">sum</span> <span class="o">+</span><span class="p">]</span> <span class="n">treestep</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sumtree == [pop 0] [] [sum +] treestep&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sumtree == [pop 0] [] [sum +] treestep&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>Running this function on an empty tree value gives zero:</p> <p>Running this function on an empty tree value gives zero:</p>
@ -178,7 +178,7 @@ all nodes in a tree with this function:</p>
<span class="mi">0</span> <span class="mi">0</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Empty tree.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Empty tree.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span>
@ -192,61 +192,61 @@ all nodes in a tree with this function:</p>
<span class="n">n</span><span class="o">+</span><span class="n">m</span> <span class="n">n</span><span class="o">+</span><span class="n">m</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23] sumtree&#39;</span><span class="p">)</span> <span class="c1"># No child trees.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23] sumtree&#39;</span><span class="p">)</span> <span class="c1"># No child trees.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 []] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Child tree, empty.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 []] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Child tree, empty.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [4]] [3]] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Non-empty child trees.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [4]] [3]] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Non-empty child trees.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">32</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">32</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Etc...</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Etc...</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep&#39;</span><span class="p">)</span> <span class="c1"># Alternate &quot;spelling&quot;.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep&#39;</span><span class="p">)</span> <span class="c1"># Alternate &quot;spelling&quot;.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep&#39;</span><span class="p">)</span> <span class="c1"># Replace each node.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep&#39;</span><span class="p">)</span> <span class="c1"># Replace each node.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[]]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep&#39;</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep&#39;</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep&#39;</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep&#39;</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span>
@ -277,7 +277,7 @@ all nodes in a tree with this function:</p>
</pre></div> </pre></div>
</div> </div>
<p>This doesn’t quite work:</p> <p>This doesn’t quite work:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] [&quot;B&quot;] [first] [i] treestep&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] [&quot;B&quot;] [first] [i] treestep&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="s1">&#39;B&#39;</span> <span class="s1">&#39;B&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="s1">&#39;B&#39;</span> <span class="s1">&#39;B&#39;</span>
@ -299,7 +299,7 @@ depositing our results directly on the stack.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="p">[</span><span class="n">flatten</span> <span class="n">cons</span><span class="p">]</span> <span class="n">treestep</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="p">[</span><span class="n">flatten</span> <span class="n">cons</span><span class="p">]</span> <span class="n">treestep</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">9</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">8</span> <span class="mi">6</span> <span class="mi">7</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">9</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">8</span> <span class="mi">6</span> <span class="mi">7</span><span class="p">]</span>
@ -322,7 +322,7 @@ depositing our results directly on the stack.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">i</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="n">swons</span> <span class="n">concat</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="n">treestep</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">i</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="n">swons</span> <span class="n">concat</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="n">treestep</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll&lt; swons concat] treestep&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll&lt; swons concat] treestep&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span><span class="p">]</span>
@ -343,7 +343,7 @@ non-empty node is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">N</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="n">C</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">N</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="n">C</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[&quot;key&quot; &quot;value&quot;] [&quot;left&quot;] [&quot;right&quot;] ] [&quot;B&quot;] [&quot;N&quot;] [&quot;C&quot;] treegrind&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[&quot;key&quot; &quot;value&quot;] [&quot;left&quot;] [&quot;right&quot;] ] [&quot;B&quot;] [&quot;N&quot;] [&quot;C&quot;] treegrind&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;key&#39;</span> <span class="s1">&#39;value&#39;</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[[</span><span class="s1">&#39;left&#39;</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;right&#39;</span><span class="p">]]</span> <span class="p">[[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;B&#39;</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="p">[</span><span class="s1">&#39;N&#39;</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;C&#39;</span><span class="p">]</span> <span class="n">genrec</span><span class="p">]</span> <span class="s1">&#39;C&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;key&#39;</span> <span class="s1">&#39;value&#39;</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[[</span><span class="s1">&#39;left&#39;</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;right&#39;</span><span class="p">]]</span> <span class="p">[[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;B&#39;</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="p">[</span><span class="s1">&#39;N&#39;</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;C&#39;</span><span class="p">]</span> <span class="n">genrec</span><span class="p">]</span> <span class="s1">&#39;C&#39;</span>
@ -353,21 +353,21 @@ non-empty node is:</p>
<section id="treegrind-with-step"> <section id="treegrind-with-step">
<h2><code class="docutils literal notranslate"><span class="pre">treegrind</span></code> with <code class="docutils literal notranslate"><span class="pre">step</span></code><a class="headerlink" href="#treegrind-with-step" title="Permalink to this headline"></a></h2> <h2><code class="docutils literal notranslate"><span class="pre">treegrind</span></code> with <code class="docutils literal notranslate"><span class="pre">step</span></code><a class="headerlink" href="#treegrind-with-step" title="Permalink to this headline"></a></h2>
<p>Iteration through the nodes</p> <p>Iteration through the nodes</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [&quot;N&quot;] [step] treegrind&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [&quot;N&quot;] [step] treegrind&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span>
</pre></div> </pre></div>
</div> </div>
<p>Sum the nodes’ keys.</p> <p>Sum the nodes’ keys.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">44</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">44</span>
</pre></div> </pre></div>
</div> </div>
<p>Rebuild the tree using <code class="docutils literal notranslate"><span class="pre">map</span></code> (imitating <code class="docutils literal notranslate"><span class="pre">treestep</span></code>.)</p> <p>Rebuild the tree using <code class="docutils literal notranslate"><span class="pre">map</span></code> (imitating <code class="docutils literal notranslate"><span class="pre">treestep</span></code>.)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">103</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">102</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">109</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">105</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">104</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">108</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">106</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">107</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">103</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">102</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">109</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">105</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">104</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">108</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">106</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">107</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
@ -449,7 +449,7 @@ equal):</p>
</pre></div> </pre></div>
</div> </div>
<p>To me, that seems simpler than the <code class="docutils literal notranslate"><span class="pre">genrec</span></code> version.</p> <p>To me, that seems simpler than the <code class="docutils literal notranslate"><span class="pre">genrec</span></code> version.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1"> T&gt; == pop [first] dip i</span> <span class="s1"> T&gt; == pop [first] dip i</span>
<span class="s1"> T&lt; == pop [second] dip i</span> <span class="s1"> T&lt; == pop [second] dip i</span>
@ -461,7 +461,7 @@ equal):</p>
<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span> <span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
<span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span> <span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
@ -473,7 +473,7 @@ equal):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
<span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span> <span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>

30
docs/sphinx_docs/_build/html/notebooks/TypeChecking.html
View File

@ -35,7 +35,7 @@
<section id="type-checking"> <section id="type-checking">
<h1>Type Checking<a class="headerlink" href="#type-checking" title="Permalink to this headline"></a></h1> <h1>Type Checking<a class="headerlink" href="#type-checking" title="Permalink to this headline"></a></h1>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">logging</span><span class="o">,</span> <span class="nn">sys</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">logging</span><span class="o">,</span> <span class="nn">sys</span>
<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span> <span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span>
<span class="nb">format</span><span class="o">=</span><span class="s1">&#39;</span><span class="si">%(message)s</span><span class="s1">&#39;</span><span class="p">,</span> <span class="nb">format</span><span class="o">=</span><span class="s1">&#39;</span><span class="si">%(message)s</span><span class="s1">&#39;</span><span class="p">,</span>
@ -44,7 +44,7 @@
<span class="p">)</span> <span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.types</span> <span class="kn">import</span> <span class="p">(</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.types</span> <span class="kn">import</span> <span class="p">(</span>
<span class="n">doc_from_stack_effect</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">,</span>
<span class="n">infer</span><span class="p">,</span> <span class="n">infer</span><span class="p">,</span>
<span class="n">reify</span><span class="p">,</span> <span class="n">reify</span><span class="p">,</span>
@ -54,14 +54,14 @@
<span class="p">)</span> <span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">FUNCTIONS</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">FUNCTIONS</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="k">del</span> <span class="n">D</span><span class="p">[</span><span class="s1">&#39;product&#39;</span><span class="p">]</span> <span class="k">del</span> <span class="n">D</span><span class="p">[</span><span class="s1">&#39;product&#39;</span><span class="p">]</span>
<span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">D</span><span class="p">)</span> <span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">D</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<section id="an-example"> <section id="an-example">
<h2>An Example<a class="headerlink" href="#an-example" title="Permalink to this headline"></a></h2> <h2>An Example<a class="headerlink" href="#an-example" title="Permalink to this headline"></a></h2>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rrest</span><span class="p">,</span> <span class="n">ccons</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rrest</span><span class="p">,</span> <span class="n">ccons</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ pop swap rolldown rrest ccons <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ pop swap rolldown rrest ccons
@ -72,31 +72,31 @@
40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘ 40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a4</span> <span class="n">a5</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a3</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a4</span> <span class="n">a5</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a3</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.parser</span> <span class="kn">import</span> <span class="n">text_to_expression</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.parser</span> <span class="kn">import</span> <span class="n">text_to_expression</span>
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">stack_to_string</span> <span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">stack_to_string</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;0 1 2 [3 4]&#39;</span><span class="p">)</span> <span class="c1"># reverse order</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;0 1 2 [3 4]&#39;</span><span class="p">)</span> <span class="c1"># reverse order</span>
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span> <span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">u</span> <span class="n">u</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">a2</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a4</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">a5</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</span><span class="p">:</span> <span class="p">()}</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">a2</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a4</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">a5</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</span><span class="p">:</span> <span class="p">()}</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -106,17 +106,17 @@
</section> </section>
<section id="unification-works-in-reverse"> <section id="unification-works-in-reverse">
<h2>Unification Works “in Reverse”<a class="headerlink" href="#unification-works-in-reverse" title="Permalink to this headline"></a></h2> <h2>Unification Works “in Reverse”<a class="headerlink" href="#unification-works-in-reverse" title="Permalink to this headline"></a></h2>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[2 3]&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[2 3]&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fo</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># output side, not input side</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fo</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># output side, not input side</span>
<span class="n">u</span> <span class="n">u</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a2</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</span><span class="p">:</span> <span class="p">()}</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a2</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</span><span class="p">:</span> <span class="p">()}</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -126,7 +126,7 @@
</section> </section>
<section id="failing-a-check"> <section id="failing-a-check">
<h2>Failing a Check<a class="headerlink" href="#failing-a-check" title="Permalink to this headline"></a></h2> <h2>Failing a Check<a class="headerlink" href="#failing-a-check" title="Permalink to this headline"></a></h2>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ dup mul <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ dup mul
@ -135,14 +135,14 @@
31 (i1 -- i2) ∘ 31 (i1 -- i2) ∘
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;&quot;two&quot;&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;&quot;two&quot;&#39;</span><span class="p">)</span>
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span> <span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;two&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;two&#39;</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
<span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)</span>
<span class="k">except</span> <span class="n">JoyTypeError</span><span class="p">,</span> <span class="n">err</span><span class="p">:</span> <span class="k">except</span> <span class="n">JoyTypeError</span><span class="p">,</span> <span class="n">err</span><span class="p">:</span>
<span class="nb">print</span> <span class="n">err</span> <span class="nb">print</span> <span class="n">err</span>

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@ -182,7 +182,7 @@ terms in the forms:</p>
<section id="compiling-popswaproll"> <section id="compiling-popswaproll">
<h3>Compiling <code class="docutils literal notranslate"><span class="pre">pop∘swap∘roll&lt;</span></code><a class="headerlink" href="#compiling-popswaproll" title="Permalink to this headline"></a></h3> <h3>Compiling <code class="docutils literal notranslate"><span class="pre">pop∘swap∘roll&lt;</span></code><a class="headerlink" href="#compiling-popswaproll" title="Permalink to this headline"></a></h3>
<p>The simplest way to “compile” this function would be something like:</p> <p>The simplest way to “compile” this function would be something like:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">poswrd</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">poswrd</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
<span class="k">return</span> <span class="n">rolldown</span><span class="p">(</span><span class="o">*</span><span class="n">swap</span><span class="p">(</span><span class="o">*</span><span class="n">pop</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">d</span><span class="p">)))</span> <span class="k">return</span> <span class="n">rolldown</span><span class="p">(</span><span class="o">*</span><span class="n">swap</span><span class="p">(</span><span class="o">*</span><span class="n">pop</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">d</span><span class="p">)))</span>
</pre></div> </pre></div>
</div> </div>
@ -193,7 +193,7 @@ terms in the forms:</p>
</pre></div> </pre></div>
</div> </div>
<p>We should be able to directly write out a Python function like:</p> <p>We should be able to directly write out a Python function like:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">poswrd</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">poswrd</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
<span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span> <span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
<span class="k">return</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span> <span class="k">return</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span>
</pre></div> </pre></div>
@ -335,7 +335,7 @@ actually pretty easy. I’ll explain below.</p>
</div> </div>
<p>From this stack effect comment it should be possible to construct the <p>From this stack effect comment it should be possible to construct the
following Python code:</p> following Python code:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
<span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span> <span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
<span class="k">return</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span> <span class="k">return</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span>
</pre></div> </pre></div>
@ -348,7 +348,7 @@ following Python code:</p>
<h3>Representing Stack Effect Comments in Python<a class="headerlink" href="#representing-stack-effect-comments-in-python" title="Permalink to this headline"></a></h3> <h3>Representing Stack Effect Comments in Python<a class="headerlink" href="#representing-stack-effect-comments-in-python" title="Permalink to this headline"></a></h3>
<p>I’m going to use pairs of tuples of type descriptors, which will be <p>I’m going to use pairs of tuples of type descriptors, which will be
integers or tuples of type descriptors:</p> integers or tuples of type descriptors:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">roll_dn</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">roll_dn</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">pop</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,),</span> <span class="p">()</span> <span class="n">pop</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,),</span> <span class="p">()</span>
@ -358,7 +358,7 @@ integers or tuples of type descriptors:</p>
</section> </section>
<section id="compose"> <section id="compose">
<h3><code class="docutils literal notranslate"><span class="pre">compose()</span></code><a class="headerlink" href="#compose" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">compose()</span></code><a class="headerlink" href="#compose" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
<span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span>
@ -403,7 +403,7 @@ integers or tuples of type descriptors:</p>
</section> </section>
<section id="unify"> <section id="unify">
<h3><code class="docutils literal notranslate"><span class="pre">unify()</span></code><a class="headerlink" href="#unify" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">unify()</span></code><a class="headerlink" href="#unify" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span> <span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">s</span> <span class="o">=</span> <span class="p">{}</span> <span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
@ -420,7 +420,7 @@ integers or tuples of type descriptors:</p>
</section> </section>
<section id="update"> <section id="update">
<h3><code class="docutils literal notranslate"><span class="pre">update()</span></code><a class="headerlink" href="#update" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">update()</span></code><a class="headerlink" href="#update" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">term</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">term</span><span class="p">):</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span> <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
<span class="k">return</span> <span class="n">s</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">term</span><span class="p">)</span> <span class="k">return</span> <span class="n">s</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">term</span><span class="p">)</span>
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">inner</span><span class="p">)</span> <span class="k">for</span> <span class="n">inner</span> <span class="ow">in</span> <span class="n">term</span><span class="p">)</span> <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">inner</span><span class="p">)</span> <span class="k">for</span> <span class="n">inner</span> <span class="ow">in</span> <span class="n">term</span><span class="p">)</span>
@ -429,7 +429,7 @@ integers or tuples of type descriptors:</p>
</section> </section>
<section id="relabel"> <section id="relabel">
<h3><code class="docutils literal notranslate"><span class="pre">relabel()</span></code><a class="headerlink" href="#relabel" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">relabel()</span></code><a class="headerlink" href="#relabel" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">relabel</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">relabel</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
<span class="k">return</span> <span class="n">left</span><span class="p">,</span> <span class="n">_1000</span><span class="p">(</span><span class="n">right</span><span class="p">)</span> <span class="k">return</span> <span class="n">left</span><span class="p">,</span> <span class="n">_1000</span><span class="p">(</span><span class="n">right</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_1000</span><span class="p">(</span><span class="n">right</span><span class="p">):</span> <span class="k">def</span> <span class="nf">_1000</span><span class="p">(</span><span class="n">right</span><span class="p">):</span>
@ -446,7 +446,7 @@ integers or tuples of type descriptors:</p>
</section> </section>
<section id="delabel"> <section id="delabel">
<h3><code class="docutils literal notranslate"><span class="pre">delabel()</span></code><a class="headerlink" href="#delabel" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">delabel()</span></code><a class="headerlink" href="#delabel" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">delabel</span><span class="p">(</span><span class="n">f</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">delabel</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="p">{</span><span class="n">u</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">u</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">_unique</span><span class="p">(</span><span class="n">f</span><span class="p">)))}</span> <span class="n">s</span> <span class="o">=</span> <span class="p">{</span><span class="n">u</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">u</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">_unique</span><span class="p">(</span><span class="n">f</span><span class="p">)))}</span>
<span class="k">return</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span> <span class="k">return</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
@ -472,38 +472,38 @@ integers or tuples of type descriptors:</p>
<p>At last we put it all together in a function <code class="docutils literal notranslate"><span class="pre">C()</span></code> that accepts two <p>At last we put it all together in a function <code class="docutils literal notranslate"><span class="pre">C()</span></code> that accepts two
stack effect comments and returns their composition (or raises and stack effect comments and returns their composition (or raises and
exception if they can’t be composed due to type conflicts.)</p> exception if they can’t be composed due to type conflicts.)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
<span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="o">=</span> <span class="n">relabel</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">)</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="o">=</span> <span class="n">relabel</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">)</span>
<span class="n">fg</span> <span class="o">=</span> <span class="n">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">)</span> <span class="n">fg</span> <span class="o">=</span> <span class="n">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">)</span>
<span class="k">return</span> <span class="n">delabel</span><span class="p">(</span><span class="n">fg</span><span class="p">)</span> <span class="k">return</span> <span class="n">delabel</span><span class="p">(</span><span class="n">fg</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>Let’s try it out.</p> <p>Let’s try it out.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">),</span> <span class="n">roll_dn</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">),</span> <span class="n">roll_dn</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">poswrd</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">poswrd</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">))</span>
<span class="n">poswrd</span> <span class="n">poswrd</span>
</pre></div> </pre></div>
</div> </div>
@ -516,12 +516,12 @@ exception if they can’t be composed due to type conflicts.)</p>
<p>Here’s that trick to represent functions like <code class="docutils literal notranslate"><span class="pre">rest</span></code> and <code class="docutils literal notranslate"><span class="pre">cons</span></code> that <p>Here’s that trick to represent functions like <code class="docutils literal notranslate"><span class="pre">rest</span></code> and <code class="docutils literal notranslate"><span class="pre">cons</span></code> that
manipulate stacks. We use a cons-list of tuples and give the tails their manipulate stacks. We use a cons-list of tuples and give the tails their
own numbers. Then everything above already works.</p> own numbers. Then everything above already works.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">rest</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">rest</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,)</span>
<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),)</span> <span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">poswrd</span><span class="p">,</span> <span class="n">rest</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">poswrd</span><span class="p">,</span> <span class="n">rest</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
@ -542,7 +542,7 @@ own numbers. Then everything above already works.</p>
<span class="p">}</span> <span class="p">}</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">))</span>
<span class="n">F</span> <span class="n">F</span>
</pre></div> </pre></div>
@ -560,10 +560,10 @@ own numbers. Then everything above already works.</p>
<h3>Dealing with <code class="docutils literal notranslate"><span class="pre">cons</span></code> and <code class="docutils literal notranslate"><span class="pre">uncons</span></code><a class="headerlink" href="#dealing-with-cons-and-uncons" title="Permalink to this headline"></a></h3> <h3>Dealing with <code class="docutils literal notranslate"><span class="pre">cons</span></code> and <code class="docutils literal notranslate"><span class="pre">uncons</span></code><a class="headerlink" href="#dealing-with-cons-and-uncons" title="Permalink to this headline"></a></h3>
<p>However, if we try to compose e.g. <code class="docutils literal notranslate"><span class="pre">cons</span></code> and <code class="docutils literal notranslate"><span class="pre">uncons</span></code> it won’t <p>However, if we try to compose e.g. <code class="docutils literal notranslate"><span class="pre">cons</span></code> and <code class="docutils literal notranslate"><span class="pre">uncons</span></code> it won’t
work:</p> work:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">uncons</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">uncons</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
<span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span> <span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
<span class="k">except</span> <span class="ne">Exception</span><span class="p">,</span> <span class="n">e</span><span class="p">:</span> <span class="k">except</span> <span class="ne">Exception</span><span class="p">,</span> <span class="n">e</span><span class="p">:</span>
<span class="nb">print</span> <span class="n">e</span> <span class="nb">print</span> <span class="n">e</span>
@ -577,7 +577,7 @@ work:</p>
<p>The problem is that the <code class="docutils literal notranslate"><span class="pre">unify()</span></code> function as written doesn’t handle <p>The problem is that the <code class="docutils literal notranslate"><span class="pre">unify()</span></code> function as written doesn’t handle
the case when both terms are tuples. We just have to add a clause to the case when both terms are tuples. We just have to add a clause to
deal with this recursively:</p> deal with this recursively:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span> <span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">s</span> <span class="o">=</span> <span class="p">{}</span> <span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">elif</span> <span class="n">s</span><span class="p">:</span> <span class="k">elif</span> <span class="n">s</span><span class="p">:</span>
@ -606,7 +606,7 @@ deal with this recursively:</p>
<span class="k">return</span> <span class="n">s</span> <span class="k">return</span> <span class="n">s</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
@ -618,13 +618,13 @@ deal with this recursively:</p>
<section id="part-iii-compiling-yin-functions"> <section id="part-iii-compiling-yin-functions">
<h2>Part III: Compiling Yin Functions<a class="headerlink" href="#part-iii-compiling-yin-functions" title="Permalink to this headline"></a></h2> <h2>Part III: Compiling Yin Functions<a class="headerlink" href="#part-iii-compiling-yin-functions" title="Permalink to this headline"></a></h2>
<p>Now consider the Python function we would like to derive:</p> <p>Now consider the Python function we would like to derive:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F_python</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F_python</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
<span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span> <span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
<span class="k">return</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span> <span class="k">return</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span>
</pre></div> </pre></div>
</div> </div>
<p>And compare it to the input stack effect comment tuple we just computed:</p> <p>And compare it to the input stack effect comment tuple we just computed:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">F</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
@ -646,7 +646,7 @@ stack effect comment tuple, just in the reverse order:</p>
</div> </div>
<p>Eh?</p> <p>Eh?</p>
<p>And the return tuple</p> <p>And the return tuple</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">)),)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">)),)</span>
@ -666,7 +666,7 @@ effect.)</p>
<h3>Python Identifiers<a class="headerlink" href="#python-identifiers" title="Permalink to this headline"></a></h3> <h3>Python Identifiers<a class="headerlink" href="#python-identifiers" title="Permalink to this headline"></a></h3>
<p>We want to substitute Python identifiers for the integers. I’m going to <p>We want to substitute Python identifiers for the integers. I’m going to
repurpose <code class="docutils literal notranslate"><span class="pre">joy.parser.Symbol</span></code> class for this:</p> repurpose <code class="docutils literal notranslate"><span class="pre">joy.parser.Symbol</span></code> class for this:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
<span class="kn">from</span> <span class="nn">joy.parser</span> <span class="kn">import</span> <span class="n">Symbol</span> <span class="kn">from</span> <span class="nn">joy.parser</span> <span class="kn">import</span> <span class="n">Symbol</span>
@ -690,7 +690,7 @@ repurpose <code class="docutils literal notranslate"><span class="pre">joy.parse
effect comment tuples to reasonable text format. There are some details effect comment tuples to reasonable text format. There are some details
in how this code works that related to stuff later in the notebook, so in how this code works that related to stuff later in the notebook, so
you should skip it for now and read it later if you’re interested.</p> you should skip it for now and read it later if you’re interested.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">):</span>
<span class="k">return</span> <span class="s1">&#39;(</span><span class="si">%s</span><span class="s1">--</span><span class="si">%s</span><span class="s1">)&#39;</span> <span class="o">%</span> <span class="p">(</span> <span class="k">return</span> <span class="s1">&#39;(</span><span class="si">%s</span><span class="s1">--</span><span class="si">%s</span><span class="s1">)&#39;</span> <span class="o">%</span> <span class="p">(</span>
<span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">_to_str</span><span class="p">,</span> <span class="n">inputs</span> <span class="o">+</span> <span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">,))),</span> <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">_to_str</span><span class="p">,</span> <span class="n">inputs</span> <span class="o">+</span> <span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">,))),</span>
<span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">_to_str</span><span class="p">,</span> <span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">,)</span> <span class="o">+</span> <span class="n">outputs</span><span class="p">))</span> <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">_to_str</span><span class="p">,</span> <span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">,)</span> <span class="o">+</span> <span class="n">outputs</span><span class="p">))</span>
@ -728,7 +728,7 @@ you should skip it for now and read it later if you’re interested.</p>
<p>Now we can write a compiler function to emit Python source code. (The <p>Now we can write a compiler function to emit Python source code. (The
underscore suffix distiguishes it from the built-in <code class="docutils literal notranslate"><span class="pre">compile()</span></code> underscore suffix distiguishes it from the built-in <code class="docutils literal notranslate"><span class="pre">compile()</span></code>
function.)</p> function.)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span> <span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span> <span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
<span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">identifiers</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">identifiers</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
@ -744,7 +744,7 @@ function.)</p>
</pre></div> </pre></div>
</div> </div>
<p>Here it is in action:</p> <p>Here it is in action:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">source</span> <span class="o">=</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;F&#39;</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">source</span> <span class="o">=</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;F&#39;</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
<span class="nb">print</span> <span class="n">source</span> <span class="nb">print</span> <span class="n">source</span>
</pre></div> </pre></div>
@ -756,13 +756,13 @@ function.)</p>
</pre></div> </pre></div>
</div> </div>
<p>Compare:</p> <p>Compare:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F_python</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F_python</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
<span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span> <span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
<span class="k">return</span> <span class="p">((</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">)</span> <span class="k">return</span> <span class="p">((</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>Next steps:</p> <p>Next steps:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">L</span> <span class="o">=</span> <span class="p">{}</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">L</span> <span class="o">=</span> <span class="p">{}</span>
<span class="nb">eval</span><span class="p">(</span><span class="nb">compile</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="s1">&#39;__main__&#39;</span><span class="p">,</span> <span class="s1">&#39;single&#39;</span><span class="p">),</span> <span class="p">{},</span> <span class="n">L</span><span class="p">)</span> <span class="nb">eval</span><span class="p">(</span><span class="nb">compile</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="s1">&#39;__main__&#39;</span><span class="p">,</span> <span class="s1">&#39;single&#39;</span><span class="p">),</span> <span class="p">{},</span> <span class="n">L</span><span class="p">)</span>
@ -773,14 +773,14 @@ function.)</p>
</pre></div> </pre></div>
</div> </div>
<p>Let’s try it out:</p> <p>Let’s try it out:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
<span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span> <span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">&#39;F&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">SimpleFunctionWrapper</span><span class="p">(</span><span class="n">L</span><span class="p">[</span><span class="s1">&#39;F&#39;</span><span class="p">])</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">&#39;F&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">SimpleFunctionWrapper</span><span class="p">(</span><span class="n">L</span><span class="p">[</span><span class="s1">&#39;F&#39;</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[4 5 ...] 2 3 1 F&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[4 5 ...] 2 3 1 F&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="o">...</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="o">...</span><span class="p">]</span>
@ -800,7 +800,7 @@ this might be less helpful.</p>
<h3>Compiling Library Functions<a class="headerlink" href="#compiling-library-functions" title="Permalink to this headline"></a></h3> <h3>Compiling Library Functions<a class="headerlink" href="#compiling-library-functions" title="Permalink to this headline"></a></h3>
<p>We can use <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> to generate many primitives in the library <p>We can use <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> to generate many primitives in the library
from their stack effect comments:</p> from their stack effect comments:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">defs</span><span class="p">():</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">defs</span><span class="p">():</span>
<span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
@ -823,7 +823,7 @@ from their stack effect comments:</p>
<span class="k">return</span> <span class="nb">locals</span><span class="p">()</span> <span class="k">return</span> <span class="nb">locals</span><span class="p">()</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">defs</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">defs</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
<span class="nb">print</span> <span class="nb">print</span>
<span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span><span class="p">)</span> <span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span><span class="p">)</span>
<span class="nb">print</span> <span class="nb">print</span>
@ -966,7 +966,7 @@ and <code class="docutils literal notranslate"><span class="pre">t</span></code>
Python class hierarchy of Joy types and use the <code class="docutils literal notranslate"><span class="pre">issubclass()</span></code> method Python class hierarchy of Joy types and use the <code class="docutils literal notranslate"><span class="pre">issubclass()</span></code> method
to establish domain ordering, as well as other handy behaviour that will to establish domain ordering, as well as other handy behaviour that will
make it fairly easy to reuse most of the code above.</p> make it fairly easy to reuse most of the code above.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">AnyJoyType</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">AnyJoyType</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;a&#39;</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;a&#39;</span>
@ -1010,12 +1010,12 @@ make it fairly easy to reuse most of the code above.</p>
</pre></div> </pre></div>
</div> </div>
<p>Mess with it a little:</p> <p>Mess with it a little:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">permutations</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">permutations</span>
</pre></div> </pre></div>
</div> </div>
<p>“Any” types can be specialized to numbers and stacks, but not vice <p>“Any” types can be specialized to numbers and stacks, but not vice
versa:</p> versa:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="mi">2</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="mi">2</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">a</span><span class="p">,</span> <span class="s1">&#39;&gt;=&#39;</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">a</span> <span class="o">&gt;=</span> <span class="n">b</span> <span class="nb">print</span> <span class="n">a</span><span class="p">,</span> <span class="s1">&#39;&gt;=&#39;</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">a</span> <span class="o">&gt;=</span> <span class="n">b</span>
</pre></div> </pre></div>
</div> </div>
@ -1030,7 +1030,7 @@ versa:</p>
<p>Our crude <a class="reference external" href="https://en.wikipedia.org/wiki/Numerical_tower">Numerical <p>Our crude <a class="reference external" href="https://en.wikipedia.org/wiki/Numerical_tower">Numerical
Tower</a> of <em>numbers</em> &gt; Tower</a> of <em>numbers</em> &gt;
<em>floats</em> &gt; <em>integers</em> works as well (but we’re not going to use it yet):</p> <em>floats</em> &gt; <em>integers</em> works as well (but we’re not going to use it yet):</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">FloatJoyType</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">IntJoyType</span><span class="p">(</span><span class="mi">0</span><span class="p">)),</span> <span class="mi">2</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">FloatJoyType</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">IntJoyType</span><span class="p">(</span><span class="mi">0</span><span class="p">)),</span> <span class="mi">2</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">a</span><span class="p">,</span> <span class="s1">&#39;&gt;=&#39;</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">a</span> <span class="o">&gt;=</span> <span class="n">b</span> <span class="nb">print</span> <span class="n">a</span><span class="p">,</span> <span class="s1">&#39;&gt;=&#39;</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">a</span> <span class="o">&gt;=</span> <span class="n">b</span>
</pre></div> </pre></div>
</div> </div>
@ -1051,18 +1051,18 @@ Tower</a> of <em>numbers</em> &gt;
</section> </section>
<section id="typing-sqr"> <section id="typing-sqr">
<h3>Typing <code class="docutils literal notranslate"><span class="pre">sqr</span></code><a class="headerlink" href="#typing-sqr" title="Permalink to this headline"></a></h3> <h3>Typing <code class="docutils literal notranslate"><span class="pre">sqr</span></code><a class="headerlink" href="#typing-sqr" title="Permalink to this headline"></a></h3>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">dup</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">dup</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">mul</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">],)</span> <span class="n">mul</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">],)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">dup</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">dup</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a1</span><span class="p">))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a1</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">mul</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">mul</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">),</span> <span class="p">(</span><span class="n">n3</span><span class="p">,))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">),</span> <span class="p">(</span><span class="n">n3</span><span class="p">,))</span>
@ -1072,7 +1072,7 @@ Tower</a> of <em>numbers</em> &gt;
<section id="modifying-the-inferencer"> <section id="modifying-the-inferencer">
<h3>Modifying the Inferencer<a class="headerlink" href="#modifying-the-inferencer" title="Permalink to this headline"></a></h3> <h3>Modifying the Inferencer<a class="headerlink" href="#modifying-the-inferencer" title="Permalink to this headline"></a></h3>
<p>Re-labeling still works fine:</p> <p>Re-labeling still works fine:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">foo</span> <span class="o">=</span> <span class="n">relabel</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">foo</span> <span class="o">=</span> <span class="n">relabel</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span>
<span class="n">foo</span> <span class="n">foo</span>
</pre></div> </pre></div>
@ -1084,7 +1084,7 @@ Tower</a> of <em>numbers</em> &gt;
<h4><code class="docutils literal notranslate"><span class="pre">delabel()</span></code> version 2<a class="headerlink" href="#delabel-version-2" title="Permalink to this headline"></a></h4> <h4><code class="docutils literal notranslate"><span class="pre">delabel()</span></code> version 2<a class="headerlink" href="#delabel-version-2" title="Permalink to this headline"></a></h4>
<p>The <code class="docutils literal notranslate"><span class="pre">delabel()</span></code> function needs an overhaul. It now has to keep track <p>The <code class="docutils literal notranslate"><span class="pre">delabel()</span></code> function needs an overhaul. It now has to keep track
of how many labels of each domain it has “seen”.</p> of how many labels of each domain it has “seen”.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">Counter</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">Counter</span>
<span class="k">def</span> <span class="nf">delabel</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">seen</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> <span class="k">def</span> <span class="nf">delabel</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">seen</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
@ -1105,7 +1105,7 @@ of how many labels of each domain it has “seen”.</p>
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">delabel</span><span class="p">(</span><span class="n">inner</span><span class="p">,</span> <span class="n">seen</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span> <span class="k">for</span> <span class="n">inner</span> <span class="ow">in</span> <span class="n">f</span><span class="p">)</span> <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">delabel</span><span class="p">(</span><span class="n">inner</span><span class="p">,</span> <span class="n">seen</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span> <span class="k">for</span> <span class="n">inner</span> <span class="ow">in</span> <span class="n">f</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">delabel</span><span class="p">(</span><span class="n">foo</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">delabel</span><span class="p">(</span><span class="n">foo</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="n">a1</span><span class="p">,),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a1</span><span class="p">)),</span> <span class="p">((</span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">),</span> <span class="p">(</span><span class="n">n3</span><span class="p">,)))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="n">a1</span><span class="p">,),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a1</span><span class="p">)),</span> <span class="p">((</span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">),</span> <span class="p">(</span><span class="n">n3</span><span class="p">,)))</span>
@ -1114,7 +1114,7 @@ of how many labels of each domain it has “seen”.</p>
</section> </section>
<section id="unify-version-3"> <section id="unify-version-3">
<h4><code class="docutils literal notranslate"><span class="pre">unify()</span></code> version 3<a class="headerlink" href="#unify-version-3" title="Permalink to this headline"></a></h4> <h4><code class="docutils literal notranslate"><span class="pre">unify()</span></code> version 3<a class="headerlink" href="#unify-version-3" title="Permalink to this headline"></a></h4>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span> <span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">s</span> <span class="o">=</span> <span class="p">{}</span> <span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">elif</span> <span class="n">s</span><span class="p">:</span> <span class="k">elif</span> <span class="n">s</span><span class="p">:</span>
@ -1162,7 +1162,7 @@ of how many labels of each domain it has “seen”.</p>
</pre></div> </pre></div>
</div> </div>
<p>Rewrite the stack effect comments:</p> <p>Rewrite the stack effect comments:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">defs</span><span class="p">():</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">defs</span><span class="p">():</span>
<span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">]),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">]),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
@ -1215,10 +1215,10 @@ of how many labels of each domain it has “seen”.</p>
<span class="k">return</span> <span class="nb">locals</span><span class="p">()</span> <span class="k">return</span> <span class="nb">locals</span><span class="p">()</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">DEFS</span> <span class="o">=</span> <span class="n">defs</span><span class="p">()</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DEFS</span> <span class="o">=</span> <span class="n">defs</span><span class="p">()</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">DEFS</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">DEFS</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
<span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">&#39;=&#39;</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span> <span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">&#39;=&#39;</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -1250,27 +1250,27 @@ of how many labels of each domain it has “seen”.</p>
<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">DEFS</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">DEFS</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
<section id="compose-dup-and-mul"> <section id="compose-dup-and-mul">
<h4>Compose <code class="docutils literal notranslate"><span class="pre">dup</span></code> and <code class="docutils literal notranslate"><span class="pre">mul</span></code><a class="headerlink" href="#compose-dup-and-mul" title="Permalink to this headline"></a></h4> <h4>Compose <code class="docutils literal notranslate"><span class="pre">dup</span></code> and <code class="docutils literal notranslate"><span class="pre">mul</span></code><a class="headerlink" href="#compose-dup-and-mul" title="Permalink to this headline"></a></h4>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">n1</span><span class="p">,),</span> <span class="p">(</span><span class="n">n2</span><span class="p">,))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">n1</span><span class="p">,),</span> <span class="p">(</span><span class="n">n2</span><span class="p">,))</span>
</pre></div> </pre></div>
</div> </div>
<p>Revisit the <code class="docutils literal notranslate"><span class="pre">F</span></code> function, works fine.</p> <p>Revisit the <code class="docutils literal notranslate"><span class="pre">F</span></code> function, works fine.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">))</span>
<span class="n">F</span> <span class="n">F</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">a3</span><span class="p">,</span> <span class="n">a4</span><span class="p">,</span> <span class="n">a5</span><span class="p">),</span> <span class="p">((</span><span class="n">a4</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">a3</span><span class="p">,</span> <span class="n">a4</span><span class="p">,</span> <span class="n">a5</span><span class="p">),</span> <span class="p">((</span><span class="n">a4</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">F</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">F</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a4</span> <span class="n">a5</span> <span class="o">--</span> <span class="p">[</span><span class="n">a4</span> <span class="n">a3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a4</span> <span class="n">a5</span> <span class="o">--</span> <span class="p">[</span><span class="n">a4</span> <span class="n">a3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
@ -1278,25 +1278,25 @@ of how many labels of each domain it has “seen”.</p>
</div> </div>
<p>Some otherwise inefficient functions are no longer to be feared. We can <p>Some otherwise inefficient functions are no longer to be feared. We can
also get the effect of combinators in some limited cases.</p> also get the effect of combinators in some limited cases.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">neato</span><span class="p">(</span><span class="o">*</span><span class="n">funcs</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">neato</span><span class="p">(</span><span class="o">*</span><span class="n">funcs</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="n">funcs</span><span class="p">))</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="n">funcs</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># e.g. [swap] dip</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># e.g. [swap] dip</span>
<span class="n">neato</span><span class="p">(</span><span class="n">rollup</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">)</span> <span class="n">neato</span><span class="p">(</span><span class="n">rollup</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a3</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a3</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># e.g. [popop] dipd</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># e.g. [popop] dipd</span>
<span class="n">neato</span><span class="p">(</span><span class="n">popdd</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">pop</span><span class="p">)</span> <span class="n">neato</span><span class="p">(</span><span class="n">popdd</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">pop</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a4</span> <span class="o">--</span> <span class="n">a3</span> <span class="n">a4</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a4</span> <span class="o">--</span> <span class="n">a3</span> <span class="n">a4</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Reverse the order of the top three items.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Reverse the order of the top three items.</span>
<span class="n">neato</span><span class="p">(</span><span class="n">rollup</span><span class="p">,</span> <span class="n">swap</span><span class="p">)</span> <span class="n">neato</span><span class="p">(</span><span class="n">rollup</span><span class="p">,</span> <span class="n">swap</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -1308,7 +1308,7 @@ also get the effect of combinators in some limited cases.</p>
<h4><code class="docutils literal notranslate"><span class="pre">compile_()</span></code> version 2<a class="headerlink" href="#compile-version-2" title="Permalink to this headline"></a></h4> <h4><code class="docutils literal notranslate"><span class="pre">compile_()</span></code> version 2<a class="headerlink" href="#compile-version-2" title="Permalink to this headline"></a></h4>
<p>Because the type labels represent themselves as valid Python identifiers <p>Because the type labels represent themselves as valid Python identifiers
the <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> function doesn’t need to generate them anymore:</p> the <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> function doesn’t need to generate them anymore:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">f</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">f</span>
<span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span> <span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">)</span> <span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">)</span>
@ -1323,7 +1323,7 @@ the <code class="docutils literal notranslate"><span class="pre">compile_()</spa
<span class="s1"> return </span><span class="si">%s</span><span class="s1">&#39;&#39;&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">doc</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span> <span class="s1"> return </span><span class="si">%s</span><span class="s1">&#39;&#39;&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">doc</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;F&#39;</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;F&#39;</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
@ -1334,7 +1334,7 @@ the <code class="docutils literal notranslate"><span class="pre">compile_()</spa
</div> </div>
<p>But it cannot magically create new functions that involve e.g. math and <p>But it cannot magically create new functions that involve e.g. math and
such. Note that this is <em>not</em> a <code class="docutils literal notranslate"><span class="pre">sqr</span></code> function implementation:</p> such. Note that this is <em>not</em> a <code class="docutils literal notranslate"><span class="pre">sqr</span></code> function implementation:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;sqr&#39;</span><span class="p">,</span> <span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;sqr&#39;</span><span class="p">,</span> <span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">sqr</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">sqr</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
@ -1356,14 +1356,14 @@ functions (at least) are already wrappers it should be straightforward.)</p>
<p>The functions that <em>can</em> be compiled are the ones that have only <p>The functions that <em>can</em> be compiled are the ones that have only
<code class="docutils literal notranslate"><span class="pre">AnyJoyType</span></code> and <code class="docutils literal notranslate"><span class="pre">StackJoyType</span></code> labels in their stack effect <code class="docutils literal notranslate"><span class="pre">AnyJoyType</span></code> and <code class="docutils literal notranslate"><span class="pre">StackJoyType</span></code> labels in their stack effect
comments. We can write a function to check that:</p> comments. We can write a function to check that:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">imap</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">imap</span>
<span class="k">def</span> <span class="nf">compilable</span><span class="p">(</span><span class="n">f</span><span class="p">):</span> <span class="k">def</span> <span class="nf">compilable</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
<span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">all</span><span class="p">(</span><span class="n">imap</span><span class="p">(</span><span class="n">compilable</span><span class="p">,</span> <span class="n">f</span><span class="p">))</span> <span class="ow">or</span> <span class="n">stacky</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">all</span><span class="p">(</span><span class="n">imap</span><span class="p">(</span><span class="n">compilable</span><span class="p">,</span> <span class="n">f</span><span class="p">))</span> <span class="ow">or</span> <span class="n">stacky</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">defs</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">defs</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
<span class="k">if</span> <span class="n">compilable</span><span class="p">(</span><span class="n">stack_effect_comment</span><span class="p">):</span> <span class="k">if</span> <span class="n">compilable</span><span class="p">(</span><span class="n">stack_effect_comment</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">&#39;=&#39;</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span> <span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">&#39;=&#39;</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span>
</pre></div> </pre></div>
@ -1465,7 +1465,7 @@ first two rules’ <code class="docutils literal notranslate"><span class="pre">
the “truthiness” of <code class="docutils literal notranslate"><span class="pre">StackJoyType</span></code> to false to let e.g. the “truthiness” of <code class="docutils literal notranslate"><span class="pre">StackJoyType</span></code> to false to let e.g.
<code class="docutils literal notranslate"><span class="pre">joy.utils.stack.concat</span></code> work with our stack effect comment cons-list <code class="docutils literal notranslate"><span class="pre">joy.utils.stack.concat</span></code> work with our stack effect comment cons-list
tuples.)</p> tuples.)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
<span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">)</span> <span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">)</span>
<span class="k">if</span> <span class="n">s</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span> <span class="c1"># s can also be the empty dict, which is ok.</span> <span class="k">if</span> <span class="n">s</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span> <span class="c1"># s can also be the empty dict, which is ok.</span>
@ -1475,7 +1475,7 @@ tuples.)</p>
</div> </div>
<p>I don’t want to rewrite all the defs myself, so I’ll write a little <p>I don’t want to rewrite all the defs myself, so I’ll write a little
conversion function instead. This is programmer’s laziness.</p> conversion function instead. This is programmer’s laziness.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">sequence_to_stack</span><span class="p">(</span><span class="n">seq</span><span class="p">,</span> <span class="n">stack</span><span class="o">=</span><span class="n">StackJoyType</span><span class="p">(</span><span class="mi">23</span><span class="p">)):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">sequence_to_stack</span><span class="p">(</span><span class="n">seq</span><span class="p">,</span> <span class="n">stack</span><span class="o">=</span><span class="n">StackJoyType</span><span class="p">(</span><span class="mi">23</span><span class="p">)):</span>
<span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">seq</span><span class="p">:</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">item</span><span class="p">,</span> <span class="n">stack</span> <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">seq</span><span class="p">:</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">item</span><span class="p">,</span> <span class="n">stack</span>
<span class="k">return</span> <span class="n">stack</span> <span class="k">return</span> <span class="n">stack</span>
@ -1488,13 +1488,13 @@ conversion function instead. This is programmer’s laziness.</p>
<span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">NEW_DEFS</span><span class="p">)</span> <span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">NEW_DEFS</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">),</span> <span class="p">(</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">),</span> <span class="p">(</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="p">(</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">))))))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="p">(</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">))))))</span>
@ -1506,7 +1506,7 @@ conversion function instead. This is programmer’s laziness.</p>
<section id="doc-from-stack-effect-version-2"> <section id="doc-from-stack-effect-version-2">
<h3><code class="docutils literal notranslate"><span class="pre">doc_from_stack_effect()</span></code> version 2<a class="headerlink" href="#doc-from-stack-effect-version-2" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">doc_from_stack_effect()</span></code> version 2<a class="headerlink" href="#doc-from-stack-effect-version-2" title="Permalink to this headline"></a></h3>
<p>Clunky junk, but it will suffice for now.</p> <p>Clunky junk, but it will suffice for now.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">):</span>
<span class="n">switch</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="c1"># Do we need to display the &#39;...&#39; for the rest of the main stack?</span> <span class="n">switch</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="c1"># Do we need to display the &#39;...&#39; for the rest of the main stack?</span>
<span class="n">i</span><span class="p">,</span> <span class="n">o</span> <span class="o">=</span> <span class="n">_f</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">switch</span><span class="p">),</span> <span class="n">_f</span><span class="p">(</span><span class="n">outputs</span><span class="p">,</span> <span class="n">switch</span><span class="p">)</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span> <span class="o">=</span> <span class="n">_f</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">switch</span><span class="p">),</span> <span class="n">_f</span><span class="p">(</span><span class="n">outputs</span><span class="p">,</span> <span class="n">switch</span><span class="p">)</span>
<span class="k">if</span> <span class="n">switch</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span> <span class="k">if</span> <span class="n">switch</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
@ -1553,7 +1553,7 @@ conversion function instead. This is programmer’s laziness.</p>
<span class="k">return</span> <span class="s1">&#39;[</span><span class="si">%s</span><span class="s1">]&#39;</span> <span class="o">%</span> <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">return</span> <span class="s1">&#39;[</span><span class="si">%s</span><span class="s1">]&#39;</span> <span class="o">%</span> <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">NEW_DEFS</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">NEW_DEFS</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
<span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">&#39;=&#39;</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span> <span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">&#39;=&#39;</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -1587,7 +1587,7 @@ conversion function instead. This is programmer’s laziness.</p>
<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack</span><span class="p">)</span>
<span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">))</span> <span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">))</span>
<span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)))</span> <span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)))</span>
<span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">cons</span><span class="p">)))</span> <span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">cons</span><span class="p">)))</span>
@ -1602,13 +1602,13 @@ conversion function instead. This is programmer’s laziness.</p>
<span class="p">(</span><span class="o">...</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</span> <span class="n">a1</span> <span class="p">[</span><span class="n">a1</span> <span class="o">...</span><span class="p">])</span> <span class="p">(</span><span class="o">...</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</span> <span class="n">a1</span> <span class="p">[</span><span class="n">a1</span> <span class="o">...</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">ccons</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">ccons</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">...</span> <span class="n">a2</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="p">[[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">...</span><span class="p">])</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">...</span> <span class="n">a2</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="p">[[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">...</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">Q</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">ccons</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">Q</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">ccons</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span>
<span class="n">Q</span> <span class="n">Q</span>
</pre></div> </pre></div>
@ -1620,7 +1620,7 @@ conversion function instead. This is programmer’s laziness.</p>
<h4><code class="docutils literal notranslate"><span class="pre">compile_()</span></code> version 3<a class="headerlink" href="#compile-version-3" title="Permalink to this headline"></a></h4> <h4><code class="docutils literal notranslate"><span class="pre">compile_()</span></code> version 3<a class="headerlink" href="#compile-version-3" title="Permalink to this headline"></a></h4>
<p>This makes the <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> function pretty simple as the stack effect <p>This makes the <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> function pretty simple as the stack effect
comments are now already in the form needed for the Python code:</p> comments are now already in the form needed for the Python code:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="n">i</span><span class="p">,</span> <span class="n">o</span> <span class="o">=</span> <span class="n">f</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span> <span class="o">=</span> <span class="n">f</span>
<span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span> <span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span> <span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span>
@ -1630,7 +1630,7 @@ comments are now already in the form needed for the Python code:</p>
<span class="s1"> return </span><span class="si">%s</span><span class="s1">&#39;&#39;&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">doc</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span> <span class="s1"> return </span><span class="si">%s</span><span class="s1">&#39;&#39;&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">doc</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;Q&#39;</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;Q&#39;</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">Q</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">Q</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
@ -1639,35 +1639,35 @@ comments are now already in the form needed for the Python code:</p>
<span class="k">return</span> <span class="p">(((</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">s2</span><span class="p">),</span> <span class="p">((</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">s2</span><span class="p">))</span> <span class="k">return</span> <span class="p">(((</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">s2</span><span class="p">),</span> <span class="p">((</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">s2</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">unstack</span> <span class="o">=</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">unstack</span> <span class="o">=</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">enstacken</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="n">enstacken</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">unstack</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">unstack</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">enstacken</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">enstacken</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">0.</span><span class="p">])</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">0.</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">unstack</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">unstack</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">enstacken</span><span class="p">))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">enstacken</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">.</span><span class="mf">2.</span><span class="p">])</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">.</span><span class="mf">2.</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">unstack</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">unstack</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span>
@ -1679,14 +1679,14 @@ comments are now already in the form needed for the Python code:</p>
<section id="part-vi-multiple-stack-effects"> <section id="part-vi-multiple-stack-effects">
<h2>Part VI: Multiple Stack Effects<a class="headerlink" href="#part-vi-multiple-stack-effects" title="Permalink to this headline"></a></h2> <h2>Part VI: Multiple Stack Effects<a class="headerlink" href="#part-vi-multiple-stack-effects" title="Permalink to this headline"></a></h2>
<p>…</p> <p>…</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">IntJoyType</span><span class="p">(</span><span class="n">NumberJoyType</span><span class="p">):</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;i&#39;</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">IntJoyType</span><span class="p">(</span><span class="n">NumberJoyType</span><span class="p">):</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;i&#39;</span>
<span class="n">F</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">FloatJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span> <span class="n">F</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">FloatJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
<span class="n">I</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">IntJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span> <span class="n">I</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">IntJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">muls</span> <span class="o">=</span> <span class="p">[</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">muls</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">((</span><span class="n">I</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">((</span><span class="n">I</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span>
<span class="p">((</span><span class="n">F</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">((</span><span class="n">F</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span>
<span class="p">((</span><span class="n">I</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">((</span><span class="n">I</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span>
@ -1694,7 +1694,7 @@ comments are now already in the form needed for the Python code:</p>
<span class="p">]</span> <span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">muls</span><span class="p">:</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">muls</span><span class="p">:</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -1704,7 +1704,7 @@ comments are now already in the form needed for the Python code:</p>
<span class="p">(</span><span class="n">f1</span> <span class="n">f2</span> <span class="o">--</span> <span class="n">f3</span><span class="p">)</span> <span class="p">(</span><span class="n">f1</span> <span class="n">f2</span> <span class="o">--</span> <span class="n">f3</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">muls</span><span class="p">:</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">muls</span><span class="p">:</span>
<span class="k">try</span><span class="p">:</span> <span class="k">try</span><span class="p">:</span>
<span class="n">e</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span> <span class="n">e</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
<span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span> <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
@ -1716,7 +1716,7 @@ comments are now already in the form needed for the Python code:</p>
<span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span> <span class="p">(</span><span class="n">f1</span> <span class="n">f2</span> <span class="o">--</span> <span class="n">f3</span><span class="p">)</span> <span class="p">(</span><span class="n">f1</span> <span class="o">--</span> <span class="n">f2</span><span class="p">)</span> <span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span> <span class="p">(</span><span class="n">f1</span> <span class="n">f2</span> <span class="o">--</span> <span class="n">f3</span><span class="p">)</span> <span class="p">(</span><span class="n">f1</span> <span class="o">--</span> <span class="n">f2</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span>
<span class="k">def</span> <span class="nf">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span> <span class="k">def</span> <span class="nf">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
@ -1731,14 +1731,14 @@ comments are now already in the form needed for the Python code:</p>
<span class="k">return</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">)))</span> <span class="k">return</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">)))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="p">[</span><span class="n">mul</span><span class="p">]):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="p">[</span><span class="n">mul</span><span class="p">]):</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="n">muls</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="n">muls</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -1793,7 +1793,7 @@ disappears:</p>
<span class="p">{</span><span class="n">c</span><span class="p">:</span> <span class="n">a</span><span class="p">,</span> <span class="n">d</span><span class="p">:</span> <span class="n">e</span><span class="p">,</span> <span class="o">.</span><span class="mf">1.</span><span class="p">:</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">}</span> <span class="p">{</span><span class="n">c</span><span class="p">:</span> <span class="n">a</span><span class="p">,</span> <span class="n">d</span><span class="p">:</span> <span class="n">e</span><span class="p">,</span> <span class="o">.</span><span class="mf">1.</span><span class="p">:</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">}</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">KleeneStar</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">KleeneStar</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="n">kind</span> <span class="o">=</span> <span class="n">AnyJoyType</span> <span class="n">kind</span> <span class="o">=</span> <span class="n">AnyJoyType</span>
@ -1840,7 +1840,7 @@ disappears:</p>
<section id="unify-version-4"> <section id="unify-version-4">
<h4><code class="docutils literal notranslate"><span class="pre">unify()</span></code> version 4<a class="headerlink" href="#unify-version-4" title="Permalink to this headline"></a></h4> <h4><code class="docutils literal notranslate"><span class="pre">unify()</span></code> version 4<a class="headerlink" href="#unify-version-4" title="Permalink to this headline"></a></h4>
<p>Can now return multiple results…</p> <p>Can now return multiple results…</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span> <span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">s</span> <span class="o">=</span> <span class="p">{}</span> <span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">elif</span> <span class="n">s</span><span class="p">:</span> <span class="k">elif</span> <span class="n">s</span><span class="p">:</span>
@ -1911,21 +1911,21 @@ disappears:</p>
<span class="k">return</span> <span class="n">thing</span><span class="o">.</span><span class="vm">__class__</span> <span class="ow">in</span> <span class="p">{</span><span class="n">AnyJoyType</span><span class="p">,</span> <span class="n">StackJoyType</span><span class="p">}</span> <span class="k">return</span> <span class="n">thing</span><span class="o">.</span><span class="vm">__class__</span> <span class="ow">in</span> <span class="p">{</span><span class="n">AnyJoyType</span><span class="p">,</span> <span class="n">StackJoyType</span><span class="p">}</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">As</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">As</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">a</span> <span class="n">a</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
<span class="n">b</span> <span class="n">b</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">a</span><span class="p">),</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">a</span><span class="p">),</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -1933,7 +1933,7 @@ disappears:</p>
<span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="n">a10001</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)}</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span> <span class="p">(</span><span class="n">a10001</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span> <span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="n">a10001</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)}</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span> <span class="p">(</span><span class="n">a10001</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">a</span><span class="p">),</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">a</span><span class="p">),</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -1948,7 +1948,7 @@ disappears:</p>
<span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span> <span class="p">[</span><span class="n">a1</span><span class="o">*</span><span class="p">]</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span><span class="o">*</span><span class="p">]</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span> <span class="p">[</span><span class="n">a1</span><span class="o">*</span><span class="p">]</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span><span class="o">*</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">sum_</span> <span class="o">=</span> <span class="p">((</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">sum_</span> <span class="o">=</span> <span class="p">((</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">sum_</span><span class="p">)</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">sum_</span><span class="p">)</span>
</pre></div> </pre></div>
@ -1956,7 +1956,7 @@ disappears:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n0</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n0</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">f</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]))),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">f</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]))),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">f</span><span class="p">)</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">f</span><span class="p">)</span>
</pre></div> </pre></div>
@ -1964,7 +1964,7 @@ disappears:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="n">n1</span> <span class="n">n2</span> <span class="n">n3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="n">n1</span> <span class="n">n2</span> <span class="n">n3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">sum_</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">f</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">sum_</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">f</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">sum_</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">sum_</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
</pre></div> </pre></div>
</div> </div>
@ -1978,7 +1978,7 @@ disappears:</p>
<section id="compose-version-3"> <section id="compose-version-3">
<h4><code class="docutils literal notranslate"><span class="pre">compose()</span></code> version 3<a class="headerlink" href="#compose-version-3" title="Permalink to this headline"></a></h4> <h4><code class="docutils literal notranslate"><span class="pre">compose()</span></code> version 3<a class="headerlink" href="#compose-version-3" title="Permalink to this headline"></a></h4>
<p>This function has to be modified to yield multiple results.</p> <p>This function has to be modified to yield multiple results.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
<span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">)</span> <span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">s</span><span class="p">:</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">s</span><span class="p">:</span>
@ -1987,7 +1987,7 @@ disappears:</p>
<span class="k">yield</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">))</span> <span class="k">yield</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
<span class="k">for</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="ow">in</span> <span class="n">product</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span> <span class="k">for</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="ow">in</span> <span class="n">product</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
<span class="k">try</span><span class="p">:</span> <span class="k">try</span><span class="p">:</span>
<span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span> <span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
@ -2002,7 +2002,7 @@ disappears:</p>
<span class="k">yield</span> <span class="n">delabel</span><span class="p">(</span><span class="n">fg</span><span class="p">)</span> <span class="k">yield</span> <span class="n">delabel</span><span class="p">(</span><span class="n">fg</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="n">muls</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="n">muls</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -2010,14 +2010,14 @@ disappears:</p>
<span class="p">(</span><span class="n">i1</span> <span class="o">--</span> <span class="n">i2</span><span class="p">)</span> <span class="p">(</span><span class="n">i1</span> <span class="o">--</span> <span class="n">i2</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">n1</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">n1</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">cons</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">cons</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
@ -2025,7 +2025,7 @@ disappears:</p>
<span class="p">(</span><span class="n">n1</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span> <span class="p">(</span><span class="n">n1</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">sum_</span> <span class="o">=</span> <span class="p">(((</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">sum_</span> <span class="o">=</span> <span class="p">(((</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">cons</span><span class="p">),</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">cons</span><span class="p">),</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">sum_</span><span class="p">),</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">sum_</span><span class="p">),</span>
@ -2036,21 +2036,21 @@ disappears:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="p">([</span><span class="n">n1</span> <span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n0</span><span class="p">)</span> <span class="p">(</span><span class="n">n1</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="p">([</span><span class="n">n1</span> <span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n0</span><span class="p">)</span> <span class="p">(</span><span class="n">n1</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">4</span><span class="p">],</span> <span class="p">(</span><span class="n">As</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">4</span><span class="p">],</span> <span class="p">(</span><span class="n">As</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])))</span>
<span class="n">a</span> <span class="n">a</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a4</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a4</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">]))</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">]))</span>
<span class="n">b</span> <span class="n">b</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s2</span><span class="p">))</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s2</span><span class="p">))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">result</span> <span class="nb">print</span> <span class="n">result</span>
</pre></div> </pre></div>
</div> </div>
@ -2058,7 +2058,7 @@ disappears:</p>
<span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="n">a4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">a2</span><span class="p">:</span> <span class="n">a10003</span><span class="p">}</span> <span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="n">a4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">a2</span><span class="p">:</span> <span class="n">a10003</span><span class="p">}</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
<span class="nb">print</span> <span class="n">result</span> <span class="nb">print</span> <span class="n">result</span>
</pre></div> </pre></div>
</div> </div>
@ -2111,7 +2111,7 @@ stack effect we have to “split universes” again and return both.</p>
<p>We need a type variable for Joy functions that can go in our expressions <p>We need a type variable for Joy functions that can go in our expressions
and be used by the hybrid inferencer/interpreter. They have to store a and be used by the hybrid inferencer/interpreter. They have to store a
name and a list of stack effects.</p> name and a list of stack effects.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">FunctionJoyType</span><span class="p">(</span><span class="n">AnyJoyType</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">FunctionJoyType</span><span class="p">(</span><span class="n">AnyJoyType</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">sec</span><span class="p">,</span> <span class="n">number</span><span class="p">):</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">sec</span><span class="p">,</span> <span class="n">number</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">name</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">name</span>
@ -2131,12 +2131,12 @@ name and a list of stack effects.</p>
<h4>Specialized for Simple Functions and Combinators<a class="headerlink" href="#specialized-for-simple-functions-and-combinators" title="Permalink to this headline"></a></h4> <h4>Specialized for Simple Functions and Combinators<a class="headerlink" href="#specialized-for-simple-functions-and-combinators" title="Permalink to this headline"></a></h4>
<p>For non-combinator functions the stack effects list contains stack <p>For non-combinator functions the stack effects list contains stack
effect comments (represented by pairs of cons-lists as described above.)</p> effect comments (represented by pairs of cons-lists as described above.)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">SymbolJoyType</span><span class="p">(</span><span class="n">FunctionJoyType</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">SymbolJoyType</span><span class="p">(</span><span class="n">FunctionJoyType</span><span class="p">):</span>
<span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;F&#39;</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;F&#39;</span>
</pre></div> </pre></div>
</div> </div>
<p>For combinators the list contains Python functions.</p> <p>For combinators the list contains Python functions.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">CombinatorJoyType</span><span class="p">(</span><span class="n">FunctionJoyType</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">CombinatorJoyType</span><span class="p">(</span><span class="n">FunctionJoyType</span><span class="p">):</span>
<span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;C&#39;</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;C&#39;</span>
@ -2155,7 +2155,7 @@ effect comments (represented by pairs of cons-lists as described above.)</p>
</div> </div>
<p>For simple combinators that have only one effect (like <code class="docutils literal notranslate"><span class="pre">dip</span></code>) you only <p>For simple combinators that have only one effect (like <code class="docutils literal notranslate"><span class="pre">dip</span></code>) you only
need one function and it can be the combinator itself.</p> need one function and it can be the combinator itself.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">joy.library</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">joy.library</span>
<span class="n">dip</span> <span class="o">=</span> <span class="n">CombinatorJoyType</span><span class="p">(</span><span class="s1">&#39;dip&#39;</span><span class="p">,</span> <span class="p">[</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">dip</span><span class="p">],</span> <span class="mi">23</span><span class="p">)</span> <span class="n">dip</span> <span class="o">=</span> <span class="n">CombinatorJoyType</span><span class="p">(</span><span class="s1">&#39;dip&#39;</span><span class="p">,</span> <span class="p">[</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">dip</span><span class="p">],</span> <span class="mi">23</span><span class="p">)</span>
</pre></div> </pre></div>
@ -2163,7 +2163,7 @@ need one function and it can be the combinator itself.</p>
<p>For combinators that can have more than one effect (like <code class="docutils literal notranslate"><span class="pre">branch</span></code>) you <p>For combinators that can have more than one effect (like <code class="docutils literal notranslate"><span class="pre">branch</span></code>) you
have to write functions that each implement the action of one of the have to write functions that each implement the action of one of the
effects.</p> effects.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">branch_true</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">branch_true</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
<span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="p">(</span><span class="n">else_</span><span class="p">,</span> <span class="p">(</span><span class="n">flag</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span> <span class="o">=</span> <span class="n">stack</span> <span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="p">(</span><span class="n">else_</span><span class="p">,</span> <span class="p">(</span><span class="n">flag</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span> <span class="o">=</span> <span class="n">stack</span>
<span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">concat</span><span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span> <span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">concat</span><span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span>
@ -2189,7 +2189,7 @@ that expression.</p>
updated along with the stack effects after doing unification or we risk updated along with the stack effects after doing unification or we risk
losing useful information. This was a straightforward, if awkward, losing useful information. This was a straightforward, if awkward,
modification to the call structure of <code class="docutils literal notranslate"><span class="pre">meta_compose()</span></code> et. al.</p> modification to the call structure of <code class="docutils literal notranslate"><span class="pre">meta_compose()</span></code> et. al.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">ID</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># Identity function.</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">ID</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># Identity function.</span>
<span class="k">def</span> <span class="nf">infer</span><span class="p">(</span><span class="o">*</span><span class="n">expression</span><span class="p">):</span> <span class="k">def</span> <span class="nf">infer</span><span class="p">(</span><span class="o">*</span><span class="n">expression</span><span class="p">):</span>
@ -2249,7 +2249,7 @@ module (FIXME link to its docs here!) should be explained… There is
cruft to convert the definitions in <code class="docutils literal notranslate"><span class="pre">DEFS</span></code> to the new cruft to convert the definitions in <code class="docutils literal notranslate"><span class="pre">DEFS</span></code> to the new
<code class="docutils literal notranslate"><span class="pre">SymbolJoyType</span></code> objects, and some combinators. Here is an example of <code class="docutils literal notranslate"><span class="pre">SymbolJoyType</span></code> objects, and some combinators. Here is an example of
output from the current code :</p> output from the current code :</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span><span class="o">/</span><span class="mi">0</span> <span class="c1"># (Don&#39;t try to run this cell! It&#39;s not going to work. This is &quot;read only&quot; code heh..)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span><span class="o">/</span><span class="mi">0</span> <span class="c1"># (Don&#39;t try to run this cell! It&#39;s not going to work. This is &quot;read only&quot; code heh..)</span>
<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span><span class="nb">format</span><span class="o">=</span><span class="s1">&#39;</span><span class="si">%(message)s</span><span class="s1">&#39;</span><span class="p">,</span> <span class="n">stream</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">stdout</span><span class="p">,</span> <span class="n">level</span><span class="o">=</span><span class="n">logging</span><span class="o">.</span><span class="n">INFO</span><span class="p">)</span> <span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span><span class="nb">format</span><span class="o">=</span><span class="s1">&#39;</span><span class="si">%(message)s</span><span class="s1">&#39;</span><span class="p">,</span> <span class="n">stream</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">stdout</span><span class="p">,</span> <span class="n">level</span><span class="o">=</span><span class="n">logging</span><span class="o">.</span><span class="n">INFO</span><span class="p">)</span>
@ -2366,7 +2366,7 @@ relational</em> nature of the stack effect comments to “compute in reverse”
as it were. There’s a working demo of this at the end of the <code class="docutils literal notranslate"><span class="pre">types</span></code> as it were. There’s a working demo of this at the end of the <code class="docutils literal notranslate"><span class="pre">types</span></code>
module. But if you’re interested in all that you should just use Prolog!</p> module. But if you’re interested in all that you should just use Prolog!</p>
<p>Anyhow, type <em>checking</em> is a few easy steps away.</p> <p>Anyhow, type <em>checking</em> is a few easy steps away.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_ge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_ge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="nb">issubclass</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="vm">__class__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">)</span> <span class="k">return</span> <span class="p">(</span><span class="nb">issubclass</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="vm">__class__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">)</span>
<span class="ow">or</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">&#39;accept&#39;</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">&#39;accept&#39;</span><span class="p">)</span>
<span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">accept</span><span class="p">))</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">accept</span><span class="p">))</span>

36
docs/sphinx_docs/_build/html/notebooks/Zipper.html
View File

@ -42,7 +42,7 @@ the original paper: <a class="reference external" href="https://www.st.cs.uni-sa
Huet</a></p> Huet</a></p>
<p>Given a datastructure on the stack we can navigate through it, modify <p>Given a datastructure on the stack we can navigate through it, modify
it, and rebuild it using the “zipper” technique.</p> it, and rebuild it using the “zipper” technique.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div> </pre></div>
</div> </div>
<section id="trees"> <section id="trees">
@ -52,7 +52,7 @@ strings, Symbols (strings that are names of functions) and sequences
(aka lists, aka quoted literals, aka aggregates, etc…), but we can build (aka lists, aka quoted literals, aka aggregates, etc…), but we can build
<a class="reference external" href="https://en.wikipedia.org/wiki/Tree_%28data_structure%29">trees</a> out <a class="reference external" href="https://en.wikipedia.org/wiki/Tree_%28data_structure%29">trees</a> out
of sequences.</p> of sequences.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8]&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8]&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
@ -75,13 +75,13 @@ datastructure used to keep track of these items is the zipper.)</p>
show the trace so you can see how it works. If we were going to use show the trace so you can see how it works. If we were going to use
these a lot it would make sense to write Python versions for efficiency, these a lot it would make sense to write Python versions for efficiency,
but see below.</p> but see below.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-down == [] swap uncons swap&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-down == [] swap uncons swap&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-up == swons swap shunt&#39;</span><span class="p">)</span> <span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-up == swons swap shunt&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-right == [swons] cons dip uncons swap&#39;</span><span class="p">)</span> <span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-right == [swons] cons dip uncons swap&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-left == swons [uncons swap] dip swap&#39;</span><span class="p">)</span> <span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-left == swons [uncons swap] dip swap&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] z-down&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] z-down&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">z</span><span class="o">-</span><span class="n">down</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">z</span><span class="o">-</span><span class="n">down</span>
@ -93,7 +93,7 @@ but see below.</p>
<span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="o">.</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="o">.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[] [[2 [3 4 25 6] 7] 8] 1 z-right&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[] [[2 [3 4 25 6] 7] 8] 1 z-right&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="n">z</span><span class="o">-</span><span class="n">right</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="n">z</span><span class="o">-</span><span class="n">right</span>
@ -113,43 +113,43 @@ but see below.</p>
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="o">.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2 [3 4 25 6] 7] z-down&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2 [3 4 25 6] 7] z-down&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">2</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">2</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [] [[3 4 25 6] 7] 2 z-right&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [] [[3 4 25 6] 7] 2 z-right&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3 4 25 6] z-down&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3 4 25 6] z-down&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">3</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">3</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [] [4 25 6] 3 z-right&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [] [4 25 6] 3 z-right&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">4</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">4</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3] [25 6] 4 z-right&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3] [25 6] 4 z-right&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">25</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">25</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [4 3] [6] 25 sqr&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [4 3] [6] 25 sqr&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [4 3] [6] 625 z-up&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [4 3] [6] 625 z-up&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
@ -168,13 +168,13 @@ but see below.</p>
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="o">.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3 4 625 6] z-up&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3 4 625 6] z-up&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2 [3 4 625 6] 7] z-up&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2 [3 4 625 6] 7] z-up&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
@ -185,7 +185,7 @@ but see below.</p>
<h2><code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code><a class="headerlink" href="#dip-and-infra" title="Permalink to this headline"></a></h2> <h2><code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code><a class="headerlink" href="#dip-and-infra" title="Permalink to this headline"></a></h2>
<p>In Joy we have the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code> combinators which can “target” <p>In Joy we have the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code> combinators which can “target”
or “address” any particular item in a Joy tree structure.</p> or “address” any particular item in a Joy tree structure.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="p">[[[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="p">[[[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span>
@ -236,11 +236,11 @@ been embedded in a nested series of quoted programs, e.g.:</p>
</pre></div> </pre></div>
</div> </div>
<p>The <code class="docutils literal notranslate"><span class="pre">Z</span></code> function isn’t hard to make.</p> <p>The <code class="docutils literal notranslate"><span class="pre">Z</span></code> function isn’t hard to make.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Z == [[] cons cons] step i&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Z == [[] cons cons] step i&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>Here it is in action in a simplified scenario.</p> <p>Here it is in action in a simplified scenario.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;1 [2 3 4] Z&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;1 [2 3 4] Z&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="n">Z</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="n">Z</span>
@ -273,7 +273,7 @@ been embedded in a nested series of quoted programs, e.g.:</p>
</pre></div> </pre></div>
</div> </div>
<p>And here it is doing the main thing.</p> <p>And here it is doing the main thing.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z&#39;</span><span class="p">)</span> <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>

9
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@ -110,6 +110,14 @@
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations within a Tolerance</a></li> <li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations within a Tolerance</a></li>
</ul> </ul>
</li> </li>
<li class="toctree-l1"><a class="reference internal" href="Square_Spiral.html">Square Spiral Example Joy Code</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html#original-form">Original Form</a></li>
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html#translation-to-joy">Translation to Joy</a></li>
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html#putting-the-pieces-together">Putting the Pieces Together</a></li>
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html#turning-it-into-a-generator-with-x">Turning it into a Generator with <code class="docutils literal notranslate"><span class="pre">x</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html#conclusion">Conclusion</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a><ul> <li class="toctree-l1"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#trees">Trees</a></li> <li class="toctree-l2"><a class="reference internal" href="Zipper.html#trees">Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#zipper-in-joy">Zipper in Joy</a></li> <li class="toctree-l2"><a class="reference internal" href="Zipper.html#zipper-in-joy">Zipper in Joy</a></li>
@ -194,6 +202,7 @@
<li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li> <li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li> <li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li> <li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html">Square Spiral Example Joy Code</a></li>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li> <li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li> <li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li> <li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li>

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@ -34,6 +34,31 @@ itself.
.. _Concatinative: https://en.wikipedia.org/wiki/Concatenative_programming_language .. _Concatinative: https://en.wikipedia.org/wiki/Concatenative_programming_language
Example Code
--------------------------------------------------
Here is an example of Joy code::
[[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
It might seem unreadable but with a little familiarity it becomes just as
legible as any other notation. Some layout helps::
[ [[abs] ii <=]
[
[<>] [pop !-] ||
] &&
]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
This function accepts two integers on the stack and increments or
decrements one of them such that the new pair of numbers is the next
coordinate pair in a square spiral (like the kind used to construct an
Ulam Spiral). For more information see :doc:`notebooks/Square_Spiral`
Quick Start Quick Start
-------------------------------------------------- --------------------------------------------------

62
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@ -76,7 +76,7 @@ E.g.:
Implementation Implementation
-------------- --------------
.. code:: python .. code:: ipython2
from functools import partial as curry from functools import partial as curry
from itertools import product from itertools import product
@ -86,7 +86,7 @@ Implementation
The empty set and the set of just the empty string. The empty set and the set of just the empty string.
.. code:: python .. code:: ipython2
phi = frozenset() # ϕ phi = frozenset() # ϕ
y = frozenset({''}) # λ y = frozenset({''}) # λ
@ -101,7 +101,7 @@ alphabet with two symbols (if you had to.)
I chose the names ``O`` and ``l`` (uppercase “o” and lowercase “L”) to I chose the names ``O`` and ``l`` (uppercase “o” and lowercase “L”) to
look like ``0`` and ``1`` (zero and one) respectively. look like ``0`` and ``1`` (zero and one) respectively.
.. code:: python .. code:: ipython2
syms = O, l = frozenset({'0'}), frozenset({'1'}) syms = O, l = frozenset({'0'}), frozenset({'1'})
@ -123,7 +123,7 @@ expression* is one of:
Where ``R`` and ``S`` stand for *regular expressions*. Where ``R`` and ``S`` stand for *regular expressions*.
.. code:: python .. code:: ipython2
AND, CONS, KSTAR, NOT, OR = 'and cons * not or'.split() # Tags are just strings. AND, CONS, KSTAR, NOT, OR = 'and cons * not or'.split() # Tags are just strings.
@ -133,7 +133,7 @@ only, these datastructures are immutable.
String Representation of RE Datastructures String Representation of RE Datastructures
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def stringy(re): def stringy(re):
''' '''
@ -175,11 +175,11 @@ Match anything. Often spelled “.”
I = (0|1)* I = (0|1)*
.. code:: python .. code:: ipython2
I = (KSTAR, (OR, O, l)) I = (KSTAR, (OR, O, l))
.. code:: python .. code:: ipython2
print stringy(I) print stringy(I)
@ -201,14 +201,14 @@ The example expression from Brzozowski:
Note that it contains one of everything. Note that it contains one of everything.
.. code:: python .. code:: ipython2
a = (CONS, I, (CONS, l, (CONS, l, (CONS, l, I)))) a = (CONS, I, (CONS, l, (CONS, l, (CONS, l, I))))
b = (CONS, I, (CONS, O, l)) b = (CONS, I, (CONS, O, l))
c = (CONS, l, (KSTAR, l)) c = (CONS, l, (KSTAR, l))
it = (AND, a, (NOT, (OR, b, c))) it = (AND, a, (NOT, (OR, b, c)))
.. code:: python .. code:: ipython2
print stringy(it) print stringy(it)
@ -223,7 +223,7 @@ Note that it contains one of everything.
Let’s get that auxiliary predicate function ``δ`` out of the way. Let’s get that auxiliary predicate function ``δ`` out of the way.
.. code:: python .. code:: ipython2
def nully(R): def nully(R):
''' '''
@ -263,7 +263,7 @@ This is the straightforward version with no “compaction”. It works fine,
but does waaaay too much work because the expressions grow each but does waaaay too much work because the expressions grow each
derivation. derivation.
.. code:: python .. code:: ipython2
def D(symbol): def D(symbol):
@ -308,7 +308,7 @@ derivation.
Compaction Rules Compaction Rules
~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def _compaction_rule(relation, one, zero, a, b): def _compaction_rule(relation, one, zero, a, b):
return ( return (
@ -320,7 +320,7 @@ Compaction Rules
An elegant symmetry. An elegant symmetry.
.. code:: python .. code:: ipython2
# R ∧ I = I ∧ R = R # R ∧ I = I ∧ R = R
# R ∧ ϕ = ϕ ∧ R = ϕ # R ∧ ϕ = ϕ ∧ R = ϕ
@ -341,7 +341,7 @@ We can save re-processing by remembering results we have already
computed. RE datastructures are immutable and the ``derv()`` functions computed. RE datastructures are immutable and the ``derv()`` functions
are *pure* so this is fine. are *pure* so this is fine.
.. code:: python .. code:: ipython2
class Memo(object): class Memo(object):
@ -365,7 +365,7 @@ With “Compaction”
This version uses the rules above to perform compaction. It keeps the This version uses the rules above to perform compaction. It keeps the
expressions from growing too large. expressions from growing too large.
.. code:: python .. code:: ipython2
def D_compaction(symbol): def D_compaction(symbol):
@ -414,7 +414,7 @@ Let’s try it out…
(FIXME: redo.) (FIXME: redo.)
.. code:: python .. code:: ipython2
o, z = D_compaction('0'), D_compaction('1') o, z = D_compaction('0'), D_compaction('1')
REs = set() REs = set()
@ -533,10 +533,10 @@ machine transition table.
Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.” Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”
.. figure:: omg.svg .. figure:: attachment:omg.svg
:alt: State Machine Graph :alt: omg.svg
State Machine Graph omg.svg
Start at ``a`` and follow the transition arrows according to their Start at ``a`` and follow the transition arrows according to their
labels. Accepting states have a double outline. (Graphic generated with labels. Accepting states have a double outline. (Graphic generated with
@ -605,20 +605,20 @@ You can see the one-way nature of the ``g`` state and the ``hij`` “trap”
in the way that the ``.111.`` on the left-hand side of the ``&`` in the way that the ``.111.`` on the left-hand side of the ``&``
disappears once it has been matched. disappears once it has been matched.
.. code:: python .. code:: ipython2
from collections import defaultdict from collections import defaultdict
from pprint import pprint from pprint import pprint
from string import ascii_lowercase from string import ascii_lowercase
.. code:: python .. code:: ipython2
d0, d1 = D_compaction('0'), D_compaction('1') d0, d1 = D_compaction('0'), D_compaction('1')
``explore()`` ``explore()``
~~~~~~~~~~~~~ ~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def explore(re): def explore(re):
@ -645,7 +645,7 @@ disappears once it has been matched.
return table, accepting return table, accepting
.. code:: python .. code:: ipython2
table, accepting = explore(it) table, accepting = explore(it)
table table
@ -678,7 +678,7 @@ disappears once it has been matched.
.. code:: python .. code:: ipython2
accepting accepting
@ -697,7 +697,7 @@ Generate Diagram
Once we have the FSM table and the set of accepting states we can Once we have the FSM table and the set of accepting states we can
generate the diagram above. generate the diagram above.
.. code:: python .. code:: ipython2
_template = '''\ _template = '''\
digraph finite_state_machine { digraph finite_state_machine {
@ -722,7 +722,7 @@ generate the diagram above.
) )
) )
.. code:: python .. code:: ipython2
print make_graph(table, accepting) print make_graph(table, accepting)
@ -776,7 +776,7 @@ Trampoline Function
Python has no GOTO statement but we can fake it with a “trampoline” Python has no GOTO statement but we can fake it with a “trampoline”
function. function.
.. code:: python .. code:: ipython2
def trampoline(input_, jump_from, accepting): def trampoline(input_, jump_from, accepting):
I = iter(input_) I = iter(input_)
@ -793,7 +793,7 @@ Stream Functions
Little helpers to process the iterator of our data (a “stream” of “1” Little helpers to process the iterator of our data (a “stream” of “1”
and “0” characters, not bits.) and “0” characters, not bits.)
.. code:: python .. code:: ipython2
getch = lambda I: int(next(I)) getch = lambda I: int(next(I))
@ -816,7 +816,7 @@ code. (You have to imagine that these are GOTO statements in C or
branches in assembly and that the state names are branch destination branches in assembly and that the state names are branch destination
labels.) labels.)
.. code:: python .. code:: ipython2
a = lambda I: c if getch(I) else b a = lambda I: c if getch(I) else b
b = lambda I: _0(I) or d b = lambda I: _0(I) or d
@ -833,12 +833,12 @@ Note that the implementations of ``h`` and ``g`` are identical ergo
``h = g`` and we could eliminate one in the code but ``h`` is an ``h = g`` and we could eliminate one in the code but ``h`` is an
accepting state and ``g`` isn’t. accepting state and ``g`` isn’t.
.. code:: python .. code:: ipython2
def acceptable(input_): def acceptable(input_):
return trampoline(input_, a, {h, i}) return trampoline(input_, a, {h, i})
.. code:: python .. code:: ipython2
for n in range(2**5): for n in range(2**5):
s = bin(n)[2:] s = bin(n)[2:]

76
docs/sphinx_docs/notebooks/Generator_Programs.rst
View File

@ -3,7 +3,7 @@ Using ``x`` to Generate Values
Cf. jp-reprod.html Cf. jp-reprod.html
.. code:: python .. code:: ipython2
from notebook_preamble import J, V, define from notebook_preamble import J, V, define
@ -57,7 +57,7 @@ We can make a generator for the Natural numbers (0, 1, 2, …) by using
Let’s try it: Let’s try it:
.. code:: python .. code:: ipython2
V('[0 swap [dup ++] dip rest cons] x') V('[0 swap [dup ++] dip rest cons] x')
@ -81,7 +81,7 @@ Let’s try it:
After one application of ``x`` the quoted program contains ``1`` and After one application of ``x`` the quoted program contains ``1`` and
``0`` is below it on the stack. ``0`` is below it on the stack.
.. code:: python .. code:: ipython2
J('[0 swap [dup ++] dip rest cons] x x x x x pop') J('[0 swap [dup ++] dip rest cons] x x x x x pop')
@ -94,11 +94,11 @@ After one application of ``x`` the quoted program contains ``1`` and
``direco`` ``direco``
---------- ----------
.. code:: python .. code:: ipython2
define('direco == dip rest cons') define('direco == dip rest cons')
.. code:: python .. code:: ipython2
V('[0 swap [dup ++] direco] x') V('[0 swap [dup ++] direco] x')
@ -149,13 +149,13 @@ Reading from the bottom up:
G == [direco] cons [swap] swap concat cons G == [direco] cons [swap] swap concat cons
G == [direco] cons [swap] swoncat cons G == [direco] cons [swap] swoncat cons
.. code:: python .. code:: ipython2
define('G == [direco] cons [swap] swoncat cons') define('G == [direco] cons [swap] swoncat cons')
Let’s try it out: Let’s try it out:
.. code:: python .. code:: ipython2
J('0 [dup ++] G') J('0 [dup ++] G')
@ -165,7 +165,7 @@ Let’s try it out:
[0 swap [dup ++] direco] [0 swap [dup ++] direco]
.. code:: python .. code:: ipython2
J('0 [dup ++] G x x x pop') J('0 [dup ++] G x x x pop')
@ -178,7 +178,7 @@ Let’s try it out:
Powers of 2 Powers of 2
~~~~~~~~~~~ ~~~~~~~~~~~
.. code:: python .. code:: ipython2
J('1 [dup 1 <<] G x x x x x x x x x pop') J('1 [dup 1 <<] G x x x x x x x x x pop')
@ -194,7 +194,7 @@ Powers of 2
If we have one of these quoted programs we can drive it using ``times`` If we have one of these quoted programs we can drive it using ``times``
with the ``x`` combinator. with the ``x`` combinator.
.. code:: python .. code:: ipython2
J('23 [dup ++] G 5 [x] times') J('23 [dup ++] G 5 [x] times')
@ -226,11 +226,11 @@ int:
And pick them off by masking with 3 (binary 11) and then shifting the And pick them off by masking with 3 (binary 11) and then shifting the
int right two bits. int right two bits.
.. code:: python .. code:: ipython2
define('PE1.1 == dup [3 &] dip 2 >>') define('PE1.1 == dup [3 &] dip 2 >>')
.. code:: python .. code:: ipython2
V('14811 PE1.1') V('14811 PE1.1')
@ -252,7 +252,7 @@ int right two bits.
If we plug ``14811`` and ``[PE1.1]`` into our generator form… If we plug ``14811`` and ``[PE1.1]`` into our generator form…
.. code:: python .. code:: ipython2
J('14811 [PE1.1] G') J('14811 [PE1.1] G')
@ -264,7 +264,7 @@ If we plug ``14811`` and ``[PE1.1]`` into our generator form…
…we get a generator that works for seven cycles before it reaches zero: …we get a generator that works for seven cycles before it reaches zero:
.. code:: python .. code:: ipython2
J('[14811 swap [PE1.1] direco] 7 [x] times') J('[14811 swap [PE1.1] direco] 7 [x] times')
@ -280,11 +280,11 @@ Reset at Zero
We need a function that checks if the int has reached zero and resets it We need a function that checks if the int has reached zero and resets it
if so. if so.
.. code:: python .. code:: ipython2
define('PE1.1.check == dup [pop 14811] [] branch') define('PE1.1.check == dup [pop 14811] [] branch')
.. code:: python .. code:: ipython2
J('14811 [PE1.1.check PE1.1] G') J('14811 [PE1.1.check PE1.1] G')
@ -294,7 +294,7 @@ if so.
[14811 swap [PE1.1.check PE1.1] direco] [14811 swap [PE1.1.check PE1.1] direco]
.. code:: python .. code:: ipython2
J('[14811 swap [PE1.1.check PE1.1] direco] 21 [x] times') J('[14811 swap [PE1.1.check PE1.1] direco] 21 [x] times')
@ -316,7 +316,7 @@ In the PE1 problem we are asked to sum all the multiples of three and
five less than 1000. It’s worked out that we need to use all seven five less than 1000. It’s worked out that we need to use all seven
numbers sixty-six times and then four more. numbers sixty-six times and then four more.
.. code:: python .. code:: ipython2
J('7 66 * 4 +') J('7 66 * 4 +')
@ -328,7 +328,7 @@ numbers sixty-six times and then four more.
If we drive our generator 466 times and sum the stack we get 999. If we drive our generator 466 times and sum the stack we get 999.
.. code:: python .. code:: ipython2
J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times') J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times')
@ -338,7 +338,7 @@ If we drive our generator 466 times and sum the stack we get 999.
3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 [57 swap [PE1.1.check PE1.1] direco] 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 [57 swap [PE1.1.check PE1.1] direco]
.. code:: python .. code:: ipython2
J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum') J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum')
@ -351,13 +351,13 @@ If we drive our generator 466 times and sum the stack we get 999.
Project Euler Problem One Project Euler Problem One
------------------------- -------------------------
.. code:: python .. code:: ipython2
define('PE1.2 == + dup [+] dip') define('PE1.2 == + dup [+] dip')
Now we can add ``PE1.2`` to the quoted program given to ``G``. Now we can add ``PE1.2`` to the quoted program given to ``G``.
.. code:: python .. code:: ipython2
J('0 0 0 [PE1.1.check PE1.1] G 466 [x [PE1.2] dip] times popop') J('0 0 0 [PE1.1.check PE1.1] G 466 [x [PE1.2] dip] times popop')
@ -445,15 +445,15 @@ Putting it all together:
F == + [popdd over] cons infra uncons F == + [popdd over] cons infra uncons
fib_gen == [1 1 F] fib_gen == [1 1 F]
.. code:: python .. code:: ipython2
define('fib == + [popdd over] cons infra uncons') define('fib == + [popdd over] cons infra uncons')
.. code:: python .. code:: ipython2
define('fib_gen == [1 1 fib]') define('fib_gen == [1 1 fib]')
.. code:: python .. code:: ipython2
J('fib_gen 10 [x] times') J('fib_gen 10 [x] times')
@ -473,14 +473,14 @@ Now that we have a generator for the Fibonacci sequence, we need a
function that adds a term in the sequence to a sum if it is even, and function that adds a term in the sequence to a sum if it is even, and
``pop``\ s it otherwise. ``pop``\ s it otherwise.
.. code:: python .. code:: ipython2
define('PE2.1 == dup 2 % [+] [pop] branch') define('PE2.1 == dup 2 % [+] [pop] branch')
And a predicate function that detects when the terms in the series And a predicate function that detects when the terms in the series
“exceed four million”. “exceed four million”.
.. code:: python .. code:: ipython2
define('>4M == 4000000 >') define('>4M == 4000000 >')
@ -488,11 +488,11 @@ Now it’s straightforward to define ``PE2`` as a recursive function that
generates terms in the Fibonacci sequence until they exceed four million generates terms in the Fibonacci sequence until they exceed four million
and sums the even ones. and sums the even ones.
.. code:: python .. code:: ipython2
define('PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec') define('PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec')
.. code:: python .. code:: ipython2
J('PE2') J('PE2')
@ -535,7 +535,7 @@ So the Fibonacci sequence considered in terms of just parity would be:
Every third term is even. Every third term is even.
.. code:: python .. code:: ipython2
J('[1 0 fib] x x x') # To start the sequence with 1 1 2 3 instead of 1 2 3. J('[1 0 fib] x x x') # To start the sequence with 1 1 2 3 instead of 1 2 3.
@ -547,7 +547,7 @@ Every third term is even.
Drive the generator three times and ``popop`` the two odd terms. Drive the generator three times and ``popop`` the two odd terms.
.. code:: python .. code:: ipython2
J('[1 0 fib] x x x [popop] dipd') J('[1 0 fib] x x x [popop] dipd')
@ -557,11 +557,11 @@ Drive the generator three times and ``popop`` the two odd terms.
2 [3 2 fib] 2 [3 2 fib]
.. code:: python .. code:: ipython2
define('PE2.2 == x x x [popop] dipd') define('PE2.2 == x x x [popop] dipd')
.. code:: python .. code:: ipython2
J('[1 0 fib] 10 [PE2.2] times') J('[1 0 fib] 10 [PE2.2] times')
@ -574,7 +574,7 @@ Drive the generator three times and ``popop`` the two odd terms.
Replace ``x`` with our new driver function ``PE2.2`` and start our Replace ``x`` with our new driver function ``PE2.2`` and start our
``fib`` generator at ``1 0``. ``fib`` generator at ``1 0``.
.. code:: python .. code:: ipython2
J('0 [1 0 fib] PE2.2 [pop >4M] [popop] [[PE2.1] dip PE2.2] primrec') J('0 [1 0 fib] PE2.2 [pop >4M] [popop] [[PE2.1] dip PE2.2] primrec')
@ -593,11 +593,11 @@ modifications to the default ``x``?
An Interesting Variation An Interesting Variation
------------------------ ------------------------
.. code:: python .. code:: ipython2
define('codireco == cons dip rest cons') define('codireco == cons dip rest cons')
.. code:: python .. code:: ipython2
V('[0 [dup ++] codireco] x') V('[0 [dup ++] codireco] x')
@ -620,11 +620,11 @@ An Interesting Variation
0 [1 [dup ++] codireco] . 0 [1 [dup ++] codireco] .
.. code:: python .. code:: ipython2
define('G == [codireco] cons cons') define('G == [codireco] cons cons')
.. code:: python .. code:: ipython2
J('230 [dup ++] G 5 [x] times pop') J('230 [dup ++] G 5 [x] times pop')

24
docs/sphinx_docs/notebooks/Newton-Raphson.rst
View File

@ -7,7 +7,7 @@ to write a function that can compute the square root of a number.
Cf. `"Why Functional Programming Matters" by John Cf. `"Why Functional Programming Matters" by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__ Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
.. code:: python .. code:: ipython3
from notebook_preamble import J, V, define from notebook_preamble import J, V, define
@ -75,11 +75,11 @@ The generator can be written as:
1 [23 over / + 2 /] [dup] swoncat make_generator 1 [23 over / + 2 /] [dup] swoncat make_generator
1 [dup 23 over / + 2 /] make_generator 1 [dup 23 over / + 2 /] make_generator
.. code:: python .. code:: ipython3
define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator') define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
.. code:: python .. code:: ipython3
J('23 gsra') J('23 gsra')
@ -92,7 +92,7 @@ The generator can be written as:
Let's drive the generator a few time (with the ``x`` combinator) and Let's drive the generator a few time (with the ``x`` combinator) and
square the approximation to see how well it works... square the approximation to see how well it works...
.. code:: python .. code:: ipython3
J('23 gsra 6 [x popd] times first sqr') J('23 gsra 6 [x popd] times first sqr')
@ -142,7 +142,7 @@ Predicate
abs(a-b) ε <= abs(a-b) ε <=
(abs(a-b)<=ε) (abs(a-b)<=ε)
.. code:: python .. code:: ipython3
define('_within_P [first - abs] dip <=') define('_within_P [first - abs] dip <=')
@ -156,7 +156,7 @@ Base-Case
[b G] first [b G] first
b b
.. code:: python .. code:: ipython3
define('_within_B roll< popop first') define('_within_B roll< popop first')
@ -184,7 +184,7 @@ Pretty straightforward:
b [c G] ε within b [c G] ε within
.. code:: python .. code:: ipython3
define('_within_R [popd x] dip') define('_within_R [popd x] dip')
@ -199,14 +199,14 @@ The recursive function we have defined so far needs a slight preamble:
[a G] x ε ... [a G] x ε ...
a [b G] ε ... a [b G] ε ...
.. code:: python .. code:: ipython3
define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec') define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec')
define('sqrt gsra within') define('sqrt gsra within')
Try it out... Try it out...
.. code:: python .. code:: ipython3
J('36 sqrt') J('36 sqrt')
@ -216,7 +216,7 @@ Try it out...
6.0 6.0
.. code:: python .. code:: ipython3
J('23 sqrt') J('23 sqrt')
@ -228,7 +228,7 @@ Try it out...
Check it. Check it.
.. code:: python .. code:: ipython3
4.795831523312719**2 4.795831523312719**2
@ -241,7 +241,7 @@ Check it.
.. code:: python .. code:: ipython3
from math import sqrt from math import sqrt

98
docs/sphinx_docs/notebooks/Ordered_Binary_Trees.rst
View File

@ -36,7 +36,7 @@ implementation under the hood. (Where does the “type” come from? It has
a contingent existence predicated on the disciplined use of these a contingent existence predicated on the disciplined use of these
functions on otherwise undistinguished Joy datastructures.) functions on otherwise undistinguished Joy datastructures.)
.. code:: python .. code:: ipython2
from notebook_preamble import D, J, V, define, DefinitionWrapper from notebook_preamble import D, J, V, define, DefinitionWrapper
@ -87,11 +87,11 @@ Definition:
Tree-new == swap [[] []] cons cons Tree-new == swap [[] []] cons cons
.. code:: python .. code:: ipython2
define('Tree-new == swap [[] []] cons cons') define('Tree-new == swap [[] []] cons cons')
.. code:: python .. code:: ipython2
J('"v" "k" Tree-new') J('"v" "k" Tree-new')
@ -163,11 +163,11 @@ comparison operator:
P < == pop roll> pop first < P < == pop roll> pop first <
P == pop roll> pop first P == pop roll> pop first
.. code:: python .. code:: ipython2
define('P == pop roll> pop first') define('P == pop roll> pop first')
.. code:: python .. code:: ipython2
J('["old_key" 23 [] []] 17 "new_key" ["..."] P') J('["old_key" 23 [] []] 17 "new_key" ["..."] P')
@ -242,11 +242,11 @@ And so ``T`` is just:
T == cons cons [dipdd] cons infra T == cons cons [dipdd] cons infra
.. code:: python .. code:: ipython2
define('T == cons cons [dipdd] cons infra') define('T == cons cons [dipdd] cons infra')
.. code:: python .. code:: ipython2
J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] T') J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] T')
@ -266,7 +266,7 @@ This is very very similar to the above:
[key_n value_n left right] value key [Tree-add] E [key_n value_n left right] value key [Tree-add] E
[key_n value_n left right] value key [Tree-add] [P <] [Te] [Ee] ifte [key_n value_n left right] value key [Tree-add] [P <] [Te] [Ee] ifte
.. code:: python .. code:: ipython2
define('E == [P <] [Te] [Ee] ifte') define('E == [P <] [Te] [Ee] ifte')
@ -278,11 +278,11 @@ instead of the right, so the only difference is that it must use
Te == cons cons [dipd] cons infra Te == cons cons [dipd] cons infra
.. code:: python .. code:: ipython2
define('Te == cons cons [dipd] cons infra') define('Te == cons cons [dipd] cons infra')
.. code:: python .. code:: ipython2
J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] Te') J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] Te')
@ -320,11 +320,11 @@ Example:
key new_value [ left right] cons cons key new_value [ left right] cons cons
[key new_value left right] [key new_value left right]
.. code:: python .. code:: ipython2
define('Ee == pop swap roll< rest rest cons cons') define('Ee == pop swap roll< rest rest cons cons')
.. code:: python .. code:: ipython2
J('["k" "old_value" "left" "right"] "new_value" "k" ["Tree-add"] Ee') J('["k" "old_value" "left" "right"] "new_value" "k" ["Tree-add"] Ee')
@ -355,14 +355,14 @@ Putting it all together:
Tree-add == [popop not] [[pop] dipd Tree-new] [] [R] genrec Tree-add == [popop not] [[pop] dipd Tree-new] [] [R] genrec
.. code:: python .. code:: ipython2
define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P >] [T] [E] ifte] genrec') define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P >] [T] [E] ifte] genrec')
Examples Examples
~~~~~~~~ ~~~~~~~~
.. code:: python .. code:: ipython2
J('[] 23 "b" Tree-add') # Initial J('[] 23 "b" Tree-add') # Initial
@ -372,7 +372,7 @@ Examples
['b' 23 [] []] ['b' 23 [] []]
.. code:: python .. code:: ipython2
J('["b" 23 [] []] 88 "c" Tree-add') # Greater than J('["b" 23 [] []] 88 "c" Tree-add') # Greater than
@ -382,7 +382,7 @@ Examples
['b' 23 [] ['c' 88 [] []]] ['b' 23 [] ['c' 88 [] []]]
.. code:: python .. code:: ipython2
J('["b" 23 [] []] 88 "a" Tree-add') # Less than J('["b" 23 [] []] 88 "a" Tree-add') # Less than
@ -392,7 +392,7 @@ Examples
['b' 23 ['a' 88 [] []] []] ['b' 23 ['a' 88 [] []] []]
.. code:: python .. code:: ipython2
J('["b" 23 [] []] 88 "b" Tree-add') # Equal to J('["b" 23 [] []] 88 "b" Tree-add') # Equal to
@ -402,7 +402,7 @@ Examples
['b' 88 [] []] ['b' 88 [] []]
.. code:: python .. code:: ipython2
J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add') # Series. J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add') # Series.
@ -412,7 +412,7 @@ Examples
['b' 23 ['a' 88 [] []] ['c' 44 [] []]] ['b' 23 ['a' 88 [] []] ['c' 44 [] []]]
.. code:: python .. code:: ipython2
J('[] [[23 "b"] [88 "a"] [44 "c"]] [i Tree-add] step') J('[] [[23 "b"] [88 "a"] [44 "c"]] [i Tree-add] step')
@ -444,7 +444,7 @@ values:
------------------------- a < b ------------------------- a < b
L L
.. code:: python .. code:: ipython2
J("1 0 ['G'] ['E'] ['L'] cmp") J("1 0 ['G'] ['E'] ['L'] cmp")
@ -454,7 +454,7 @@ values:
'G' 'G'
.. code:: python .. code:: ipython2
J("1 1 ['G'] ['E'] ['L'] cmp") J("1 1 ['G'] ['E'] ['L'] cmp")
@ -464,7 +464,7 @@ values:
'E' 'E'
.. code:: python .. code:: ipython2
J("0 1 ['G'] ['E'] ['L'] cmp") J("0 1 ['G'] ['E'] ['L'] cmp")
@ -514,7 +514,7 @@ Or just:
P == over [popop popop first] nullary P == over [popop popop first] nullary
.. code:: python .. code:: ipython2
define('P == over [popop popop first] nullary') define('P == over [popop popop first] nullary')
@ -541,11 +541,11 @@ to understand:
Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec
.. code:: python .. code:: ipython2
define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec') define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec')
.. code:: python .. code:: ipython2
J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add') # Still works. J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add') # Still works.
@ -685,14 +685,14 @@ Working backward:
Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec
.. code:: python .. code:: ipython2
define('Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec') define('Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec')
Examples Examples
~~~~~~~~ ~~~~~~~~
.. code:: python .. code:: ipython2
J('[] [foo] Tree-iter') # It doesn't matter what F is as it won't be used. J('[] [foo] Tree-iter') # It doesn't matter what F is as it won't be used.
@ -702,7 +702,7 @@ Examples
.. code:: python .. code:: ipython2
J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [first] Tree-iter") J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [first] Tree-iter")
@ -712,7 +712,7 @@ Examples
'b' 'a' 'c' 'b' 'a' 'c'
.. code:: python .. code:: ipython2
J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [second] Tree-iter") J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [second] Tree-iter")
@ -731,7 +731,7 @@ to it will only occur once within it, and we can query it in
`:math:`O(\log_2 N)` <https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2>`__ `:math:`O(\log_2 N)` <https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2>`__
time. time.
.. code:: python .. code:: ipython2
J('[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step') J('[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step')
@ -741,11 +741,11 @@ time.
[3 0 [2 0 [] []] [9 0 [5 0 [4 0 [] []] [8 0 [6 0 [] [7 0 [] []]] []]] []]] [3 0 [2 0 [] []] [9 0 [5 0 [4 0 [] []] [8 0 [6 0 [] [7 0 [] []]] []]] []]]
.. code:: python .. code:: ipython2
define('to_set == [] swap [0 swap Tree-add] step') define('to_set == [] swap [0 swap Tree-add] step')
.. code:: python .. code:: ipython2
J('[3 9 5 2 8 6 7 8 4] to_set') J('[3 9 5 2 8 6 7 8 4] to_set')
@ -758,11 +758,11 @@ time.
And with that we can write a little program ``unique`` to remove And with that we can write a little program ``unique`` to remove
duplicate items from a list. duplicate items from a list.
.. code:: python .. code:: ipython2
define('unique == [to_set [first] Tree-iter] cons run') define('unique == [to_set [first] Tree-iter] cons run')
.. code:: python .. code:: ipython2
J('[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique') # Filter duplicate items. J('[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique') # Filter duplicate items.
@ -872,7 +872,7 @@ Let’s do a little semantic factoring:
Now we can sort sequences. Now we can sort sequences.
.. code:: python .. code:: ipython2
#define('Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec') #define('Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec')
@ -892,7 +892,7 @@ Now we can sort sequences.
.. code:: python .. code:: ipython2
J('[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order') J('[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order')
@ -1070,7 +1070,7 @@ So:
Tree-get == [pop not] swap [] [P [T>] [E] [T<] cmp] genrec Tree-get == [pop not] swap [] [P [T>] [E] [T<] cmp] genrec
.. code:: python .. code:: ipython2
# I don't want to deal with name conflicts with the above so I'm inlining everything here. # I don't want to deal with name conflicts with the above so I'm inlining everything here.
# The original Joy system has "hide" which is a meta-command which allows you to use named # The original Joy system has "hide" which is a meta-command which allows you to use named
@ -1088,7 +1088,7 @@ So:
] genrec ] genrec
''') ''')
.. code:: python .. code:: ipython2
J('["gary" 23 [] []] "mike" [popd " not in tree" +] Tree-get') J('["gary" 23 [] []] "mike" [popd " not in tree" +] Tree-get')
@ -1098,7 +1098,7 @@ So:
'mike not in tree' 'mike not in tree'
.. code:: python .. code:: ipython2
J('["gary" 23 [] []] "gary" [popop "err"] Tree-get') J('["gary" 23 [] []] "gary" [popop "err"] Tree-get')
@ -1108,7 +1108,7 @@ So:
23 23
.. code:: python .. code:: ipython2
J(''' J('''
@ -1124,7 +1124,7 @@ So:
2 2
.. code:: python .. code:: ipython2
J(''' J('''
@ -1500,7 +1500,7 @@ Refactoring
By the standards of the code I’ve written so far, this is a *huge* Joy By the standards of the code I’ve written so far, this is a *huge* Joy
program. program.
.. code:: python .. code:: ipython2
DefinitionWrapper.add_definitions(''' DefinitionWrapper.add_definitions('''
first_two == uncons uncons pop first_two == uncons uncons pop
@ -1519,7 +1519,7 @@ program.
Tree-Delete == [pop not] [pop] [R0] [R1] genrec Tree-Delete == [pop not] [pop] [R0] [R1] genrec
''', D) ''', D)
.. code:: python .. code:: ipython2
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'c' Tree-Delete ") J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'c' Tree-Delete ")
@ -1529,7 +1529,7 @@ program.
['a' 23 [] ['b' 88 [] []]] ['a' 23 [] ['b' 88 [] []]]
.. code:: python .. code:: ipython2
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'b' Tree-Delete ") J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'b' Tree-Delete ")
@ -1539,7 +1539,7 @@ program.
['a' 23 [] ['c' 44 [] []]] ['a' 23 [] ['c' 44 [] []]]
.. code:: python .. code:: ipython2
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'a' Tree-Delete ") J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'a' Tree-Delete ")
@ -1549,7 +1549,7 @@ program.
['b' 88 [] ['c' 44 [] []]] ['b' 88 [] ['c' 44 [] []]]
.. code:: python .. code:: ipython2
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' Tree-Delete ") J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' Tree-Delete ")
@ -1559,7 +1559,7 @@ program.
['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] ['a' 23 [] ['b' 88 [] ['c' 44 [] []]]]
.. code:: python .. code:: ipython2
J('[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step') J('[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step')
@ -1569,7 +1569,7 @@ program.
[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] [4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]]
.. code:: python .. code:: ipython2
J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete ") J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete ")
@ -1579,7 +1579,7 @@ program.
[4 0 [2 0 [1 0 [] []] []] [6 0 [5 0 [] []] [7 0 [] []]]] [4 0 [2 0 [1 0 [] []] []] [6 0 [5 0 [] []] [7 0 [] []]]]
.. code:: python .. code:: ipython2
J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete ") J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete ")

8
docs/sphinx_docs/notebooks/Quadratic.rst
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@ -1,4 +1,4 @@
.. code:: python .. code:: ipython2
from notebook_preamble import J, V, define from notebook_preamble import J, V, define
@ -81,13 +81,13 @@ the variables:
The three arguments are to the left, so we can “chop off” everything to The three arguments are to the left, so we can “chop off” everything to
the right and say it’s the definition of the ``quadratic`` function: the right and say it’s the definition of the ``quadratic`` function:
.. code:: python .. code:: ipython2
define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2') define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2')
Let’s try it out: Let’s try it out:
.. code:: python .. code:: ipython2
J('3 1 1 quadratic') J('3 1 1 quadratic')
@ -102,7 +102,7 @@ lines are the ``dip`` and ``dipd`` combinators building the main program
by incorporating the values on the stack. Then that program runs and you by incorporating the values on the stack. Then that program runs and you
get the results. This is pretty typical of Joy code. get the results. This is pretty typical of Joy code.
.. code:: python .. code:: ipython2
V('-5 1 4 quadratic') V('-5 1 4 quadratic')

54
docs/sphinx_docs/notebooks/Recursion_Combinators.rst
View File

@ -1,4 +1,4 @@
.. code:: python .. code:: ipython2
from notebook_preamble import D, DefinitionWrapper, J, V, define from notebook_preamble import D, DefinitionWrapper, J, V, define
@ -80,7 +80,7 @@ is a recursive function ``H :: A -> C`` that converts a value of type
It may be helpful to see this function implemented in imperative Python It may be helpful to see this function implemented in imperative Python
code. code.
.. code:: python .. code:: ipython2
def hylomorphism(c, F, P, G): def hylomorphism(c, F, P, G):
'''Return a hylomorphism function H.''' '''Return a hylomorphism function H.'''
@ -185,7 +185,7 @@ the left so we have a definition for ``hylomorphism``:
hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec
.. code:: python .. code:: ipython2
define('hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec') define('hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec')
@ -203,13 +203,13 @@ To sum a range of integers from 0 to *n* - 1:
- ``[G]`` is ``[-- dup]`` - ``[G]`` is ``[-- dup]``
- ``[F]`` is ``[+]`` - ``[F]`` is ``[+]``
.. code:: python .. code:: ipython2
define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism') define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism')
Let’s try it: Let’s try it:
.. code:: python .. code:: ipython2
J('5 triangular_number') J('5 triangular_number')
@ -219,7 +219,7 @@ Let’s try it:
10 10
.. code:: python .. code:: ipython2
J('[0 1 2 3 4 5 6] [triangular_number] map') J('[0 1 2 3 4 5 6] [triangular_number] map')
@ -391,10 +391,8 @@ values.
A == [P] [] [G] [swons] hylomorphism A == [P] [] [G] [swons] hylomorphism
``range`` et. al. ``range`` et. al. An example of an anamorphism is the ``range`` function which generates the list of integers from 0 to *n* - 1 given *n*.
~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
An example of an anamorphism is the ``range`` function which generates the list of integers from 0 to *n* - 1 given *n*.
Each of the above variations can be used to make four slightly different Each of the above variations can be used to make four slightly different
``range`` functions. ``range`` functions.
@ -407,11 +405,11 @@ Each of the above variations can be used to make four slightly different
H1 == [P] [pop c] [G] [dip F] genrec H1 == [P] [pop c] [G] [dip F] genrec
== [0 <=] [pop []] [-- dup] [dip swons] genrec == [0 <=] [pop []] [-- dup] [dip swons] genrec
.. code:: python .. code:: ipython2
define('range == [0 <=] [] [-- dup] [swons] hylomorphism') define('range == [0 <=] [] [-- dup] [swons] hylomorphism')
.. code:: python .. code:: ipython2
J('5 range') J('5 range')
@ -429,11 +427,11 @@ Each of the above variations can be used to make four slightly different
H2 == c swap [P] [pop] [G [F] dip] primrec H2 == c swap [P] [pop] [G [F] dip] primrec
== [] swap [0 <=] [pop] [-- dup [swons] dip] primrec == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec
.. code:: python .. code:: ipython2
define('range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec') define('range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec')
.. code:: python .. code:: ipython2
J('5 range_reverse') J('5 range_reverse')
@ -451,11 +449,11 @@ Each of the above variations can be used to make four slightly different
H3 == [P] [pop c] [[G] dupdip] [dip F] genrec H3 == [P] [pop c] [[G] dupdip] [dip F] genrec
== [0 <=] [pop []] [[--] dupdip] [dip swons] genrec == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec
.. code:: python .. code:: ipython2
define('ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec') define('ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec')
.. code:: python .. code:: ipython2
J('5 ranger') J('5 ranger')
@ -473,11 +471,11 @@ Each of the above variations can be used to make four slightly different
H4 == c swap [P] [pop] [[F] dupdip G ] primrec H4 == c swap [P] [pop] [[F] dupdip G ] primrec
== [] swap [0 <=] [pop] [[swons] dupdip --] primrec == [] swap [0 <=] [pop] [[swons] dupdip --] primrec
.. code:: python .. code:: ipython2
define('ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec') define('ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec')
.. code:: python .. code:: ipython2
J('5 ranger_reverse') J('5 ranger_reverse')
@ -503,7 +501,7 @@ and makes some new value.
C == [not] c [uncons swap] [F] hylomorphism C == [not] c [uncons swap] [F] hylomorphism
.. code:: python .. code:: ipython2
define('swuncons == uncons swap') # Awkward name. define('swuncons == uncons swap') # Awkward name.
@ -513,11 +511,11 @@ An example of a catamorphism is the sum function.
sum == [not] 0 [swuncons] [+] hylomorphism sum == [not] 0 [swuncons] [+] hylomorphism
.. code:: python .. code:: ipython2
define('sum == [not] 0 [swuncons] [+] hylomorphism') define('sum == [not] 0 [swuncons] [+] hylomorphism')
.. code:: python .. code:: ipython2
J('[5 4 3 2 1] sum') J('[5 4 3 2 1] sum')
@ -533,7 +531,7 @@ The ``step`` combinator
The ``step`` combinator will usually be better to use than The ``step`` combinator will usually be better to use than
``catamorphism``. ``catamorphism``.
.. code:: python .. code:: ipython2
J('[step] help') J('[step] help')
@ -562,11 +560,11 @@ The ``step`` combinator will usually be better to use than
.. code:: python .. code:: ipython2
define('sum == 0 swap [+] step') define('sum == 0 swap [+] step')
.. code:: python .. code:: ipython2
J('[5 4 3 2 1] sum') J('[5 4 3 2 1] sum')
@ -594,11 +592,11 @@ With:
G == -- G == --
P == 1 <= P == 1 <=
.. code:: python .. code:: ipython2
define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec') define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec')
.. code:: python .. code:: ipython2
J('5 factorial') J('5 factorial')
@ -637,11 +635,11 @@ We would use:
G == rest dup G == rest dup
P == not P == not
.. code:: python .. code:: ipython2
define('tails == [] swap [not] [pop] [rest dup [swons] dip] primrec') define('tails == [] swap [not] [pop] [rest dup [swons] dip] primrec')
.. code:: python .. code:: ipython2
J('[1 2 3] tails') J('[1 2 3] tails')

10
docs/sphinx_docs/notebooks/Replacing.rst
View File

@ -9,14 +9,14 @@ dictionary. However, there’s no function that does that. Adding a new
function to the dictionary is a meta-interpreter action, you have to do function to the dictionary is a meta-interpreter action, you have to do
it in Python, not Joy. it in Python, not Joy.
.. code:: python .. code:: ipython2
from notebook_preamble import D, J, V from notebook_preamble import D, J, V
A long trace A long trace
------------ ------------
.. code:: python .. code:: ipython2
V('[23 18] average') V('[23 18] average')
@ -81,7 +81,7 @@ An efficient ``sum`` function is already in the library. But for
``size`` we can use a “compiled” version hand-written in Python to speed ``size`` we can use a “compiled” version hand-written in Python to speed
up evaluation and make the trace more readable. up evaluation and make the trace more readable.
.. code:: python .. code:: ipython2
from joy.library import SimpleFunctionWrapper from joy.library import SimpleFunctionWrapper
from joy.utils.stack import iter_stack from joy.utils.stack import iter_stack
@ -99,7 +99,7 @@ up evaluation and make the trace more readable.
Now we replace the old version in the dictionary with the new version, Now we replace the old version in the dictionary with the new version,
and re-evaluate the expression. and re-evaluate the expression.
.. code:: python .. code:: ipython2
D['size'] = size D['size'] = size
@ -108,7 +108,7 @@ A shorter trace
You can see that ``size`` now executes in a single step. You can see that ``size`` now executes in a single step.
.. code:: python .. code:: ipython2
V('[23 18] average') V('[23 18] average')

421
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@ -0,0 +1,421 @@
.. code:: ipython3
from notebook_preamble import J, V, define
Square Spiral Example Joy Code
==============================
Here is the example of Joy code from the ``README`` file:
::
[[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
It might seem unreadable but with a little familiarity it becomes just
as legible as any other notation. Some layout helps:
::
[ [[abs] ii <=]
[
[<>] [pop !-] ||
] &&
]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
This function accepts two integers on the stack and increments or
decrements one of them such that the new pair of numbers is the next
coordinate pair in a square spiral (like the kind used to construct an
Ulam Spiral).
Original Form
-------------
It's adapted from `the original code on
StackOverflow <https://stackoverflow.com/questions/398299/looping-in-a-spiral/31864777#31864777>`__:
If all you're trying to do is generate the first N points in the
spiral (without the original problem's constraint of masking to an N
x M region), the code becomes very simple:
::
void spiral(const int N)
{
int x = 0;
int y = 0;
for(int i = 0; i < N; ++i)
{
cout << x << '\t' << y << '\n';
if(abs(x) <= abs(y) && (x != y || x >= 0))
x += ((y >= 0) ? 1 : -1);
else
y += ((x >= 0) ? -1 : 1);
}
}
Translation to Joy
------------------
I'm going to make a function that take two ints (``x`` and ``y``) and
generates the next pair, we'll turn it into a generator later using the
``x`` combinator.
First Boolean Predicate
~~~~~~~~~~~~~~~~~~~~~~~
We need a function that computes ``abs(x) <= abs(y)``, we can use ``ii``
to apply ``abs`` to both values and then compare them with ``<=``:
::
[abs] ii <=
I've defined two short-circuiting Boolean combinators ``&&`` and ``||``
that each accept two quoted predicate programs, run the first, and
conditionally run the second only if required (to compute the final
Boolean value). They run their predicate arguments ``nullary``.
.. code:: ipython3
define('&& [nullary] cons [nullary [0]] dip branch')
define('|| [nullary] cons [nullary] dip [1] branch')
Given those, we can define ``x != y || x >= 0`` as:
::
[<>] [pop 0 >=] ||
And ``(abs(x) <= abs(y) && (x != y || x >= 0))`` as:
::
[[abs] ii <=] [[<>] [pop 0 >=] ||] &&
It's a little rough, but, as I say, with a little familiarity it becomes
legible.
The Increment / Decrement Branches
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Turning to the branches of the main ``if`` statement:
::
x += ((y >= 0) ? 1 : -1);
Rewrite as a hybrid (pseudo-code) ``ifte`` expression:
::
[y >= 0] [x += 1] [X -= 1] ifte
Change each C phrase to Joy code:
::
[0 >=] [[++] dip] [[--] dip] ifte
Factor out the dip from each branch:
::
[0 >=] [[++]] [[--]] ifte dip
Similar logic applies to the other branch:
::
y += ((x >= 0) ? -1 : 1);
[x >= 0] [y -= 1] [y += 1] ifte
[pop 0 >=] [--] [++] ifte
"Not Negative"
~~~~~~~~~~~~~~
.. code:: ipython3
define('!- 0 >=')
Putting the Pieces Together
---------------------------
We can assemble the three functions we just defined in quotes and give
them them to the ``ifte`` combinator. With some arrangement to show off
the symmetry of the two branches, we have:
::
[[[abs] ii <=] [[<>] [pop !-] ||] &&]
[[ !-] [[++]] [[--]] ifte dip]
[[pop !-] [--] [++] ifte ]
ifte
As I was writing this up I realized that, since the ``&&`` combinator
doesn't consume the stack (below its quoted args), I can unquote the
predicate, swap the branches, and use the ``branch`` combinator instead
of ``ifte``:
::
[[abs] ii <=] [[<>] [pop !-] ||] &&
[[pop !-] [--] [++] ifte ]
[[ !-] [[++]] [[--]] ifte dip]
branch
.. code:: ipython3
define('spiral_next [[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte')
Let's try it out:
.. code:: ipython3
J('0 0 spiral_next')
.. parsed-literal::
1 0
.. code:: ipython3
J('1 0 spiral_next')
.. parsed-literal::
1 -1
.. code:: ipython3
J('1 -1 spiral_next')
.. parsed-literal::
0 -1
.. code:: ipython3
J('0 -1 spiral_next')
.. parsed-literal::
-1 -1
Turning it into a Generator with ``x``
--------------------------------------
It can be used with the x combinator to make a kind of generator for
spiral square coordinates.
We can use ``codireco`` to make a generator
::
codireco ::= cons dip rest cons
It will look like this:
::
[value [F] codireco]
Here's a trace of how it works:
::
[0 [dup ++] codireco] . x
[0 [dup ++] codireco] . 0 [dup ++] codireco
[0 [dup ++] codireco] 0 . [dup ++] codireco
[0 [dup ++] codireco] 0 [dup ++] . codireco
[0 [dup ++] codireco] 0 [dup ++] . cons dip rest cons
[0 [dup ++] codireco] [0 dup ++] . dip rest cons
. 0 dup ++ [0 [dup ++] codireco] rest cons
0 . dup ++ [0 [dup ++] codireco] rest cons
0 0 . ++ [0 [dup ++] codireco] rest cons
0 1 . [0 [dup ++] codireco] rest cons
0 1 [0 [dup ++] codireco] . rest cons
0 1 [[dup ++] codireco] . cons
0 [1 [dup ++] codireco] .
But first we have to change the ``spiral_next`` function to work on a
quoted pair of integers, and leave a copy of the pair on the stack.
From:
::
y x spiral_next
---------------------
y' x'
to:
::
[x y] [spiral_next] infra
-------------------------------
[x' y']
.. code:: ipython3
J('[0 0] [spiral_next] infra')
.. parsed-literal::
[0 1]
So our generator is:
::
[[x y] [dup [spiral_next] infra] codireco]
Or rather:
::
[[0 0] [dup [spiral_next] infra] codireco]
There is a function ``make_generator`` that will build the generator for
us out of the value and stepper function:
::
[0 0] [dup [spiral_next] infra] make_generator
----------------------------------------------------
[[0 0] [dup [spiral_next] infra] codireco]
Here it is in action:
.. code:: ipython3
J('[0 0] [dup [spiral_next] infra] make_generator x x x x pop')
.. parsed-literal::
[0 0] [0 1] [-1 1] [-1 0]
Four ``x`` combinators, four pairs of coordinates.
Conclusion
----------
So that's an example of Joy code. It's a straightforward translation of
the original. It's a little long for a single definition, you might
break it up like so:
::
_spn_P ::= [[abs] ii <=] [[<>] [pop !-] ||] &&
_spn_T ::= [ !-] [[++]] [[--]] ifte dip
_spn_E ::= [pop !-] [--] [++] ifte
spiral_next ::= _spn_P [_spn_E] [_spn_T] branch
This way it's easy to see that the function is a branch with two
quasi-symmetrical paths.
We then used this function to make a simple generator of coordinate
pairs, where the next pair in the series can be generated at any time by
using the ``x`` combinator on the generator (which is just a quoted
expression containing a copy of the current pair and the "stepper
function" to generate the next pair from that.)
.. code:: ipython3
define('_spn_P [[abs] ii <=] [[<>] [pop !-] ||] &&')
define('_spn_T [!-] [[++]] [[--]] ifte dip')
define('_spn_E [pop !-] [--] [++] ifte')
define('spiral_next _spn_P [_spn_E] [_spn_T] branch')
.. code:: ipython3
V('23 18 spiral_next')
.. parsed-literal::
. 23 18 spiral_next
23 . 18 spiral_next
23 18 . spiral_next
23 18 . _spn_P [_spn_E] [_spn_T] branch
23 18 . [[abs] ii <=] [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . && [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . [nullary] cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[<>] [pop !-] ||] [nullary] . cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] . [nullary [0]] dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] [nullary [0]] . dip branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . nullary [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] . [stack] dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [stack] . dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [[abs] ii <=] [stack] . dip infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . stack [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [18 23] . [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [18 23] [[abs] ii <=] . infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . [abs] ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . [dip] dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] [dip] . dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . dip [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 . abs 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 . 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [abs] . i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . abs <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 . <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
False . [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
False [18 23] . swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 [False] . first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False . [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False [0] . [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
23 18 False [0] [[[<>] [pop !-] ||] nullary] . branch [_spn_E] [_spn_T] branch
23 18 . 0 [_spn_E] [_spn_T] branch
23 18 0 . [_spn_E] [_spn_T] branch
23 18 0 [_spn_E] . [_spn_T] branch
23 18 0 [_spn_E] [_spn_T] . branch
23 18 . _spn_E
23 18 . [pop !-] [--] [++] ifte
23 18 [pop !-] . [--] [++] ifte
23 18 [pop !-] [--] . [++] ifte
23 18 [pop !-] [--] [++] . ifte
23 18 [pop !-] [--] [++] . [nullary not] dipd branch
23 18 [pop !-] [--] [++] [nullary not] . dipd branch
23 18 [pop !-] . nullary not [--] [++] branch
23 18 [pop !-] . [stack] dinfrirst not [--] [++] branch
23 18 [pop !-] [stack] . dinfrirst not [--] [++] branch
23 18 [pop !-] [stack] . dip infra first not [--] [++] branch
23 18 . stack [pop !-] infra first not [--] [++] branch
23 18 [18 23] . [pop !-] infra first not [--] [++] branch
23 18 [18 23] [pop !-] . infra first not [--] [++] branch
23 18 . pop !- [18 23] swaack first not [--] [++] branch
23 . !- [18 23] swaack first not [--] [++] branch
23 . 0 >= [18 23] swaack first not [--] [++] branch
23 0 . >= [18 23] swaack first not [--] [++] branch
True . [18 23] swaack first not [--] [++] branch
True [18 23] . swaack first not [--] [++] branch
23 18 [True] . first not [--] [++] branch
23 18 True . not [--] [++] branch
23 18 False . [--] [++] branch
23 18 False [--] . [++] branch
23 18 False [--] [++] . branch
23 18 . --
23 17 .

48
docs/sphinx_docs/notebooks/Treestep.rst
View File

@ -148,11 +148,11 @@ Working backwards:
Define ``treestep`` Define ``treestep``
------------------- -------------------
.. code:: python .. code:: ipython2
from notebook_preamble import D, J, V, define, DefinitionWrapper from notebook_preamble import D, J, V, define, DefinitionWrapper
.. code:: python .. code:: ipython2
DefinitionWrapper.add_definitions(''' DefinitionWrapper.add_definitions('''
@ -173,7 +173,7 @@ all nodes in a tree with this function:
sumtree == [pop 0] [] [sum +] treestep sumtree == [pop 0] [] [sum +] treestep
.. code:: python .. code:: ipython2
define('sumtree == [pop 0] [] [sum +] treestep') define('sumtree == [pop 0] [] [sum +] treestep')
@ -185,7 +185,7 @@ Running this function on an empty tree value gives zero:
------------------------------------ ------------------------------------
0 0
.. code:: python .. code:: ipython2
J('[] sumtree') # Empty tree. J('[] sumtree') # Empty tree.
@ -205,7 +205,7 @@ Running it on a non-empty node:
n m + n m +
n+m n+m
.. code:: python .. code:: ipython2
J('[23] sumtree') # No child trees. J('[23] sumtree') # No child trees.
@ -215,7 +215,7 @@ Running it on a non-empty node:
23 23
.. code:: python .. code:: ipython2
J('[23 []] sumtree') # Child tree, empty. J('[23 []] sumtree') # Child tree, empty.
@ -225,7 +225,7 @@ Running it on a non-empty node:
23 23
.. code:: python .. code:: ipython2
J('[23 [2 [4]] [3]] sumtree') # Non-empty child trees. J('[23 [2 [4]] [3]] sumtree') # Non-empty child trees.
@ -235,7 +235,7 @@ Running it on a non-empty node:
32 32
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] sumtree') # Etc... J('[23 [2 [8] [9]] [3] [4 []]] sumtree') # Etc...
@ -245,7 +245,7 @@ Running it on a non-empty node:
49 49
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep') # Alternate "spelling". J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep') # Alternate "spelling".
@ -255,7 +255,7 @@ Running it on a non-empty node:
49 49
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep') # Replace each node. J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep') # Replace each node.
@ -265,7 +265,7 @@ Running it on a non-empty node:
[23 [23 [23] [23]] [23] [23 []]] [23 [23 [23] [23]] [23] [23 []]]
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep') J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep')
@ -275,7 +275,7 @@ Running it on a non-empty node:
[1 [1 [1] [1]] [1] [1 []]] [1 [1 [1] [1]] [1] [1 []]]
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree') J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree')
@ -285,7 +285,7 @@ Running it on a non-empty node:
6 6
.. code:: python .. code:: ipython2
J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function. J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function.
@ -295,7 +295,7 @@ Running it on a non-empty node:
6 6
.. code:: python .. code:: ipython2
J('[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function. J('[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function.
@ -339,7 +339,7 @@ Traversal
This doesn’t quite work: This doesn’t quite work:
.. code:: python .. code:: ipython2
J('[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep') J('[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep')
@ -369,7 +369,7 @@ So:
[] [first] [flatten cons] treestep [] [first] [flatten cons] treestep
.. code:: python .. code:: ipython2
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep') J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep')
@ -401,7 +401,7 @@ So:
[] [i roll< swons concat] [first] treestep [] [i roll< swons concat] [first] treestep
.. code:: python .. code:: ipython2
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll< swons concat] treestep') J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll< swons concat] treestep')
@ -429,7 +429,7 @@ Plugging in our BTree structure:
[key value] N [left right] [K] C [key value] N [left right] [K] C
.. code:: python .. code:: ipython2
J('[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind') J('[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind')
@ -444,7 +444,7 @@ Plugging in our BTree structure:
Iteration through the nodes Iteration through the nodes
.. code:: python .. code:: ipython2
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] ["N"] [step] treegrind') J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] ["N"] [step] treegrind')
@ -456,7 +456,7 @@ Iteration through the nodes
Sum the nodes’ keys. Sum the nodes’ keys.
.. code:: python .. code:: ipython2
J('0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind') J('0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind')
@ -468,7 +468,7 @@ Sum the nodes’ keys.
Rebuild the tree using ``map`` (imitating ``treestep``.) Rebuild the tree using ``map`` (imitating ``treestep``.)
.. code:: python .. code:: ipython2
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind') J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind')
@ -574,7 +574,7 @@ Putting it together
To me, that seems simpler than the ``genrec`` version. To me, that seems simpler than the ``genrec`` version.
.. code:: python .. code:: ipython2
DefinitionWrapper.add_definitions(''' DefinitionWrapper.add_definitions('''
@ -587,7 +587,7 @@ To me, that seems simpler than the ``genrec`` version.
''', D) ''', D)
.. code:: python .. code:: ipython2
J('''\ J('''\
@ -603,7 +603,7 @@ To me, that seems simpler than the ``genrec`` version.
15 15
.. code:: python .. code:: ipython2
J('''\ J('''\

30
docs/sphinx_docs/notebooks/TypeChecking.rst
View File

@ -1,7 +1,7 @@
Type Checking Type Checking
============= =============
.. code:: python .. code:: ipython2
import logging, sys import logging, sys
@ -11,7 +11,7 @@ Type Checking
level=logging.INFO, level=logging.INFO,
) )
.. code:: python .. code:: ipython2
from joy.utils.types import ( from joy.utils.types import (
doc_from_stack_effect, doc_from_stack_effect,
@ -22,7 +22,7 @@ Type Checking
JoyTypeError, JoyTypeError,
) )
.. code:: python .. code:: ipython2
D = FUNCTIONS.copy() D = FUNCTIONS.copy()
del D['product'] del D['product']
@ -31,7 +31,7 @@ Type Checking
An Example An Example
---------- ----------
.. code:: python .. code:: ipython2
fi, fo = infer(pop, swap, rolldown, rrest, ccons)[0] fi, fo = infer(pop, swap, rolldown, rrest, ccons)[0]
@ -46,7 +46,7 @@ An Example
40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘ 40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
.. code:: python .. code:: ipython2
print doc_from_stack_effect(fi, fo) print doc_from_stack_effect(fi, fo)
@ -56,13 +56,13 @@ An Example
([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1])
.. code:: python .. code:: ipython2
from joy.parser import text_to_expression from joy.parser import text_to_expression
from joy.utils.stack import stack_to_string from joy.utils.stack import stack_to_string
.. code:: python .. code:: ipython2
e = text_to_expression('0 1 2 [3 4]') # reverse order e = text_to_expression('0 1 2 [3 4]') # reverse order
print stack_to_string(e) print stack_to_string(e)
@ -73,7 +73,7 @@ An Example
[3 4] 2 1 0 [3 4] 2 1 0
.. code:: python .. code:: ipython2
u = unify(e, fi)[0] u = unify(e, fi)[0]
u u
@ -87,7 +87,7 @@ An Example
.. code:: python .. code:: ipython2
g = reify(u, (fi, fo)) g = reify(u, (fi, fo))
print doc_from_stack_effect(*g) print doc_from_stack_effect(*g)
@ -101,11 +101,11 @@ An Example
Unification Works “in Reverse” Unification Works “in Reverse”
------------------------------ ------------------------------
.. code:: python .. code:: ipython2
e = text_to_expression('[2 3]') e = text_to_expression('[2 3]')
.. code:: python .. code:: ipython2
u = unify(e, fo)[0] # output side, not input side u = unify(e, fo)[0] # output side, not input side
u u
@ -119,7 +119,7 @@ Unification Works “in Reverse”
.. code:: python .. code:: ipython2
g = reify(u, (fi, fo)) g = reify(u, (fi, fo))
print doc_from_stack_effect(*g) print doc_from_stack_effect(*g)
@ -133,7 +133,7 @@ Unification Works “in Reverse”
Failing a Check Failing a Check
--------------- ---------------
.. code:: python .. code:: ipython2
fi, fo = infer(dup, mul)[0] fi, fo = infer(dup, mul)[0]
@ -146,7 +146,7 @@ Failing a Check
31 (i1 -- i2) ∘ 31 (i1 -- i2) ∘
.. code:: python .. code:: ipython2
e = text_to_expression('"two"') e = text_to_expression('"two"')
print stack_to_string(e) print stack_to_string(e)
@ -157,7 +157,7 @@ Failing a Check
'two' 'two'
.. code:: python .. code:: ipython2
try: try:
unify(e, fi) unify(e, fi)

228
docs/sphinx_docs/notebooks/Types.rst
View File

@ -184,7 +184,7 @@ Compiling ``pop∘swap∘roll<``
The simplest way to “compile” this function would be something like: The simplest way to “compile” this function would be something like:
.. code:: python .. code:: ipython2
def poswrd(s, e, d): def poswrd(s, e, d):
return rolldown(*swap(*pop(s, e, d))) return rolldown(*swap(*pop(s, e, d)))
@ -200,7 +200,7 @@ Looking ahead for a moment, from the stack effect comment:
We should be able to directly write out a Python function like: We should be able to directly write out a Python function like:
.. code:: python .. code:: ipython2
def poswrd(stack): def poswrd(stack):
(_, (a, (b, (c, stack)))) = stack (_, (a, (b, (c, stack)))) = stack
@ -393,7 +393,7 @@ And there you have it, the stack effect for
From this stack effect comment it should be possible to construct the From this stack effect comment it should be possible to construct the
following Python code: following Python code:
.. code:: python .. code:: ipython2
def F(stack): def F(stack):
(_, (d, (c, ((a, (b, S0)), stack)))) = stack (_, (d, (c, ((a, (b, S0)), stack)))) = stack
@ -408,7 +408,7 @@ Representing Stack Effect Comments in Python
I’m going to use pairs of tuples of type descriptors, which will be I’m going to use pairs of tuples of type descriptors, which will be
integers or tuples of type descriptors: integers or tuples of type descriptors:
.. code:: python .. code:: ipython2
roll_dn = (1, 2, 3), (2, 3, 1) roll_dn = (1, 2, 3), (2, 3, 1)
@ -419,7 +419,7 @@ integers or tuples of type descriptors:
``compose()`` ``compose()``
~~~~~~~~~~~~~ ~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def compose(f, g): def compose(f, g):
@ -465,7 +465,7 @@ integers or tuples of type descriptors:
``unify()`` ``unify()``
~~~~~~~~~~~ ~~~~~~~~~~~
.. code:: python .. code:: ipython2
def unify(u, v, s=None): def unify(u, v, s=None):
if s is None: if s is None:
@ -483,7 +483,7 @@ integers or tuples of type descriptors:
``update()`` ``update()``
~~~~~~~~~~~~ ~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def update(s, term): def update(s, term):
if not isinstance(term, tuple): if not isinstance(term, tuple):
@ -493,7 +493,7 @@ integers or tuples of type descriptors:
``relabel()`` ``relabel()``
~~~~~~~~~~~~~ ~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def relabel(left, right): def relabel(left, right):
return left, _1000(right) return left, _1000(right)
@ -517,7 +517,7 @@ integers or tuples of type descriptors:
``delabel()`` ``delabel()``
~~~~~~~~~~~~~ ~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
def delabel(f): def delabel(f):
s = {u: i for i, u in enumerate(sorted(_unique(f)))} s = {u: i for i, u in enumerate(sorted(_unique(f)))}
@ -551,7 +551,7 @@ At last we put it all together in a function ``C()`` that accepts two
stack effect comments and returns their composition (or raises and stack effect comments and returns their composition (or raises and
exception if they can’t be composed due to type conflicts.) exception if they can’t be composed due to type conflicts.)
.. code:: python .. code:: ipython2
def C(f, g): def C(f, g):
f, g = relabel(f, g) f, g = relabel(f, g)
@ -560,7 +560,7 @@ exception if they can’t be composed due to type conflicts.)
Let’s try it out. Let’s try it out.
.. code:: python .. code:: ipython2
C(pop, swap) C(pop, swap)
@ -573,7 +573,7 @@ Let’s try it out.
.. code:: python .. code:: ipython2
C(C(pop, swap), roll_dn) C(C(pop, swap), roll_dn)
@ -586,7 +586,7 @@ Let’s try it out.
.. code:: python .. code:: ipython2
C(swap, roll_dn) C(swap, roll_dn)
@ -599,7 +599,7 @@ Let’s try it out.
.. code:: python .. code:: ipython2
C(pop, C(swap, roll_dn)) C(pop, C(swap, roll_dn))
@ -612,7 +612,7 @@ Let’s try it out.
.. code:: python .. code:: ipython2
poswrd = reduce(C, (pop, swap, roll_dn)) poswrd = reduce(C, (pop, swap, roll_dn))
poswrd poswrd
@ -633,13 +633,13 @@ Here’s that trick to represent functions like ``rest`` and ``cons`` that
manipulate stacks. We use a cons-list of tuples and give the tails their manipulate stacks. We use a cons-list of tuples and give the tails their
own numbers. Then everything above already works. own numbers. Then everything above already works.
.. code:: python .. code:: ipython2
rest = ((1, 2),), (2,) rest = ((1, 2),), (2,)
cons = (1, 2), ((1, 2),) cons = (1, 2), ((1, 2),)
.. code:: python .. code:: ipython2
C(poswrd, rest) C(poswrd, rest)
@ -671,7 +671,7 @@ The translation table, if you will, would be:
0: 0, 0: 0,
} }
.. code:: python .. code:: ipython2
F = reduce(C, (pop, swap, roll_dn, rest, rest, cons, cons)) F = reduce(C, (pop, swap, roll_dn, rest, rest, cons, cons))
@ -699,11 +699,11 @@ Dealing with ``cons`` and ``uncons``
However, if we try to compose e.g. ``cons`` and ``uncons`` it won’t However, if we try to compose e.g. ``cons`` and ``uncons`` it won’t
work: work:
.. code:: python .. code:: ipython2
uncons = ((1, 2),), (1, 2) uncons = ((1, 2),), (1, 2)
.. code:: python .. code:: ipython2
try: try:
C(cons, uncons) C(cons, uncons)
@ -723,7 +723,7 @@ The problem is that the ``unify()`` function as written doesn’t handle
the case when both terms are tuples. We just have to add a clause to the case when both terms are tuples. We just have to add a clause to
deal with this recursively: deal with this recursively:
.. code:: python .. code:: ipython2
def unify(u, v, s=None): def unify(u, v, s=None):
if s is None: if s is None:
@ -753,7 +753,7 @@ deal with this recursively:
return s return s
.. code:: python .. code:: ipython2
C(cons, uncons) C(cons, uncons)
@ -771,7 +771,7 @@ Part III: Compiling Yin Functions
Now consider the Python function we would like to derive: Now consider the Python function we would like to derive:
.. code:: python .. code:: ipython2
def F_python(stack): def F_python(stack):
(_, (d, (c, ((a, (b, S0)), stack)))) = stack (_, (d, (c, ((a, (b, S0)), stack)))) = stack
@ -779,7 +779,7 @@ Now consider the Python function we would like to derive:
And compare it to the input stack effect comment tuple we just computed: And compare it to the input stack effect comment tuple we just computed:
.. code:: python .. code:: ipython2
F[0] F[0]
@ -816,7 +816,7 @@ Eh?
And the return tuple And the return tuple
.. code:: python .. code:: ipython2
F[1] F[1]
@ -848,7 +848,7 @@ Python Identifiers
We want to substitute Python identifiers for the integers. I’m going to We want to substitute Python identifiers for the integers. I’m going to
repurpose ``joy.parser.Symbol`` class for this: repurpose ``joy.parser.Symbol`` class for this:
.. code:: python .. code:: ipython2
from collections import defaultdict from collections import defaultdict
from joy.parser import Symbol from joy.parser import Symbol
@ -874,7 +874,7 @@ effect comment tuples to reasonable text format. There are some details
in how this code works that related to stuff later in the notebook, so in how this code works that related to stuff later in the notebook, so
you should skip it for now and read it later if you’re interested. you should skip it for now and read it later if you’re interested.
.. code:: python .. code:: ipython2
def doc_from_stack_effect(inputs, outputs): def doc_from_stack_effect(inputs, outputs):
return '(%s--%s)' % ( return '(%s--%s)' % (
@ -914,7 +914,7 @@ Now we can write a compiler function to emit Python source code. (The
underscore suffix distiguishes it from the built-in ``compile()`` underscore suffix distiguishes it from the built-in ``compile()``
function.) function.)
.. code:: python .. code:: ipython2
def compile_(name, f, doc=None): def compile_(name, f, doc=None):
if doc is None: if doc is None:
@ -932,7 +932,7 @@ function.)
Here it is in action: Here it is in action:
.. code:: python .. code:: ipython2
source = compile_('F', F) source = compile_('F', F)
@ -949,7 +949,7 @@ Here it is in action:
Compare: Compare:
.. code:: python .. code:: ipython2
def F_python(stack): def F_python(stack):
(_, (d, (c, ((a, (b, S0)), stack)))) = stack (_, (d, (c, ((a, (b, S0)), stack)))) = stack
@ -957,7 +957,7 @@ Compare:
Next steps: Next steps:
.. code:: python .. code:: ipython2
L = {} L = {}
@ -976,16 +976,16 @@ Next steps:
Let’s try it out: Let’s try it out:
.. code:: python .. code:: ipython2
from notebook_preamble import D, J, V from notebook_preamble import D, J, V
from joy.library import SimpleFunctionWrapper from joy.library import SimpleFunctionWrapper
.. code:: python .. code:: ipython2
D['F'] = SimpleFunctionWrapper(L['F']) D['F'] = SimpleFunctionWrapper(L['F'])
.. code:: python .. code:: ipython2
J('[4 5 ...] 2 3 1 F') J('[4 5 ...] 2 3 1 F')
@ -1012,7 +1012,7 @@ Compiling Library Functions
We can use ``compile_()`` to generate many primitives in the library We can use ``compile_()`` to generate many primitives in the library
from their stack effect comments: from their stack effect comments:
.. code:: python .. code:: ipython2
def defs(): def defs():
@ -1036,7 +1036,7 @@ from their stack effect comments:
return locals() return locals()
.. code:: python .. code:: ipython2
for name, stack_effect_comment in sorted(defs().items()): for name, stack_effect_comment in sorted(defs().items()):
print print
@ -1205,7 +1205,7 @@ Python class hierarchy of Joy types and use the ``issubclass()`` method
to establish domain ordering, as well as other handy behaviour that will to establish domain ordering, as well as other handy behaviour that will
make it fairly easy to reuse most of the code above. make it fairly easy to reuse most of the code above.
.. code:: python .. code:: ipython2
class AnyJoyType(object): class AnyJoyType(object):
@ -1251,14 +1251,14 @@ make it fairly easy to reuse most of the code above.
Mess with it a little: Mess with it a little:
.. code:: python .. code:: ipython2
from itertools import permutations from itertools import permutations
“Any” types can be specialized to numbers and stacks, but not vice “Any” types can be specialized to numbers and stacks, but not vice
versa: versa:
.. code:: python .. code:: ipython2
for a, b in permutations((A[0], N[0], S[0]), 2): for a, b in permutations((A[0], N[0], S[0]), 2):
print a, '>=', b, '->', a >= b print a, '>=', b, '->', a >= b
@ -1278,7 +1278,7 @@ Our crude `Numerical
Tower <https://en.wikipedia.org/wiki/Numerical_tower>`__ of *numbers* > Tower <https://en.wikipedia.org/wiki/Numerical_tower>`__ of *numbers* >
*floats* > *integers* works as well (but we’re not going to use it yet): *floats* > *integers* works as well (but we’re not going to use it yet):
.. code:: python .. code:: ipython2
for a, b in permutations((A[0], N[0], FloatJoyType(0), IntJoyType(0)), 2): for a, b in permutations((A[0], N[0], FloatJoyType(0), IntJoyType(0)), 2):
print a, '>=', b, '->', a >= b print a, '>=', b, '->', a >= b
@ -1303,13 +1303,13 @@ Tower <https://en.wikipedia.org/wiki/Numerical_tower>`__ of *numbers* >
Typing ``sqr`` Typing ``sqr``
~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
dup = (A[1],), (A[1], A[1]) dup = (A[1],), (A[1], A[1])
mul = (N[1], N[2]), (N[3],) mul = (N[1], N[2]), (N[3],)
.. code:: python .. code:: ipython2
dup dup
@ -1322,7 +1322,7 @@ Typing ``sqr``
.. code:: python .. code:: ipython2
mul mul
@ -1340,7 +1340,7 @@ Modifying the Inferencer
Re-labeling still works fine: Re-labeling still works fine:
.. code:: python .. code:: ipython2
foo = relabel(dup, mul) foo = relabel(dup, mul)
@ -1361,7 +1361,7 @@ Re-labeling still works fine:
The ``delabel()`` function needs an overhaul. It now has to keep track The ``delabel()`` function needs an overhaul. It now has to keep track
of how many labels of each domain it has “seen”. of how many labels of each domain it has “seen”.
.. code:: python .. code:: ipython2
from collections import Counter from collections import Counter
@ -1383,7 +1383,7 @@ of how many labels of each domain it has “seen”.
return tuple(delabel(inner, seen, c) for inner in f) return tuple(delabel(inner, seen, c) for inner in f)
.. code:: python .. code:: ipython2
delabel(foo) delabel(foo)
@ -1399,7 +1399,7 @@ of how many labels of each domain it has “seen”.
``unify()`` version 3 ``unify()`` version 3
^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^
.. code:: python .. code:: ipython2
def unify(u, v, s=None): def unify(u, v, s=None):
if s is None: if s is None:
@ -1449,7 +1449,7 @@ of how many labels of each domain it has “seen”.
Rewrite the stack effect comments: Rewrite the stack effect comments:
.. code:: python .. code:: ipython2
def defs(): def defs():
@ -1503,11 +1503,11 @@ Rewrite the stack effect comments:
return locals() return locals()
.. code:: python .. code:: ipython2
DEFS = defs() DEFS = defs()
.. code:: python .. code:: ipython2
for name, stack_effect_comment in sorted(DEFS.items()): for name, stack_effect_comment in sorted(DEFS.items()):
print name, '=', doc_from_stack_effect(*stack_effect_comment) print name, '=', doc_from_stack_effect(*stack_effect_comment)
@ -1543,14 +1543,14 @@ Rewrite the stack effect comments:
uncons = ([a1 .1.] -- a1 [.1.]) uncons = ([a1 .1.] -- a1 [.1.])
.. code:: python .. code:: ipython2
globals().update(DEFS) globals().update(DEFS)
Compose ``dup`` and ``mul`` Compose ``dup`` and ``mul``
^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. code:: python .. code:: ipython2
C(dup, mul) C(dup, mul)
@ -1565,7 +1565,7 @@ Compose ``dup`` and ``mul``
Revisit the ``F`` function, works fine. Revisit the ``F`` function, works fine.
.. code:: python .. code:: ipython2
F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons)) F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons))
F F
@ -1579,7 +1579,7 @@ Revisit the ``F`` function, works fine.
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*F) print doc_from_stack_effect(*F)
@ -1592,12 +1592,12 @@ Revisit the ``F`` function, works fine.
Some otherwise inefficient functions are no longer to be feared. We can Some otherwise inefficient functions are no longer to be feared. We can
also get the effect of combinators in some limited cases. also get the effect of combinators in some limited cases.
.. code:: python .. code:: ipython2
def neato(*funcs): def neato(*funcs):
print doc_from_stack_effect(*reduce(C, funcs)) print doc_from_stack_effect(*reduce(C, funcs))
.. code:: python .. code:: ipython2
# e.g. [swap] dip # e.g. [swap] dip
neato(rollup, swap, rolldown) neato(rollup, swap, rolldown)
@ -1608,7 +1608,7 @@ also get the effect of combinators in some limited cases.
(a1 a2 a3 -- a2 a1 a3) (a1 a2 a3 -- a2 a1 a3)
.. code:: python .. code:: ipython2
# e.g. [popop] dipd # e.g. [popop] dipd
neato(popdd, rolldown, pop) neato(popdd, rolldown, pop)
@ -1619,7 +1619,7 @@ also get the effect of combinators in some limited cases.
(a1 a2 a3 a4 -- a3 a4) (a1 a2 a3 a4 -- a3 a4)
.. code:: python .. code:: ipython2
# Reverse the order of the top three items. # Reverse the order of the top three items.
neato(rollup, swap) neato(rollup, swap)
@ -1636,7 +1636,7 @@ also get the effect of combinators in some limited cases.
Because the type labels represent themselves as valid Python identifiers Because the type labels represent themselves as valid Python identifiers
the ``compile_()`` function doesn’t need to generate them anymore: the ``compile_()`` function doesn’t need to generate them anymore:
.. code:: python .. code:: ipython2
def compile_(name, f, doc=None): def compile_(name, f, doc=None):
inputs, outputs = f inputs, outputs = f
@ -1652,7 +1652,7 @@ the ``compile_()`` function doesn’t need to generate them anymore:
%s = stack %s = stack
return %s''' % (name, doc, i, o) return %s''' % (name, doc, i, o)
.. code:: python .. code:: ipython2
print compile_('F', F) print compile_('F', F)
@ -1668,7 +1668,7 @@ the ``compile_()`` function doesn’t need to generate them anymore:
But it cannot magically create new functions that involve e.g. math and But it cannot magically create new functions that involve e.g. math and
such. Note that this is *not* a ``sqr`` function implementation: such. Note that this is *not* a ``sqr`` function implementation:
.. code:: python .. code:: ipython2
print compile_('sqr', C(dup, mul)) print compile_('sqr', C(dup, mul))
@ -1696,7 +1696,7 @@ The functions that *can* be compiled are the ones that have only
``AnyJoyType`` and ``StackJoyType`` labels in their stack effect ``AnyJoyType`` and ``StackJoyType`` labels in their stack effect
comments. We can write a function to check that: comments. We can write a function to check that:
.. code:: python .. code:: ipython2
from itertools import imap from itertools import imap
@ -1704,7 +1704,7 @@ comments. We can write a function to check that:
def compilable(f): def compilable(f):
return isinstance(f, tuple) and all(imap(compilable, f)) or stacky(f) return isinstance(f, tuple) and all(imap(compilable, f)) or stacky(f)
.. code:: python .. code:: ipython2
for name, stack_effect_comment in sorted(defs().items()): for name, stack_effect_comment in sorted(defs().items()):
if compilable(stack_effect_comment): if compilable(stack_effect_comment):
@ -1828,7 +1828,7 @@ the “truthiness” of ``StackJoyType`` to false to let e.g.
``joy.utils.stack.concat`` work with our stack effect comment cons-list ``joy.utils.stack.concat`` work with our stack effect comment cons-list
tuples.) tuples.)
.. code:: python .. code:: ipython2
def compose(f, g): def compose(f, g):
(f_in, f_out), (g_in, g_out) = f, g (f_in, f_out), (g_in, g_out) = f, g
@ -1840,7 +1840,7 @@ tuples.)
I don’t want to rewrite all the defs myself, so I’ll write a little I don’t want to rewrite all the defs myself, so I’ll write a little
conversion function instead. This is programmer’s laziness. conversion function instead. This is programmer’s laziness.
.. code:: python .. code:: ipython2
def sequence_to_stack(seq, stack=StackJoyType(23)): def sequence_to_stack(seq, stack=StackJoyType(23)):
for item in seq: stack = item, stack for item in seq: stack = item, stack
@ -1854,7 +1854,7 @@ conversion function instead. This is programmer’s laziness.
NEW_DEFS['swaack'] = (S[1], S[0]), (S[0], S[1]) NEW_DEFS['swaack'] = (S[1], S[0]), (S[0], S[1])
globals().update(NEW_DEFS) globals().update(NEW_DEFS)
.. code:: python .. code:: ipython2
C(stack, uncons) C(stack, uncons)
@ -1867,7 +1867,7 @@ conversion function instead. This is programmer’s laziness.
.. code:: python .. code:: ipython2
reduce(C, (stack, uncons, uncons)) reduce(C, (stack, uncons, uncons))
@ -1887,7 +1887,7 @@ The display function should be changed too.
Clunky junk, but it will suffice for now. Clunky junk, but it will suffice for now.
.. code:: python .. code:: ipython2
def doc_from_stack_effect(inputs, outputs): def doc_from_stack_effect(inputs, outputs):
switch = [False] # Do we need to display the '...' for the rest of the main stack? switch = [False] # Do we need to display the '...' for the rest of the main stack?
@ -1935,7 +1935,7 @@ Clunky junk, but it will suffice for now.
a.append(end) a.append(end)
return '[%s]' % ' '.join(a) return '[%s]' % ' '.join(a)
.. code:: python .. code:: ipython2
for name, stack_effect_comment in sorted(NEW_DEFS.items()): for name, stack_effect_comment in sorted(NEW_DEFS.items()):
print name, '=', doc_from_stack_effect(*stack_effect_comment) print name, '=', doc_from_stack_effect(*stack_effect_comment)
@ -1973,7 +1973,7 @@ Clunky junk, but it will suffice for now.
uncons = ([a1 .1.] -- a1 [.1.]) uncons = ([a1 .1.] -- a1 [.1.])
.. code:: python .. code:: ipython2
print ; print doc_from_stack_effect(*stack) print ; print doc_from_stack_effect(*stack)
print ; print doc_from_stack_effect(*C(stack, uncons)) print ; print doc_from_stack_effect(*C(stack, uncons))
@ -1993,7 +1993,7 @@ Clunky junk, but it will suffice for now.
(... a1 -- ... a1 [a1 ...]) (... a1 -- ... a1 [a1 ...])
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*C(ccons, stack)) print doc_from_stack_effect(*C(ccons, stack))
@ -2003,7 +2003,7 @@ Clunky junk, but it will suffice for now.
(... a2 a1 [.1.] -- ... [a2 a1 .1.] [[a2 a1 .1.] ...]) (... a2 a1 [.1.] -- ... [a2 a1 .1.] [[a2 a1 .1.] ...])
.. code:: python .. code:: ipython2
Q = C(ccons, stack) Q = C(ccons, stack)
@ -2024,7 +2024,7 @@ Clunky junk, but it will suffice for now.
This makes the ``compile_()`` function pretty simple as the stack effect This makes the ``compile_()`` function pretty simple as the stack effect
comments are now already in the form needed for the Python code: comments are now already in the form needed for the Python code:
.. code:: python .. code:: ipython2
def compile_(name, f, doc=None): def compile_(name, f, doc=None):
i, o = f i, o = f
@ -2035,7 +2035,7 @@ comments are now already in the form needed for the Python code:
%s = stack %s = stack
return %s''' % (name, doc, i, o) return %s''' % (name, doc, i, o)
.. code:: python .. code:: ipython2
print compile_('Q', Q) print compile_('Q', Q)
@ -2053,12 +2053,12 @@ comments are now already in the form needed for the Python code:
.. code:: python .. code:: ipython2
unstack = (S[1], S[0]), S[1] unstack = (S[1], S[0]), S[1]
enstacken = S[0], (S[0], S[1]) enstacken = S[0], (S[0], S[1])
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*unstack) print doc_from_stack_effect(*unstack)
@ -2068,7 +2068,7 @@ comments are now already in the form needed for the Python code:
([.1.] --) ([.1.] --)
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*enstacken) print doc_from_stack_effect(*enstacken)
@ -2078,7 +2078,7 @@ comments are now already in the form needed for the Python code:
(-- [.0.]) (-- [.0.])
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*C(cons, unstack)) print doc_from_stack_effect(*C(cons, unstack))
@ -2088,7 +2088,7 @@ comments are now already in the form needed for the Python code:
(a1 [.1.] -- a1) (a1 [.1.] -- a1)
.. code:: python .. code:: ipython2
print doc_from_stack_effect(*C(cons, enstacken)) print doc_from_stack_effect(*C(cons, enstacken))
@ -2098,7 +2098,7 @@ comments are now already in the form needed for the Python code:
(a1 [.1.] -- [[a1 .1.] .2.]) (a1 [.1.] -- [[a1 .1.] .2.])
.. code:: python .. code:: ipython2
C(cons, unstack) C(cons, unstack)
@ -2117,7 +2117,7 @@ Part VI: Multiple Stack Effects
… …
.. code:: python .. code:: ipython2
class IntJoyType(NumberJoyType): prefix = 'i' class IntJoyType(NumberJoyType): prefix = 'i'
@ -2125,7 +2125,7 @@ Part VI: Multiple Stack Effects
F = map(FloatJoyType, _R) F = map(FloatJoyType, _R)
I = map(IntJoyType, _R) I = map(IntJoyType, _R)
.. code:: python .. code:: ipython2
muls = [ muls = [
((I[2], (I[1], S[0])), (I[3], S[0])), ((I[2], (I[1], S[0])), (I[3], S[0])),
@ -2134,7 +2134,7 @@ Part VI: Multiple Stack Effects
((F[2], (F[1], S[0])), (F[3], S[0])), ((F[2], (F[1], S[0])), (F[3], S[0])),
] ]
.. code:: python .. code:: ipython2
for f in muls: for f in muls:
print doc_from_stack_effect(*f) print doc_from_stack_effect(*f)
@ -2148,7 +2148,7 @@ Part VI: Multiple Stack Effects
(f1 f2 -- f3) (f1 f2 -- f3)
.. code:: python .. code:: ipython2
for f in muls: for f in muls:
try: try:
@ -2164,7 +2164,7 @@ Part VI: Multiple Stack Effects
(a1 -- a1 a1) (f1 f2 -- f3) (f1 -- f2) (a1 -- a1 a1) (f1 f2 -- f3) (f1 -- f2)
.. code:: python .. code:: ipython2
from itertools import product from itertools import product
@ -2180,7 +2180,7 @@ Part VI: Multiple Stack Effects
def MC(F, G): def MC(F, G):
return sorted(set(meta_compose(F, G))) return sorted(set(meta_compose(F, G)))
.. code:: python .. code:: ipython2
for f in MC([dup], [mul]): for f in MC([dup], [mul]):
print doc_from_stack_effect(*f) print doc_from_stack_effect(*f)
@ -2191,7 +2191,7 @@ Part VI: Multiple Stack Effects
(n1 -- n2) (n1 -- n2)
.. code:: python .. code:: ipython2
for f in MC([dup], muls): for f in MC([dup], muls):
print doc_from_stack_effect(*f) print doc_from_stack_effect(*f)
@ -2264,7 +2264,7 @@ Giving us two unifiers:
{c: a, d: b, .1.: .0.} {c: a, d: b, .1.: .0.}
{c: a, d: e, .1.: A* b .0.} {c: a, d: e, .1.: A* b .0.}
.. code:: python .. code:: ipython2
class KleeneStar(object): class KleeneStar(object):
@ -2314,7 +2314,7 @@ Giving us two unifiers:
Can now return multiple results… Can now return multiple results…
.. code:: python .. code:: ipython2
def unify(u, v, s=None): def unify(u, v, s=None):
if s is None: if s is None:
@ -2386,7 +2386,7 @@ Can now return multiple results…
def stacky(thing): def stacky(thing):
return thing.__class__ in {AnyJoyType, StackJoyType} return thing.__class__ in {AnyJoyType, StackJoyType}
.. code:: python .. code:: ipython2
a = (As[1], S[1]) a = (As[1], S[1])
a a
@ -2400,7 +2400,7 @@ Can now return multiple results…
.. code:: python .. code:: ipython2
b = (A[1], S[2]) b = (A[1], S[2])
b b
@ -2414,7 +2414,7 @@ Can now return multiple results…
.. code:: python .. code:: ipython2
for result in unify(b, a): for result in unify(b, a):
print result, '->', update(result, a), update(result, b) print result, '->', update(result, a), update(result, b)
@ -2426,7 +2426,7 @@ Can now return multiple results…
{a1: a10001, s2: (a1*, s1)} -> (a1*, s1) (a10001, (a1*, s1)) {a1: a10001, s2: (a1*, s1)} -> (a1*, s1) (a10001, (a1*, s1))
.. code:: python .. code:: ipython2
for result in unify(a, b): for result in unify(a, b):
print result, '->', update(result, a), update(result, b) print result, '->', update(result, a), update(result, b)
@ -2446,7 +2446,7 @@ Can now return multiple results…
(a1*, s1) [a1*] (a2, (a1*, s1)) [a2 a1*] (a1*, s1) [a1*] (a2, (a1*, s1)) [a2 a1*]
.. code:: python .. code:: ipython2
sum_ = ((Ns[1], S[1]), S[0]), (N[0], S[0]) sum_ = ((Ns[1], S[1]), S[0]), (N[0], S[0])
@ -2458,7 +2458,7 @@ Can now return multiple results…
([n1* .1.] -- n0) ([n1* .1.] -- n0)
.. code:: python .. code:: ipython2
f = (N[1], (N[2], (N[3], S[1]))), S[0] f = (N[1], (N[2], (N[3], S[1]))), S[0]
@ -2470,7 +2470,7 @@ Can now return multiple results…
(-- [n1 n2 n3 .1.]) (-- [n1 n2 n3 .1.])
.. code:: python .. code:: ipython2
for result in unify(sum_[0], f): for result in unify(sum_[0], f):
print result, '->', update(result, sum_[1]) print result, '->', update(result, sum_[1])
@ -2489,7 +2489,7 @@ Can now return multiple results…
This function has to be modified to yield multiple results. This function has to be modified to yield multiple results.
.. code:: python .. code:: ipython2
def compose(f, g): def compose(f, g):
(f_in, f_out), (g_in, g_out) = f, g (f_in, f_out), (g_in, g_out) = f, g
@ -2501,7 +2501,7 @@ This function has to be modified to yield multiple results.
.. code:: python .. code:: ipython2
def meta_compose(F, G): def meta_compose(F, G):
for f, g in product(F, G): for f, g in product(F, G):
@ -2517,7 +2517,7 @@ This function has to be modified to yield multiple results.
for fg in compose(f, g): for fg in compose(f, g):
yield delabel(fg) yield delabel(fg)
.. code:: python .. code:: ipython2
for f in MC([dup], muls): for f in MC([dup], muls):
print doc_from_stack_effect(*f) print doc_from_stack_effect(*f)
@ -2529,7 +2529,7 @@ This function has to be modified to yield multiple results.
(i1 -- i2) (i1 -- i2)
.. code:: python .. code:: ipython2
@ -2542,7 +2542,7 @@ This function has to be modified to yield multiple results.
([n1* .1.] -- [n1* .1.] n1) ([n1* .1.] -- [n1* .1.] n1)
.. code:: python .. code:: ipython2
@ -2556,7 +2556,7 @@ This function has to be modified to yield multiple results.
(n1 [n1* .1.] -- n2) (n1 [n1* .1.] -- n2)
.. code:: python .. code:: ipython2
sum_ = (((N[1], (Ns[1], S[1])), S[0]), (N[0], S[0])) sum_ = (((N[1], (Ns[1], S[1])), S[0]), (N[0], S[0]))
print doc_from_stack_effect(*cons), print doc_from_stack_effect(*cons),
@ -2571,7 +2571,7 @@ This function has to be modified to yield multiple results.
(a1 [.1.] -- [a1 .1.]) ([n1 n1* .1.] -- n0) (n1 [n1* .1.] -- n2) (a1 [.1.] -- [a1 .1.]) ([n1 n1* .1.] -- n0) (n1 [n1* .1.] -- n2)
.. code:: python .. code:: ipython2
a = (A[4], (As[1], (A[3], S[1]))) a = (A[4], (As[1], (A[3], S[1])))
a a
@ -2585,7 +2585,7 @@ This function has to be modified to yield multiple results.
.. code:: python .. code:: ipython2
b = (A[1], (A[2], S[2])) b = (A[1], (A[2], S[2]))
b b
@ -2599,7 +2599,7 @@ This function has to be modified to yield multiple results.
.. code:: python .. code:: ipython2
for result in unify(b, a): for result in unify(b, a):
print result print result
@ -2611,7 +2611,7 @@ This function has to be modified to yield multiple results.
{a1: a4, s2: (a1*, (a3, s1)), a2: a10003} {a1: a4, s2: (a1*, (a3, s1)), a2: a10003}
.. code:: python .. code:: ipython2
for result in unify(a, b): for result in unify(a, b):
print result print result
@ -2681,7 +2681,7 @@ We need a type variable for Joy functions that can go in our expressions
and be used by the hybrid inferencer/interpreter. They have to store a and be used by the hybrid inferencer/interpreter. They have to store a
name and a list of stack effects. name and a list of stack effects.
.. code:: python .. code:: ipython2
class FunctionJoyType(AnyJoyType): class FunctionJoyType(AnyJoyType):
@ -2703,14 +2703,14 @@ Specialized for Simple Functions and Combinators
For non-combinator functions the stack effects list contains stack For non-combinator functions the stack effects list contains stack
effect comments (represented by pairs of cons-lists as described above.) effect comments (represented by pairs of cons-lists as described above.)
.. code:: python .. code:: ipython2
class SymbolJoyType(FunctionJoyType): class SymbolJoyType(FunctionJoyType):
prefix = 'F' prefix = 'F'
For combinators the list contains Python functions. For combinators the list contains Python functions.
.. code:: python .. code:: ipython2
class CombinatorJoyType(FunctionJoyType): class CombinatorJoyType(FunctionJoyType):
@ -2731,7 +2731,7 @@ For combinators the list contains Python functions.
For simple combinators that have only one effect (like ``dip``) you only For simple combinators that have only one effect (like ``dip``) you only
need one function and it can be the combinator itself. need one function and it can be the combinator itself.
.. code:: python .. code:: ipython2
import joy.library import joy.library
@ -2741,7 +2741,7 @@ For combinators that can have more than one effect (like ``branch``) you
have to write functions that each implement the action of one of the have to write functions that each implement the action of one of the
effects. effects.
.. code:: python .. code:: ipython2
def branch_true(stack, expression, dictionary): def branch_true(stack, expression, dictionary):
(then, (else_, (flag, stack))) = stack (then, (else_, (flag, stack))) = stack
@ -2771,7 +2771,7 @@ updated along with the stack effects after doing unification or we risk
losing useful information. This was a straightforward, if awkward, losing useful information. This was a straightforward, if awkward,
modification to the call structure of ``meta_compose()`` et. al. modification to the call structure of ``meta_compose()`` et. al.
.. code:: python .. code:: ipython2
ID = S[0], S[0] # Identity function. ID = S[0], S[0] # Identity function.
@ -2833,7 +2833,7 @@ cruft to convert the definitions in ``DEFS`` to the new
``SymbolJoyType`` objects, and some combinators. Here is an example of ``SymbolJoyType`` objects, and some combinators. Here is an example of
output from the current code : output from the current code :
.. code:: python .. code:: ipython2
1/0 # (Don't try to run this cell! It's not going to work. This is "read only" code heh..) 1/0 # (Don't try to run this cell! It's not going to work. This is "read only" code heh..)
@ -2956,7 +2956,7 @@ module. But if you’re interested in all that you should just use Prolog!
Anyhow, type *checking* is a few easy steps away. Anyhow, type *checking* is a few easy steps away.
.. code:: python .. code:: ipython2
def _ge(self, other): def _ge(self, other):
return (issubclass(other.__class__, self.__class__) return (issubclass(other.__class__, self.__class__)

36
docs/sphinx_docs/notebooks/Zipper.rst
View File

@ -10,7 +10,7 @@ Huet <https://www.st.cs.uni-saarland.de/edu/seminare/2005/advanced-fp/docs/huet-
Given a datastructure on the stack we can navigate through it, modify Given a datastructure on the stack we can navigate through it, modify
it, and rebuild it using the “zipper” technique. it, and rebuild it using the “zipper” technique.
.. code:: python .. code:: ipython2
from notebook_preamble import J, V, define from notebook_preamble import J, V, define
@ -23,7 +23,7 @@ strings, Symbols (strings that are names of functions) and sequences
`trees <https://en.wikipedia.org/wiki/Tree_%28data_structure%29>`__ out `trees <https://en.wikipedia.org/wiki/Tree_%28data_structure%29>`__ out
of sequences. of sequences.
.. code:: python .. code:: ipython2
J('[1 [2 [3 4 25 6] 7] 8]') J('[1 [2 [3 4 25 6] 7] 8]')
@ -54,14 +54,14 @@ show the trace so you can see how it works. If we were going to use
these a lot it would make sense to write Python versions for efficiency, these a lot it would make sense to write Python versions for efficiency,
but see below. but see below.
.. code:: python .. code:: ipython2
define('z-down == [] swap uncons swap') define('z-down == [] swap uncons swap')
define('z-up == swons swap shunt') define('z-up == swons swap shunt')
define('z-right == [swons] cons dip uncons swap') define('z-right == [swons] cons dip uncons swap')
define('z-left == swons [uncons swap] dip swap') define('z-left == swons [uncons swap] dip swap')
.. code:: python .. code:: ipython2
V('[1 [2 [3 4 25 6] 7] 8] z-down') V('[1 [2 [3 4 25 6] 7] 8] z-down')
@ -77,7 +77,7 @@ but see below.
[] [[2 [3 4 25 6] 7] 8] 1 . [] [[2 [3 4 25 6] 7] 8] 1 .
.. code:: python .. code:: ipython2
V('[] [[2 [3 4 25 6] 7] 8] 1 z-right') V('[] [[2 [3 4 25 6] 7] 8] 1 z-right')
@ -101,7 +101,7 @@ but see below.
[1] [8] [2 [3 4 25 6] 7] . [1] [8] [2 [3 4 25 6] 7] .
.. code:: python .. code:: ipython2
J('[1] [8] [2 [3 4 25 6] 7] z-down') J('[1] [8] [2 [3 4 25 6] 7] z-down')
@ -111,7 +111,7 @@ but see below.
[1] [8] [] [[3 4 25 6] 7] 2 [1] [8] [] [[3 4 25 6] 7] 2
.. code:: python .. code:: ipython2
J('[1] [8] [] [[3 4 25 6] 7] 2 z-right') J('[1] [8] [] [[3 4 25 6] 7] 2 z-right')
@ -121,7 +121,7 @@ but see below.
[1] [8] [2] [7] [3 4 25 6] [1] [8] [2] [7] [3 4 25 6]
.. code:: python .. code:: ipython2
J('[1] [8] [2] [7] [3 4 25 6] z-down') J('[1] [8] [2] [7] [3 4 25 6] z-down')
@ -131,7 +131,7 @@ but see below.
[1] [8] [2] [7] [] [4 25 6] 3 [1] [8] [2] [7] [] [4 25 6] 3
.. code:: python .. code:: ipython2
J('[1] [8] [2] [7] [] [4 25 6] 3 z-right') J('[1] [8] [2] [7] [] [4 25 6] 3 z-right')
@ -141,7 +141,7 @@ but see below.
[1] [8] [2] [7] [3] [25 6] 4 [1] [8] [2] [7] [3] [25 6] 4
.. code:: python .. code:: ipython2
J('[1] [8] [2] [7] [3] [25 6] 4 z-right') J('[1] [8] [2] [7] [3] [25 6] 4 z-right')
@ -151,7 +151,7 @@ but see below.
[1] [8] [2] [7] [4 3] [6] 25 [1] [8] [2] [7] [4 3] [6] 25
.. code:: python .. code:: ipython2
J('[1] [8] [2] [7] [4 3] [6] 25 sqr') J('[1] [8] [2] [7] [4 3] [6] 25 sqr')
@ -161,7 +161,7 @@ but see below.
[1] [8] [2] [7] [4 3] [6] 625 [1] [8] [2] [7] [4 3] [6] 625
.. code:: python .. code:: ipython2
V('[1] [8] [2] [7] [4 3] [6] 625 z-up') V('[1] [8] [2] [7] [4 3] [6] 625 z-up')
@ -184,7 +184,7 @@ but see below.
[1] [8] [2] [7] [3 4 625 6] . [1] [8] [2] [7] [3 4 625 6] .
.. code:: python .. code:: ipython2
J('[1] [8] [2] [7] [3 4 625 6] z-up') J('[1] [8] [2] [7] [3 4 625 6] z-up')
@ -194,7 +194,7 @@ but see below.
[1] [8] [2 [3 4 625 6] 7] [1] [8] [2 [3 4 625 6] 7]
.. code:: python .. code:: ipython2
J('[1] [8] [2 [3 4 625 6] 7] z-up') J('[1] [8] [2 [3 4 625 6] 7] z-up')
@ -210,7 +210,7 @@ but see below.
In Joy we have the ``dip`` and ``infra`` combinators which can “target” In Joy we have the ``dip`` and ``infra`` combinators which can “target”
or “address” any particular item in a Joy tree structure. or “address” any particular item in a Joy tree structure.
.. code:: python .. code:: ipython2
V('[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra') V('[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra')
@ -270,13 +270,13 @@ been embedded in a nested series of quoted programs, e.g.:
The ``Z`` function isn’t hard to make. The ``Z`` function isn’t hard to make.
.. code:: python .. code:: ipython2
define('Z == [[] cons cons] step i') define('Z == [[] cons cons] step i')
Here it is in action in a simplified scenario. Here it is in action in a simplified scenario.
.. code:: python .. code:: ipython2
V('1 [2 3 4] Z') V('1 [2 3 4] Z')
@ -314,7 +314,7 @@ Here it is in action in a simplified scenario.
And here it is doing the main thing. And here it is doing the main thing.
.. code:: python .. code:: ipython2
J('[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z') J('[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z')

1
docs/sphinx_docs/notebooks/index.rst
View File

@ -16,6 +16,7 @@ These essays are adapted from Jupyter notebooks. I hope to have those hosted so
Treestep Treestep
Generator_Programs Generator_Programs
Newton-Raphson Newton-Raphson
Square_Spiral
Zipper Zipper
Types Types
TypeChecking TypeChecking