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Still converting syntax highlighter spec.

This commit is contained in:
Simon Forman 2021-11-19 13:59:00 -08:00
parent 3f40e30c6f
commit a69b7e2a56
41 changed files with 1874 additions and 1874 deletions
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@ -76,7 +76,7 @@ E.g.:
Implementation Implementation
-------------- --------------
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
def stringy(re): def stringy(re):
''' '''
@ -175,11 +175,11 @@ Match anything. Often spelled “.”
I = (0|1)* I = (0|1)*
.. code:: ipython2 .. code:: python
I = (KSTAR, (OR, O, l)) I = (KSTAR, (OR, O, l))
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
def D(symbol): def D(symbol):
@ -308,7 +308,7 @@ derivation.
Compaction Rules Compaction Rules
~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
# 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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
def D_compaction(symbol): def D_compaction(symbol):
@ -414,7 +414,7 @@ Let’s try it out…
(FIXME: redo.) (FIXME: redo.)
.. code:: ipython2 .. code:: python
o, z = D_compaction('0'), D_compaction('1') o, z = D_compaction('0'), D_compaction('1')
REs = set() REs = set()
@ -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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
d0, d1 = D_compaction('0'), D_compaction('1') d0, d1 = D_compaction('0'), D_compaction('1')
``explore()`` ``explore()``
~~~~~~~~~~~~~ ~~~~~~~~~~~~~
.. code:: ipython2 .. code:: python
def explore(re): def explore(re):
@ -645,7 +645,7 @@ disappears once it has been matched.
return table, accepting return table, accepting
.. code:: ipython2 .. code:: python
table, accepting = explore(it) table, accepting = explore(it)
table table
@ -678,7 +678,7 @@ disappears once it has been matched.
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
_template = '''\ _template = '''\
digraph finite_state_machine { digraph finite_state_machine {
@ -722,7 +722,7 @@ generate the diagram above.
) )
) )
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
def acceptable(input_): def acceptable(input_):
return trampoline(input_, a, {h, i}) return trampoline(input_, a, {h, i})
.. code:: ipython2 .. code:: python
for n in range(2**5): for n in range(2**5):
s = bin(n)[2:] s = bin(n)[2:]

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@ -12,7 +12,7 @@ As an example of developing a program in Joy let's take the first problem from t
Find the sum of all the multiples of 3 or 5 below 1000. Find the sum of all the multiples of 3 or 5 below 1000.
.. code:: ipython2 .. code:: python
from notebook_preamble import J, V, define from notebook_preamble import J, V, define
@ -22,11 +22,11 @@ Sum a range filtered by a predicate
Let's create a predicate that returns ``True`` if a number is a multiple Let's create a predicate that returns ``True`` if a number is a multiple
of 3 or 5 and ``False`` otherwise. of 3 or 5 and ``False`` otherwise.
.. code:: ipython2 .. code:: python
define('P == [3 % not] dupdip 5 % not or') define('P == [3 % not] dupdip 5 % not or')
.. code:: ipython2 .. code:: python
V('80 P') V('80 P')
@ -108,11 +108,11 @@ the counter to the running sum. This function will do that:
PE1.1 == + [+] dupdip PE1.1 == + [+] dupdip
.. code:: ipython2 .. code:: python
define('PE1.1 == + [+] dupdip') define('PE1.1 == + [+] dupdip')
.. code:: ipython2 .. code:: python
V('0 0 3 PE1.1') V('0 0 3 PE1.1')
@ -131,7 +131,7 @@ the counter to the running sum. This function will do that:
3 3 . 3 3 .
.. code:: ipython2 .. code:: python
V('0 0 [3 2 1 3 1 2 3] [PE1.1] step') V('0 0 [3 2 1 3 1 2 3] [PE1.1] step')
@ -219,7 +219,7 @@ total to 60.
How many multiples to sum? How many multiples to sum?
^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^
.. code:: ipython2 .. code:: python
1000 / 15 1000 / 15
@ -232,7 +232,7 @@ How many multiples to sum?
.. code:: ipython2 .. code:: python
66 * 15 66 * 15
@ -245,7 +245,7 @@ How many multiples to sum?
.. code:: ipython2 .. code:: python
1000 - 990 1000 - 990
@ -260,7 +260,7 @@ How many multiples to sum?
We only want the terms *less than* 1000. We only want the terms *less than* 1000.
.. code:: ipython2 .. code:: python
999 - 990 999 - 990
@ -276,11 +276,11 @@ We only want the terms *less than* 1000.
That means we want to run the full list of numbers sixty-six times to That means we want to run the full list of numbers sixty-six times to
get to 990 and then the first four numbers 3 2 1 3 to get to 999. get to 990 and then the first four numbers 3 2 1 3 to get to 999.
.. code:: ipython2 .. code:: python
define('PE1 == 0 0 66 [[3 2 1 3 1 2 3] [PE1.1] step] times [3 2 1 3] [PE1.1] step pop') define('PE1 == 0 0 66 [[3 2 1 3 1 2 3] [PE1.1] step] times [3 2 1 3] [PE1.1] step pop')
.. code:: ipython2 .. code:: python
J('PE1') J('PE1')
@ -305,7 +305,7 @@ integer terms from the list.
3 2 1 3 1 2 3 3 2 1 3 1 2 3
0b 11 10 01 11 01 10 11 == 14811 0b 11 10 01 11 01 10 11 == 14811
.. code:: ipython2 .. code:: python
0b11100111011011 0b11100111011011
@ -318,11 +318,11 @@ integer terms from the list.
.. code:: ipython2 .. code:: python
define('PE1.2 == [3 & PE1.1] dupdip 2 >>') define('PE1.2 == [3 & PE1.1] dupdip 2 >>')
.. code:: ipython2 .. code:: python
V('0 0 14811 PE1.2') V('0 0 14811 PE1.2')
@ -349,7 +349,7 @@ integer terms from the list.
3 3 3702 . 3 3 3702 .
.. code:: ipython2 .. code:: python
V('3 3 3702 PE1.2') V('3 3 3702 PE1.2')
@ -376,7 +376,7 @@ integer terms from the list.
8 5 925 . 8 5 925 .
.. code:: ipython2 .. code:: python
V('0 0 14811 7 [PE1.2] times pop') V('0 0 14811 7 [PE1.2] times pop')
@ -518,11 +518,11 @@ integer terms from the list.
And so we have at last: And so we have at last:
.. code:: ipython2 .. code:: python
define('PE1 == 0 0 66 [14811 7 [PE1.2] times pop] times 14811 4 [PE1.2] times popop') define('PE1 == 0 0 66 [14811 7 [PE1.2] times pop] times 14811 4 [PE1.2] times popop')
.. code:: ipython2 .. code:: python
J('PE1') J('PE1')
@ -542,17 +542,17 @@ Let's refactor
14811 n [PE1.2] times pop 14811 n [PE1.2] times pop
n 14811 swap [PE1.2] times pop n 14811 swap [PE1.2] times pop
.. code:: ipython2 .. code:: python
define('PE1.3 == 14811 swap [PE1.2] times pop') define('PE1.3 == 14811 swap [PE1.2] times pop')
Now we can simplify the definition above: Now we can simplify the definition above:
.. code:: ipython2 .. code:: python
define('PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop') define('PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop')
.. code:: ipython2 .. code:: python
J('PE1') J('PE1')
@ -581,11 +581,11 @@ then four more. In the *Generator Programs* notebook we derive a
generator that can be repeatedly driven by the ``x`` combinator to generator that can be repeatedly driven by the ``x`` combinator to
produce a stream of the seven numbers repeating over and over again. produce a stream of the seven numbers repeating over and over again.
.. code:: ipython2 .. code:: python
define('PE1.terms == [0 swap [dup [pop 14811] [] branch [3 &] dupdip 2 >>] dip rest cons]') define('PE1.terms == [0 swap [dup [pop 14811] [] branch [3 &] dupdip 2 >>] dip rest cons]')
.. code:: ipython2 .. code:: python
J('PE1.terms 21 [x] times') J('PE1.terms 21 [x] times')
@ -598,7 +598,7 @@ produce a stream of the seven numbers repeating over and over again.
We know from above that we need sixty-six times seven then four more We know from above that we need sixty-six times seven then four more
terms to reach up to but not over one thousand. terms to reach up to but not over one thousand.
.. code:: ipython2 .. code:: python
J('7 66 * 4 +') J('7 66 * 4 +')
@ -611,7 +611,7 @@ terms to reach up to but not over one thousand.
Here they are... Here they are...
~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~
.. code:: ipython2 .. code:: python
J('PE1.terms 466 [x] times pop') J('PE1.terms 466 [x] times pop')
@ -624,7 +624,7 @@ Here they are...
...and they do sum to 999. ...and they do sum to 999.
~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: ipython2 .. code:: python
J('[PE1.terms 466 [x] times pop] run sum') J('[PE1.terms 466 [x] times pop] run sum')
@ -638,7 +638,7 @@ Now we can use ``PE1.1`` to accumulate the terms as we go, and then
``pop`` the generator and the counter from the stack when we're done, ``pop`` the generator and the counter from the stack when we're done,
leaving just the sum. leaving just the sum.
.. code:: ipython2 .. code:: python
J('0 0 PE1.terms 466 [x [PE1.1] dip] times popop') J('0 0 PE1.terms 466 [x [PE1.1] dip] times popop')
@ -654,7 +654,7 @@ A little further analysis renders iteration unnecessary.
Consider finding the sum of the positive integers less than or equal to Consider finding the sum of the positive integers less than or equal to
ten. ten.
.. code:: ipython2 .. code:: python
J('[10 9 8 7 6 5 4 3 2 1] sum') J('[10 9 8 7 6 5 4 3 2 1] sum')
@ -686,11 +686,11 @@ positive integers is:
(The formula also works for odd values of N, I'll leave that to you if (The formula also works for odd values of N, I'll leave that to you if
you want to work it out or you can take my word for it.) you want to work it out or you can take my word for it.)
.. code:: ipython2 .. code:: python
define('F == dup ++ * 2 floordiv') define('F == dup ++ * 2 floordiv')
.. code:: ipython2 .. code:: python
V('10 F') V('10 F')
@ -727,7 +727,7 @@ And ending with:
If we reverse one of these two blocks and sum pairs... If we reverse one of these two blocks and sum pairs...
.. code:: ipython2 .. code:: python
J('[3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip') J('[3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip')
@ -737,7 +737,7 @@ If we reverse one of these two blocks and sum pairs...
[[978 15] [980 12] [981 10] [984 9] [985 6] [987 5] [990 3]] [[978 15] [980 12] [981 10] [984 9] [985 6] [987 5] [990 3]]
.. code:: ipython2 .. code:: python
J('[3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip [sum] map') J('[3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip [sum] map')
@ -750,7 +750,7 @@ If we reverse one of these two blocks and sum pairs...
(Interesting that the sequence of seven numbers appears again in the (Interesting that the sequence of seven numbers appears again in the
rightmost digit of each term.) rightmost digit of each term.)
.. code:: ipython2 .. code:: python
J('[ 3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip [sum] map sum') J('[ 3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip [sum] map sum')
@ -771,7 +771,7 @@ additional unpaired terms between 990 and 1000:
So we can give the "sum of all the multiples of 3 or 5 below 1000" like So we can give the "sum of all the multiples of 3 or 5 below 1000" like
so: so:
.. code:: ipython2 .. code:: python
J('6945 33 * [993 995 996 999] cons sum') J('6945 33 * [993 995 996 999] cons sum')

76
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@ -3,7 +3,7 @@ Using ``x`` to Generate Values
Cf. jp-reprod.html Cf. jp-reprod.html
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('direco == dip rest cons') define('direco == dip rest cons')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('PE1.1 == dup [3 &] dip 2 >>') define('PE1.1 == dup [3 &] dip 2 >>')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('PE1.1.check == dup [pop 14811] [] branch') define('PE1.1.check == dup [pop 14811] [] branch')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('fib == + [popdd over] cons infra uncons') define('fib == + [popdd over] cons infra uncons')
.. code:: ipython2 .. code:: python
define('fib_gen == [1 1 fib]') define('fib_gen == [1 1 fib]')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('PE2.2 == x x x [popop] dipd') define('PE2.2 == x x x [popop] dipd')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('codireco == cons dip rest cons') define('codireco == cons dip rest cons')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('G == [codireco] cons cons') define('G == [codireco] cons cons')
.. code:: ipython2 .. code:: python
J('230 [dup ++] G 5 [x] times pop') J('230 [dup ++] G 5 [x] times pop')

14
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@ -150,7 +150,7 @@ TBD (look in the :module: joy.parser module.)
Examples Examples
~~~~~~~~~~~ ~~~~~~~~~~~
.. code:: ipython2 .. code:: python
joy.parser.text_to_expression('1 2 3 4 5') # A simple sequence. joy.parser.text_to_expression('1 2 3 4 5') # A simple sequence.
@ -160,7 +160,7 @@ Examples
(1, (2, (3, (4, (5, ()))))) (1, (2, (3, (4, (5, ())))))
.. code:: ipython2 .. code:: python
joy.parser.text_to_expression('[1 2 3] 4 5') # Three items, the first is a list with three items joy.parser.text_to_expression('[1 2 3] 4 5') # Three items, the first is a list with three items
@ -170,7 +170,7 @@ Examples
((1, (2, (3, ()))), (4, (5, ()))) ((1, (2, (3, ()))), (4, (5, ())))
.. code:: ipython2 .. code:: python
joy.parser.text_to_expression('1 23 ["four" [-5.0] cons] 8888') # A mixed bag. cons is joy.parser.text_to_expression('1 23 ["four" [-5.0] cons] 8888') # A mixed bag. cons is
# a Symbol, no lookup at # a Symbol, no lookup at
@ -184,7 +184,7 @@ Examples
.. code:: ipython2 .. code:: python
joy.parser.text_to_expression('[][][][][]') # Five empty lists. joy.parser.text_to_expression('[][][][][]') # Five empty lists.
@ -197,7 +197,7 @@ Examples
.. code:: ipython2 .. code:: python
joy.parser.text_to_expression('[[[[[]]]]]') # Five nested lists. joy.parser.text_to_expression('[[[[[]]]]]') # Five nested lists.
@ -221,7 +221,7 @@ provide control-flow and higher-order operations.
Many of the functions are defined in Python, like ``dip``: Many of the functions are defined in Python, like ``dip``:
.. code:: ipython2 .. code:: python
print inspect.getsource(joy.library.dip) print inspect.getsource(joy.library.dip)
@ -239,7 +239,7 @@ When the interpreter executes a definition function that function just
pushes its body expression onto the pending expression (the pushes its body expression onto the pending expression (the
continuation) and returns control to the interpreter. continuation) and returns control to the interpreter.
.. code:: ipython2 .. code:: python
print joy.library.definitions print joy.library.definitions

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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('Tree-new == swap [[] []] cons cons') define('Tree-new == swap [[] []] cons cons')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('P == pop roll> pop first') define('P == pop roll> pop first')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('T == cons cons [dipdd] cons infra') define('T == cons cons [dipdd] cons infra')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('Te == cons cons [dipd] cons infra') define('Te == cons cons [dipd] cons infra')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('Ee == pop swap roll< rest rest cons cons') define('Ee == pop swap roll< rest rest cons cons')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
J('[] 23 "b" Tree-add') # Initial J('[] 23 "b" Tree-add') # Initial
@ -372,7 +372,7 @@ Examples
['b' 23 [] []] ['b' 23 [] []]
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
J("1 0 ['G'] ['E'] ['L'] cmp") J("1 0 ['G'] ['E'] ['L'] cmp")
@ -454,7 +454,7 @@ values:
'G' 'G'
.. code:: ipython2 .. code:: python
J("1 1 ['G'] ['E'] ['L'] cmp") J("1 1 ['G'] ['E'] ['L'] cmp")
@ -464,7 +464,7 @@ values:
'E' 'E'
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('to_set == [] swap [0 swap Tree-add] step') define('to_set == [] swap [0 swap Tree-add] step')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('unique == [to_set [first] Tree-iter] cons run') define('unique == [to_set [first] Tree-iter] cons run')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
#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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
# 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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
J('["gary" 23 [] []] "gary" [popop "err"] Tree-get') J('["gary" 23 [] []] "gary" [popop "err"] Tree-get')
@ -1108,7 +1108,7 @@ So:
23 23
.. code:: ipython2 .. code:: python
J(''' J('''
@ -1124,7 +1124,7 @@ So:
2 2
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
V('-5 1 4 quadratic') V('-5 1 4 quadratic')

48
docs/sphinx_docs/_build/html/_sources/notebooks/Recursion_Combinators.rst.txt
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@ -1,4 +1,4 @@
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism') define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism')
Let’s try it: Let’s try it:
.. code:: ipython2 .. code:: python
J('5 triangular_number') J('5 triangular_number')
@ -219,7 +219,7 @@ Let’s try it:
10 10
.. code:: ipython2 .. code:: python
J('[0 1 2 3 4 5 6] [triangular_number] map') J('[0 1 2 3 4 5 6] [triangular_number] map')
@ -405,11 +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:: ipython2 .. code:: python
define('range == [0 <=] [] [-- dup] [swons] hylomorphism') define('range == [0 <=] [] [-- dup] [swons] hylomorphism')
.. code:: ipython2 .. code:: python
J('5 range') J('5 range')
@ -427,11 +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:: ipython2 .. code:: python
define('range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec') define('range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec')
.. code:: ipython2 .. code:: python
J('5 range_reverse') J('5 range_reverse')
@ -449,11 +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:: ipython2 .. code:: python
define('ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec') define('ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec')
.. code:: ipython2 .. code:: python
J('5 ranger') J('5 ranger')
@ -471,11 +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:: ipython2 .. code:: python
define('ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec') define('ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec')
.. code:: ipython2 .. code:: python
J('5 ranger_reverse') J('5 ranger_reverse')
@ -501,7 +501,7 @@ and makes some new value.
C == [not] c [uncons swap] [F] hylomorphism C == [not] c [uncons swap] [F] hylomorphism
.. code:: ipython2 .. code:: python
define('swuncons == uncons swap') # Awkward name. define('swuncons == uncons swap') # Awkward name.
@ -511,11 +511,11 @@ An example of a catamorphism is the sum function.
sum == [not] 0 [swuncons] [+] hylomorphism sum == [not] 0 [swuncons] [+] hylomorphism
.. code:: ipython2 .. code:: python
define('sum == [not] 0 [swuncons] [+] hylomorphism') define('sum == [not] 0 [swuncons] [+] hylomorphism')
.. code:: ipython2 .. code:: python
J('[5 4 3 2 1] sum') J('[5 4 3 2 1] sum')
@ -531,7 +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:: ipython2 .. code:: python
J('[step] help') J('[step] help')
@ -560,11 +560,11 @@ The ``step`` combinator will usually be better to use than
.. code:: ipython2 .. code:: python
define('sum == 0 swap [+] step') define('sum == 0 swap [+] step')
.. code:: ipython2 .. code:: python
J('[5 4 3 2 1] sum') J('[5 4 3 2 1] sum')
@ -592,11 +592,11 @@ With:
G == -- G == --
P == 1 <= P == 1 <=
.. code:: ipython2 .. code:: python
define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec') define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec')
.. code:: ipython2 .. code:: python
J('5 factorial') J('5 factorial')
@ -635,11 +635,11 @@ We would use:
G == rest dup G == rest dup
P == not P == not
.. code:: ipython2 .. code:: python
define('tails == [] swap [not] [pop] [rest dup [swons] dip] primrec') define('tails == [] swap [not] [pop] [rest dup [swons] dip] primrec')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
from notebook_preamble import D, J, V from notebook_preamble import D, J, V
A long trace A long trace
------------ ------------
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
V('[23 18] average') V('[23 18] average')

48
docs/sphinx_docs/_build/html/_sources/notebooks/Treestep.rst.txt
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@ -148,11 +148,11 @@ Working backwards:
Define ``treestep`` Define ``treestep``
------------------- -------------------
.. code:: ipython2 .. code:: python
from notebook_preamble import D, J, V, define, DefinitionWrapper from notebook_preamble import D, J, V, define, DefinitionWrapper
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
DefinitionWrapper.add_definitions(''' DefinitionWrapper.add_definitions('''
@ -587,7 +587,7 @@ To me, that seems simpler than the ``genrec`` version.
''', D) ''', D)
.. code:: ipython2 .. code:: python
J('''\ J('''\
@ -603,7 +603,7 @@ To me, that seems simpler than the ``genrec`` version.
15 15
.. code:: ipython2 .. code:: python
J('''\ J('''\

30
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@ -1,7 +1,7 @@
Type Checking Type Checking
============= =============
.. code:: ipython2 .. code:: python
import logging, sys import logging, sys
@ -11,7 +11,7 @@ Type Checking
level=logging.INFO, level=logging.INFO,
) )
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
D = FUNCTIONS.copy() D = FUNCTIONS.copy()
del D['product'] del D['product']
@ -31,7 +31,7 @@ Type Checking
An Example An Example
---------- ----------
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
u = unify(e, fi)[0] u = unify(e, fi)[0]
u u
@ -87,7 +87,7 @@ An Example
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
e = text_to_expression('[2 3]') e = text_to_expression('[2 3]')
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
def compose(f, g): def compose(f, g):
@ -465,7 +465,7 @@ integers or tuples of type descriptors:
``unify()`` ``unify()``
~~~~~~~~~~~ ~~~~~~~~~~~
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
C(pop, swap) C(pop, swap)
@ -573,7 +573,7 @@ Let’s try it out.
.. code:: ipython2 .. code:: python
C(C(pop, swap), roll_dn) C(C(pop, swap), roll_dn)
@ -586,7 +586,7 @@ Let’s try it out.
.. code:: ipython2 .. code:: python
C(swap, roll_dn) C(swap, roll_dn)
@ -599,7 +599,7 @@ Let’s try it out.
.. code:: ipython2 .. code:: python
C(pop, C(swap, roll_dn)) C(pop, C(swap, roll_dn))
@ -612,7 +612,7 @@ Let’s try it out.
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
rest = ((1, 2),), (2,) rest = ((1, 2),), (2,)
cons = (1, 2), ((1, 2),) cons = (1, 2), ((1, 2),)
.. code:: ipython2 .. code:: python
C(poswrd, rest) C(poswrd, rest)
@ -671,7 +671,7 @@ The translation table, if you will, would be:
0: 0, 0: 0,
} }
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
uncons = ((1, 2),), (1, 2) uncons = ((1, 2),), (1, 2)
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
F[0] F[0]
@ -816,7 +816,7 @@ Eh?
And the return tuple And the return tuple
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
source = compile_('F', F) source = compile_('F', F)
@ -949,7 +949,7 @@ Here it is in action:
Compare: Compare:
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
L = {} L = {}
@ -976,16 +976,16 @@ Next steps:
Let’s try it out: Let’s try it out:
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
D['F'] = SimpleFunctionWrapper(L['F']) D['F'] = SimpleFunctionWrapper(L['F'])
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
def defs(): def defs():
@ -1036,7 +1036,7 @@ from their stack effect comments:
return locals() return locals()
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
dup dup
@ -1322,7 +1322,7 @@ Typing ``sqr``
.. code:: ipython2 .. code:: python
mul mul
@ -1340,7 +1340,7 @@ Modifying the Inferencer
Re-labeling still works fine: Re-labeling still works fine:
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
def defs(): def defs():
@ -1503,11 +1503,11 @@ Rewrite the stack effect comments:
return locals() return locals()
.. code:: ipython2 .. code:: python
DEFS = defs() DEFS = defs()
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
globals().update(DEFS) globals().update(DEFS)
Compose ``dup`` and ``mul`` Compose ``dup`` and ``mul``
^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
def neato(*funcs): def neato(*funcs):
print doc_from_stack_effect(*reduce(C, funcs)) print doc_from_stack_effect(*reduce(C, funcs))
.. code:: ipython2 .. code:: python
# 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:: ipython2 .. code:: python
# 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:: ipython2 .. code:: python
# 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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
C(stack, uncons) C(stack, uncons)
@ -1867,7 +1867,7 @@ conversion function instead. This is programmer’s laziness.
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
C(cons, unstack) C(cons, unstack)
@ -2117,7 +2117,7 @@ Part VI: Multiple Stack Effects
… …
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
a = (As[1], S[1]) a = (As[1], S[1])
a a
@ -2400,7 +2400,7 @@ Can now return multiple results…
.. code:: ipython2 .. code:: python
b = (A[1], S[2]) b = (A[1], S[2])
b b
@ -2414,7 +2414,7 @@ Can now return multiple results…
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
@ -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:: ipython2 .. code:: python
@ -2556,7 +2556,7 @@ This function has to be modified to yield multiple results.
(n1 [n1* .1.] -- n2) (n1 [n1* .1.] -- n2)
.. code:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
def _ge(self, other): def _ge(self, other):
return (issubclass(other.__class__, self.__class__) return (issubclass(other.__class__, self.__class__)

36
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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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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:: ipython2 .. code:: python
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')

258
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@ -35,7 +35,7 @@
<section id="functions-grouped-by-er-function-with-examples"> <section id="functions-grouped-by-er-function-with-examples">
<h1>Functions Grouped by, er, Function with Examples<a class="headerlink" href="#functions-grouped-by-er-function-with-examples" title="Permalink to this headline"></a></h1> <h1>Functions Grouped by, er, Function with Examples<a class="headerlink" href="#functions-grouped-by-er-function-with-examples" title="Permalink to this headline"></a></h1>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V <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>
</pre></div> </pre></div>
</div> </div>
<section id="stack-chatter"> <section id="stack-chatter">
@ -48,7 +48,7 @@ static for the duration of the computation. This remains to be done but
it’s “off the shelf” technology.)</p> it’s “off the shelf” technology.)</p>
<section id="clear"> <section id="clear">
<h3><code class="docutils literal notranslate"><span class="pre">clear</span></code><a class="headerlink" href="#clear" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">clear</span></code><a class="headerlink" href="#clear" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 clear&#39;) <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 clear&#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="n">nothing</span><span class="p">)</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">nothing</span><span class="p">)</span>
@ -57,13 +57,13 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="dup-dupd"> <section id="dup-dupd">
<h3><code class="docutils literal notranslate"><span class="pre">dup</span></code> <code class="docutils literal notranslate"><span class="pre">dupd</span></code><a class="headerlink" href="#dup-dupd" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">dup</span></code> <code class="docutils literal notranslate"><span class="pre">dupd</span></code><a class="headerlink" href="#dup-dupd" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 dup&#39;) <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 dup&#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">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 dupd&#39;) <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 dupd&#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">1</span> <span class="mi">2</span> <span class="mi">2</span> <span class="mi">3</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">2</span> <span class="mi">3</span>
@ -74,27 +74,27 @@ it’s “off the shelf” technology.)</p>
<h3><code class="docutils literal notranslate"><span class="pre">enstacken</span></code> <code class="docutils literal notranslate"><span class="pre">disenstacken</span></code> <code class="docutils literal notranslate"><span class="pre">stack</span></code> <code class="docutils literal notranslate"><span class="pre">unstack</span></code><a class="headerlink" href="#enstacken-disenstacken-stack-unstack" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">enstacken</span></code> <code class="docutils literal notranslate"><span class="pre">disenstacken</span></code> <code class="docutils literal notranslate"><span class="pre">stack</span></code> <code class="docutils literal notranslate"><span class="pre">unstack</span></code><a class="headerlink" href="#enstacken-disenstacken-stack-unstack" title="Permalink to this headline"></a></h3>
<p>(I may have these paired up wrong. I.e. <code class="docutils literal notranslate"><span class="pre">disenstacken</span></code> should be <p>(I may have these paired up wrong. I.e. <code class="docutils literal notranslate"><span class="pre">disenstacken</span></code> should be
<code class="docutils literal notranslate"><span class="pre">unstack</span></code> and vice versa.)</p> <code class="docutils literal notranslate"><span class="pre">unstack</span></code> and vice versa.)</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 enstacken&#39;) # Replace the stack with a quote of itself. <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 enstacken&#39;</span><span class="p">)</span> <span class="c1"># Replace the stack with a quote of itself.</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">1</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">1</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;4 5 6 [3 2 1] disenstacken&#39;) # Unpack a list onto the stack. <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 6 [3 2 1] disenstacken&#39;</span><span class="p">)</span> <span class="c1"># Unpack a list onto the stack.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 stack&#39;) # Get the stack on the stack. <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 stack&#39;</span><span class="p">)</span> <span class="c1"># Get the stack on the stack.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="p">[</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="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 [4 5 6] unstack&#39;) # Replace the stack with the list on top. <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 5 6] unstack&#39;</span><span class="p">)</span> <span class="c1"># Replace the stack with the list on top.</span>
# The items appear reversed but they are not, <span class="c1"># The items appear reversed but they are not,</span>
# 4 is on the top of both the list and the stack. <span class="c1"># 4 is on the top of both the list and the stack.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span> <span class="mi">5</span> <span class="mi">4</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span> <span class="mi">5</span> <span class="mi">4</span>
@ -103,19 +103,19 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="pop-popd-popop"> <section id="pop-popd-popop">
<h3><code class="docutils literal notranslate"><span class="pre">pop</span></code> <code class="docutils literal notranslate"><span class="pre">popd</span></code> <code class="docutils literal notranslate"><span class="pre">popop</span></code><a class="headerlink" href="#pop-popd-popop" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">pop</span></code> <code class="docutils literal notranslate"><span class="pre">popd</span></code> <code class="docutils literal notranslate"><span class="pre">popop</span></code><a class="headerlink" href="#pop-popd-popop" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 pop&#39;) <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 pop&#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">1</span> <span class="mi">2</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 popd&#39;) <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 popd&#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">1</span> <span class="mi">3</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">3</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 popop&#39;) <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 popop&#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">1</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span>
@ -126,13 +126,13 @@ it’s “off the shelf” technology.)</p>
<h3><code class="docutils literal notranslate"><span class="pre">roll&lt;</span></code> <code class="docutils literal notranslate"><span class="pre">rolldown</span></code> <code class="docutils literal notranslate"><span class="pre">roll&gt;</span></code> <code class="docutils literal notranslate"><span class="pre">rollup</span></code><a class="headerlink" href="#roll-rolldown-roll-rollup" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">roll&lt;</span></code> <code class="docutils literal notranslate"><span class="pre">rolldown</span></code> <code class="docutils literal notranslate"><span class="pre">roll&gt;</span></code> <code class="docutils literal notranslate"><span class="pre">rollup</span></code><a class="headerlink" href="#roll-rolldown-roll-rollup" title="Permalink to this headline"></a></h3>
<p>The “down” and “up” refer to the movement of two of the top three items <p>The “down” and “up” refer to the movement of two of the top three items
(displacing the third.)</p> (displacing the third.)</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 roll&lt;&#39;) <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 roll&lt;&#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">1</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">1</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 roll&gt;&#39;) <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 roll&gt;&#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="mi">1</span> <span class="mi">2</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span>
@ -141,7 +141,7 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="swap"> <section id="swap">
<h3><code class="docutils literal notranslate"><span class="pre">swap</span></code><a class="headerlink" href="#swap" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">swap</span></code><a class="headerlink" href="#swap" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 swap&#39;) <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 swap&#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">1</span> <span class="mi">3</span> <span class="mi">2</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">2</span>
@ -150,13 +150,13 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="tuck-over"> <section id="tuck-over">
<h3><code class="docutils literal notranslate"><span class="pre">tuck</span></code> <code class="docutils literal notranslate"><span class="pre">over</span></code><a class="headerlink" href="#tuck-over" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">tuck</span></code> <code class="docutils literal notranslate"><span class="pre">over</span></code><a class="headerlink" href="#tuck-over" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 tuck&#39;) <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 tuck&#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">1</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">3</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">3</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 over&#39;) <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 over&#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">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">2</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">2</span>
@ -165,25 +165,25 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="unit-quoted-unquoted"> <section id="unit-quoted-unquoted">
<h3><code class="docutils literal notranslate"><span class="pre">unit</span></code> <code class="docutils literal notranslate"><span class="pre">quoted</span></code> <code class="docutils literal notranslate"><span class="pre">unquoted</span></code><a class="headerlink" href="#unit-quoted-unquoted" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">unit</span></code> <code class="docutils literal notranslate"><span class="pre">quoted</span></code> <code class="docutils literal notranslate"><span class="pre">unquoted</span></code><a class="headerlink" href="#unit-quoted-unquoted" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 unit&#39;) <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 unit&#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">1</span> <span class="mi">2</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="mi">1</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 quoted&#39;) <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 quoted&#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">1</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="mi">3</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="mi">3</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 [2] 3 unquoted&#39;) <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 unquoted&#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">1</span> <span class="mi">2</span> <span class="mi">3</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;1 [dup] 3 unquoted&#39;) # Unquoting evaluates. Be aware. <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 [dup] 3 unquoted&#39;</span><span class="p">)</span> <span class="c1"># Unquoting evaluates. Be aware.</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="n">dup</span><span class="p">]</span> <span class="mi">3</span> <span class="n">unquoted</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="n">dup</span><span class="p">]</span> <span class="mi">3</span> <span class="n">unquoted</span>
@ -204,19 +204,19 @@ it’s “off the shelf” technology.)</p>
<h2>List words<a class="headerlink" href="#list-words" title="Permalink to this headline"></a></h2> <h2>List words<a class="headerlink" href="#list-words" title="Permalink to this headline"></a></h2>
<section id="concat-swoncat-shunt"> <section id="concat-swoncat-shunt">
<h3><code class="docutils literal notranslate"><span class="pre">concat</span></code> <code class="docutils literal notranslate"><span class="pre">swoncat</span></code> <code class="docutils literal notranslate"><span class="pre">shunt</span></code><a class="headerlink" href="#concat-swoncat-shunt" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">concat</span></code> <code class="docutils literal notranslate"><span class="pre">swoncat</span></code> <code class="docutils literal notranslate"><span class="pre">shunt</span></code><a class="headerlink" href="#concat-swoncat-shunt" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3] [4 5 6] concat&#39;) <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 5 6] concat&#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="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="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="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3] [4 5 6] swoncat&#39;) <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 5 6] swoncat&#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">5</span> <span class="mi">6</span> <span class="mi">1</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">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3] [4 5 6] shunt&#39;) <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 5 6] shunt&#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">6</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">1</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">6</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span>
@ -225,19 +225,19 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="cons-swons-uncons"> <section id="cons-swons-uncons">
<h3><code class="docutils literal notranslate"><span class="pre">cons</span></code> <code class="docutils literal notranslate"><span class="pre">swons</span></code> <code class="docutils literal notranslate"><span class="pre">uncons</span></code><a class="headerlink" href="#cons-swons-uncons" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">cons</span></code> <code class="docutils literal notranslate"><span class="pre">swons</span></code> <code class="docutils literal notranslate"><span class="pre">uncons</span></code><a class="headerlink" href="#cons-swons-uncons" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 [2 3] cons&#39;) <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] cons&#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="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="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[2 3] 1 swons&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[2 3] 1 swons&#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="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="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3] uncons&#39;) <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] uncons&#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">1</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="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span>
@ -246,25 +246,25 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="first-second-third-rest"> <section id="first-second-third-rest">
<h3><code class="docutils literal notranslate"><span class="pre">first</span></code> <code class="docutils literal notranslate"><span class="pre">second</span></code> <code class="docutils literal notranslate"><span class="pre">third</span></code> <code class="docutils literal notranslate"><span class="pre">rest</span></code><a class="headerlink" href="#first-second-third-rest" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">first</span></code> <code class="docutils literal notranslate"><span class="pre">second</span></code> <code class="docutils literal notranslate"><span class="pre">third</span></code> <code class="docutils literal notranslate"><span class="pre">rest</span></code><a class="headerlink" href="#first-second-third-rest" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 4] first&#39;) <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] first&#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">1</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 4] second&#39;) <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] second&#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> <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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 4] third&#39;) <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] third&#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> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 4] rest&#39;) <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] rest&#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="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="p">]</span>
@ -273,7 +273,7 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="flatten"> <section id="flatten">
<h3><code class="docutils literal notranslate"><span class="pre">flatten</span></code><a class="headerlink" href="#flatten" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">flatten</span></code><a class="headerlink" href="#flatten" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[1] [2 [3] 4] [5 6]] flatten&#39;) <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] [5 6]] flatten&#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="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="mi">4</span> <span class="mi">5</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="mi">2</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span><span class="p">]</span>
@ -283,31 +283,31 @@ it’s “off the shelf” technology.)</p>
<section id="getitem-at-of-drop-take"> <section id="getitem-at-of-drop-take">
<h3><code class="docutils literal notranslate"><span class="pre">getitem</span></code> <code class="docutils literal notranslate"><span class="pre">at</span></code> <code class="docutils literal notranslate"><span class="pre">of</span></code> <code class="docutils literal notranslate"><span class="pre">drop</span></code> <code class="docutils literal notranslate"><span class="pre">take</span></code><a class="headerlink" href="#getitem-at-of-drop-take" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">getitem</span></code> <code class="docutils literal notranslate"><span class="pre">at</span></code> <code class="docutils literal notranslate"><span class="pre">of</span></code> <code class="docutils literal notranslate"><span class="pre">drop</span></code> <code class="docutils literal notranslate"><span class="pre">take</span></code><a class="headerlink" href="#getitem-at-of-drop-take" title="Permalink to this headline"></a></h3>
<p><code class="docutils literal notranslate"><span class="pre">at</span></code> and <code class="docutils literal notranslate"><span class="pre">getitem</span></code> are the same function. <code class="docutils literal notranslate"><span class="pre">of</span> <span class="pre">==</span> <span class="pre">swap</span> <span class="pre">at</span></code></p> <p><code class="docutils literal notranslate"><span class="pre">at</span></code> and <code class="docutils literal notranslate"><span class="pre">getitem</span></code> are the same function. <code class="docutils literal notranslate"><span class="pre">of</span> <span class="pre">==</span> <span class="pre">swap</span> <span class="pre">at</span></code></p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[10 11 12 13 14] 2 getitem&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[10 11 12 13 14] 2 getitem&#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">12</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">12</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 4] 0 at&#39;) <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] 0 at&#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">1</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;2 [1 2 3 4] of&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;2 [1 2 3 4] of&#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> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 4] 2 drop&#39;) <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] 2 drop&#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">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="mi">4</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 4] 2 take&#39;) # reverses the order <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] 2 take&#39;</span><span class="p">)</span> <span class="c1"># reverses the order</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">1</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">1</span><span class="p">]</span>
@ -317,7 +317,7 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="remove"> <section id="remove">
<h3><code class="docutils literal notranslate"><span class="pre">remove</span></code><a class="headerlink" href="#remove" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">remove</span></code><a class="headerlink" href="#remove" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 1 4] 1 remove&#39;) <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 1 4] 1 remove&#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">1</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">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">4</span><span class="p">]</span>
@ -326,7 +326,7 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="reverse"> <section id="reverse">
<h3><code class="docutils literal notranslate"><span class="pre">reverse</span></code><a class="headerlink" href="#reverse" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">reverse</span></code><a class="headerlink" href="#reverse" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 4] reverse&#39;) <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] 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">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">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span><span class="p">]</span>
@ -335,7 +335,7 @@ it’s “off the shelf” technology.)</p>
</section> </section>
<section id="size"> <section id="size">
<h3><code class="docutils literal notranslate"><span class="pre">size</span></code><a class="headerlink" href="#size" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">size</span></code><a class="headerlink" href="#size" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 1 1 1] size&#39;) <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 1 1 1] size&#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">4</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4</span>
@ -347,7 +347,7 @@ it’s “off the shelf” technology.)</p>
<p>“Swap stack” swap the list on the top of the stack for the stack, and <p>“Swap stack” swap the list on the top of the stack for the stack, and
put the old stack on top of the new one. Think of it as a context put the old stack on top of the new one. Think of it as a context
switch. Niether of the lists/stacks change their order.</p> switch. Niether of the lists/stacks change their order.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 [4 5 6] swaack&#39;) <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 5 6] swaack&#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> <span class="mi">5</span> <span class="mi">4</span> <span class="p">[</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="mi">6</span> <span class="mi">5</span> <span class="mi">4</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span><span class="p">]</span>
@ -356,25 +356,25 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="choice-select"> <section id="choice-select">
<h3><code class="docutils literal notranslate"><span class="pre">choice</span></code> <code class="docutils literal notranslate"><span class="pre">select</span></code><a class="headerlink" href="#choice-select" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">choice</span></code> <code class="docutils literal notranslate"><span class="pre">select</span></code><a class="headerlink" href="#choice-select" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 1 choice&#39;) <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 9 1 choice&#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">9</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">9</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 0 choice&#39;) <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 9 0 choice&#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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 9 7] 1 select&#39;) # select is basically getitem, should retire it? <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 9 7] 1 select&#39;</span><span class="p">)</span> <span class="c1"># select is basically getitem, should retire it?</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">9</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">9</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 9 7] 0 select&#39;) <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 9 7] 0 select&#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>
@ -383,13 +383,13 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="zip"> <section id="zip">
<h3><code class="docutils literal notranslate"><span class="pre">zip</span></code><a class="headerlink" href="#zip" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">zip</span></code><a class="headerlink" href="#zip" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3] [6 5 4] zip&#39;) <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] [6 5 4] zip&#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">6</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</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">6</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3] [6 5 4] zip [sum] map&#39;) <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] [6 5 4] zip [sum] 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">7</span> <span class="mi">7</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">7</span> <span class="mi">7</span> <span class="mi">7</span><span class="p">]</span>
@ -401,7 +401,7 @@ switch. Niether of the lists/stacks change their order.</p>
<h2>Math words<a class="headerlink" href="#math-words" title="Permalink to this headline"></a></h2> <h2>Math words<a class="headerlink" href="#math-words" title="Permalink to this headline"></a></h2>
<section id="add"> <section id="add">
<h3><code class="docutils literal notranslate"><span class="pre">+</span></code> <code class="docutils literal notranslate"><span class="pre">add</span></code><a class="headerlink" href="#add" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">+</span></code> <code class="docutils literal notranslate"><span class="pre">add</span></code><a class="headerlink" href="#add" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 +&#39;) <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 9 +&#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">32</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">32</span>
@ -410,7 +410,7 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="sub"> <section id="sub">
<h3><code class="docutils literal notranslate"><span class="pre">-</span></code> <code class="docutils literal notranslate"><span class="pre">sub</span></code><a class="headerlink" href="#sub" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">-</span></code> <code class="docutils literal notranslate"><span class="pre">sub</span></code><a class="headerlink" href="#sub" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 -&#39;) <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 9 -&#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">14</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">14</span>
@ -419,7 +419,7 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="mul"> <section id="mul">
<h3><code class="docutils literal notranslate"><span class="pre">*</span></code> <code class="docutils literal notranslate"><span class="pre">mul</span></code><a class="headerlink" href="#mul" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">*</span></code> <code class="docutils literal notranslate"><span class="pre">mul</span></code><a class="headerlink" href="#mul" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 *&#39;) <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 9 *&#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">207</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">207</span>
@ -428,37 +428,37 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="div-floordiv-truediv"> <section id="div-floordiv-truediv">
<h3><code class="docutils literal notranslate"><span class="pre">/</span></code> <code class="docutils literal notranslate"><span class="pre">div</span></code> <code class="docutils literal notranslate"><span class="pre">floordiv</span></code> <code class="docutils literal notranslate"><span class="pre">truediv</span></code><a class="headerlink" href="#div-floordiv-truediv" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">/</span></code> <code class="docutils literal notranslate"><span class="pre">div</span></code> <code class="docutils literal notranslate"><span class="pre">floordiv</span></code> <code class="docutils literal notranslate"><span class="pre">truediv</span></code><a class="headerlink" href="#div-floordiv-truediv" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 /&#39;) <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 9 /&#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">2.5555555555555554</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">2.5555555555555554</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 -9 truediv&#39;) <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 -9 truediv&#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">2.5555555555555554</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mf">2.5555555555555554</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 div&#39;) <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 9 div&#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> <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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 floordiv&#39;) <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 9 floordiv&#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> <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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 -9 div&#39;) <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 -9 div&#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">3</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mi">3</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 -9 floordiv&#39;) <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 -9 floordiv&#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">3</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mi">3</span>
@ -467,7 +467,7 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="mod-modulus-rem-remainder"> <section id="mod-modulus-rem-remainder">
<h3><code class="docutils literal notranslate"><span class="pre">%</span></code> <code class="docutils literal notranslate"><span class="pre">mod</span></code> <code class="docutils literal notranslate"><span class="pre">modulus</span></code> <code class="docutils literal notranslate"><span class="pre">rem</span></code> <code class="docutils literal notranslate"><span class="pre">remainder</span></code><a class="headerlink" href="#mod-modulus-rem-remainder" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">%</span></code> <code class="docutils literal notranslate"><span class="pre">mod</span></code> <code class="docutils literal notranslate"><span class="pre">modulus</span></code> <code class="docutils literal notranslate"><span class="pre">rem</span></code> <code class="docutils literal notranslate"><span class="pre">remainder</span></code><a class="headerlink" href="#mod-modulus-rem-remainder" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 %&#39;) <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 9 %&#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">5</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">5</span>
@ -476,7 +476,7 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="neg"> <section id="neg">
<h3><code class="docutils literal notranslate"><span class="pre">neg</span></code><a class="headerlink" href="#neg" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">neg</span></code><a class="headerlink" href="#neg" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 neg -5 neg&#39;) <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 neg -5 neg&#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">23</span> <span class="mi">5</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mi">23</span> <span class="mi">5</span>
@ -485,7 +485,7 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="pow"> <section id="pow">
<h3><code class="docutils literal notranslate"><span class="pre">pow</span></code><a class="headerlink" href="#pow" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">pow</span></code><a class="headerlink" href="#pow" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;2 10 pow&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;2 10 pow&#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">1024</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1024</span>
@ -494,13 +494,13 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="sqr-sqrt"> <section id="sqr-sqrt">
<h3><code class="docutils literal notranslate"><span class="pre">sqr</span></code> <code class="docutils literal notranslate"><span class="pre">sqrt</span></code><a class="headerlink" href="#sqr-sqrt" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">sqr</span></code> <code class="docutils literal notranslate"><span class="pre">sqrt</span></code><a class="headerlink" href="#sqr-sqrt" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 sqr&#39;) <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 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="mi">529</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">529</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 sqrt&#39;) <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>
</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>
@ -509,13 +509,13 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="succ-pred"> <section id="succ-pred">
<h3><code class="docutils literal notranslate"><span class="pre">++</span></code> <code class="docutils literal notranslate"><span class="pre">succ</span></code> <code class="docutils literal notranslate"><span class="pre">--</span></code> <code class="docutils literal notranslate"><span class="pre">pred</span></code><a class="headerlink" href="#succ-pred" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">++</span></code> <code class="docutils literal notranslate"><span class="pre">succ</span></code> <code class="docutils literal notranslate"><span class="pre">--</span></code> <code class="docutils literal notranslate"><span class="pre">pred</span></code><a class="headerlink" href="#succ-pred" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 ++&#39;) <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 ++&#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> <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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 --&#39;) <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 --&#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">0</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span>
@ -524,13 +524,13 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="lshift-rshift"> <section id="lshift-rshift">
<h3><code class="docutils literal notranslate"><span class="pre">&lt;&lt;</span></code> <code class="docutils literal notranslate"><span class="pre">lshift</span></code> <code class="docutils literal notranslate"><span class="pre">&gt;&gt;</span></code> <code class="docutils literal notranslate"><span class="pre">rshift</span></code><a class="headerlink" href="#lshift-rshift" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">&lt;&lt;</span></code> <code class="docutils literal notranslate"><span class="pre">lshift</span></code> <code class="docutils literal notranslate"><span class="pre">&gt;&gt;</span></code> <code class="docutils literal notranslate"><span class="pre">rshift</span></code><a class="headerlink" href="#lshift-rshift" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;8 1 &lt;&lt;&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;8 1 &lt;&lt;&#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">16</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">16</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;8 1 &gt;&gt;&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;8 1 &gt;&gt;&#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">4</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4</span>
@ -539,7 +539,7 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="average"> <section id="average">
<h3><code class="docutils literal notranslate"><span class="pre">average</span></code><a class="headerlink" href="#average" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">average</span></code><a class="headerlink" href="#average" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 5] average&#39;) <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 5] 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="mf">2.75</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">2.75</span>
@ -548,19 +548,19 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="range-range-to-zero-down-to-zero"> <section id="range-range-to-zero-down-to-zero">
<h3><code class="docutils literal notranslate"><span class="pre">range</span></code> <code class="docutils literal notranslate"><span class="pre">range_to_zero</span></code> <code class="docutils literal notranslate"><span class="pre">down_to_zero</span></code><a class="headerlink" href="#range-range-to-zero-down-to-zero" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">range</span></code> <code class="docutils literal notranslate"><span class="pre">range_to_zero</span></code> <code class="docutils literal notranslate"><span class="pre">down_to_zero</span></code><a class="headerlink" href="#range-range-to-zero-down-to-zero" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 range&#39;) <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>
</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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 range_to_zero&#39;) <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_to_zero&#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="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">0</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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 down_to_zero&#39;) <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 down_to_zero&#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">5</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> <div class="highlight-default notranslate"><div class="highlight"><pre><span></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="mi">0</span>
@ -569,7 +569,7 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="product"> <section id="product">
<h3><code class="docutils literal notranslate"><span class="pre">product</span></code><a class="headerlink" href="#product" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">product</span></code><a class="headerlink" href="#product" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 5] product&#39;) <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 5] product&#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">30</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">30</span>
@ -578,7 +578,7 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="sum"> <section id="sum">
<h3><code class="docutils literal notranslate"><span class="pre">sum</span></code><a class="headerlink" href="#sum" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">sum</span></code><a class="headerlink" href="#sum" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 5] sum&#39;) <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 5] 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">11</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">11</span>
@ -587,7 +587,7 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="min"> <section id="min">
<h3><code class="docutils literal notranslate"><span class="pre">min</span></code><a class="headerlink" href="#min" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">min</span></code><a class="headerlink" href="#min" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3 5] min&#39;) <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 5] min&#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">1</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span>
@ -596,7 +596,7 @@ switch. Niether of the lists/stacks change their order.</p>
</section> </section>
<section id="gcd"> <section id="gcd">
<h3><code class="docutils literal notranslate"><span class="pre">gcd</span></code><a class="headerlink" href="#gcd" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">gcd</span></code><a class="headerlink" href="#gcd" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;45 30 gcd&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;45 30 gcd&#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>
@ -607,13 +607,13 @@ switch. Niether of the lists/stacks change their order.</p>
<h3><code class="docutils literal notranslate"><span class="pre">least_fraction</span></code><a class="headerlink" href="#least-fraction" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">least_fraction</span></code><a class="headerlink" href="#least-fraction" title="Permalink to this headline"></a></h3>
<p>If we represent fractions as a quoted pair of integers [q d] this word <p>If we represent fractions as a quoted pair of integers [q d] this word
reduces them to their … least common factors or whatever.</p> reduces them to their … least common factors or whatever.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[45 30] least_fraction&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[45 30] least_fraction&#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="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="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 12] least_fraction&#39;) <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 12] least_fraction&#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">23</span> <span class="mi">12</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="mi">12</span><span class="p">]</span>
@ -626,19 +626,19 @@ reduces them to their … least common factors or whatever.</p>
<section id="truthy"> <section id="truthy">
<h3><code class="docutils literal notranslate"><span class="pre">?</span></code> <code class="docutils literal notranslate"><span class="pre">truthy</span></code><a class="headerlink" href="#truthy" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">?</span></code> <code class="docutils literal notranslate"><span class="pre">truthy</span></code><a class="headerlink" href="#truthy" title="Permalink to this headline"></a></h3>
<p>Get the Boolean value of the item on the top of the stack.</p> <p>Get the Boolean value of the item on the top of the stack.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 truthy&#39;) <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 truthy&#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="kc">True</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kc">True</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] truthy&#39;) # Python semantics. <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] truthy&#39;</span><span class="p">)</span> <span class="c1"># Python semantics.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kc">False</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kc">False</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;0 truthy&#39;) <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 truthy&#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="kc">False</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kc">False</span>
@ -647,7 +647,7 @@ reduces them to their … least common factors or whatever.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>? == dup truthy <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>? == dup truthy
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;23 ?&#39;) <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 ?&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> . 23 ? <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> . 23 ?
@ -657,13 +657,13 @@ reduces them to their … least common factors or whatever.</p>
23 True . 23 True .
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] ?&#39;) <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;</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="kc">False</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="kc">False</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;0 ?&#39;) <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 ?&#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">0</span> <span class="kc">False</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="kc">False</span>
@ -672,7 +672,7 @@ reduces them to their … least common factors or whatever.</p>
</section> </section>
<section id="and"> <section id="and">
<h3><code class="docutils literal notranslate"><span class="pre">&amp;</span></code> <code class="docutils literal notranslate"><span class="pre">and</span></code><a class="headerlink" href="#and" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">&amp;</span></code> <code class="docutils literal notranslate"><span class="pre">and</span></code><a class="headerlink" href="#and" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 &amp;&#39;) <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 9 &amp;&#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">1</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span>
@ -681,7 +681,7 @@ reduces them to their … least common factors or whatever.</p>
</section> </section>
<section id="ne"> <section id="ne">
<h3><code class="docutils literal notranslate"><span class="pre">!=</span></code> <code class="docutils literal notranslate"><span class="pre">&lt;&gt;</span></code> <code class="docutils literal notranslate"><span class="pre">ne</span></code><a class="headerlink" href="#ne" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">!=</span></code> <code class="docutils literal notranslate"><span class="pre">&lt;&gt;</span></code> <code class="docutils literal notranslate"><span class="pre">ne</span></code><a class="headerlink" href="#ne" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 9 !=&#39;) <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 9 !=&#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="kc">True</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kc">True</span>
@ -694,13 +694,13 @@ reduces them to their … least common factors or whatever.</p>
</section> </section>
<section id="xor"> <section id="xor">
<h3><code class="docutils literal notranslate"><span class="pre">^</span></code> <code class="docutils literal notranslate"><span class="pre">xor</span></code><a class="headerlink" href="#xor" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">^</span></code> <code class="docutils literal notranslate"><span class="pre">xor</span></code><a class="headerlink" href="#xor" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 1 ^&#39;) <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 1 ^&#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">0</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 0 ^&#39;) <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 0 ^&#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">1</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span>
@ -712,7 +712,7 @@ reduces them to their … least common factors or whatever.</p>
<h2>Miscellaneous<a class="headerlink" href="#miscellaneous" title="Permalink to this headline"></a></h2> <h2>Miscellaneous<a class="headerlink" href="#miscellaneous" title="Permalink to this headline"></a></h2>
<section id="help"> <section id="help">
<h3><code class="docutils literal notranslate"><span class="pre">help</span></code><a class="headerlink" href="#help" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">help</span></code><a class="headerlink" href="#help" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[help] help&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[help] 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">Accepts</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">symbol</span> <span class="n">on</span> <span class="n">the</span> <span class="n">top</span> <span class="n">of</span> <span class="n">the</span> <span class="n">stack</span> <span class="ow">and</span> <span class="n">prints</span> <span class="n">its</span> <span class="n">docs</span><span class="o">.</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Accepts</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">symbol</span> <span class="n">on</span> <span class="n">the</span> <span class="n">top</span> <span class="n">of</span> <span class="n">the</span> <span class="n">stack</span> <span class="ow">and</span> <span class="n">prints</span> <span class="n">its</span> <span class="n">docs</span><span class="o">.</span>
@ -721,13 +721,13 @@ reduces them to their … least common factors or whatever.</p>
</section> </section>
<section id="parse"> <section id="parse">
<h3><code class="docutils literal notranslate"><span class="pre">parse</span></code><a class="headerlink" href="#parse" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">parse</span></code><a class="headerlink" href="#parse" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[parse] help&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[parse] 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">Parse</span> <span class="n">the</span> <span class="n">string</span> <span class="n">on</span> <span class="n">the</span> <span class="n">stack</span> <span class="n">to</span> <span class="n">a</span> <span class="n">Joy</span> <span class="n">expression</span><span class="o">.</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Parse</span> <span class="n">the</span> <span class="n">string</span> <span class="n">on</span> <span class="n">the</span> <span class="n">stack</span> <span class="n">to</span> <span class="n">a</span> <span class="n">Joy</span> <span class="n">expression</span><span class="o">.</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 &quot;2 [3] dup&quot; parse&#39;) <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 &quot;2 [3] dup&quot; parse&#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">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="n">dup</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></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="n">dup</span><span class="p">]</span>
@ -737,7 +737,7 @@ reduces them to their … least common factors or whatever.</p>
<section id="run"> <section id="run">
<h3><code class="docutils literal notranslate"><span class="pre">run</span></code><a class="headerlink" href="#run" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">run</span></code><a class="headerlink" href="#run" title="Permalink to this headline"></a></h3>
<p>Evaluate a quoted Joy sequence.</p> <p>Evaluate a quoted Joy sequence.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 dup + +] run&#39;) <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 dup + +] run&#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="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">5</span><span class="p">]</span>
@ -749,7 +749,7 @@ reduces them to their … least common factors or whatever.</p>
<h2>Combinators<a class="headerlink" href="#combinators" title="Permalink to this headline"></a></h2> <h2>Combinators<a class="headerlink" href="#combinators" title="Permalink to this headline"></a></h2>
<section id="app1-app2-app3"> <section id="app1-app2-app3">
<h3><code class="docutils literal notranslate"><span class="pre">app1</span></code> <code class="docutils literal notranslate"><span class="pre">app2</span></code> <code class="docutils literal notranslate"><span class="pre">app3</span></code><a class="headerlink" href="#app1-app2-app3" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">app1</span></code> <code class="docutils literal notranslate"><span class="pre">app2</span></code> <code class="docutils literal notranslate"><span class="pre">app3</span></code><a class="headerlink" href="#app1-app2-app3" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[app1] help&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[app1] 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">Given</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">program</span> <span class="n">on</span> <span class="n">TOS</span> <span class="ow">and</span> <span class="n">anything</span> <span class="k">as</span> <span class="n">the</span> <span class="n">second</span> <span class="n">stack</span> <span class="n">item</span> <span class="n">run</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Given</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">program</span> <span class="n">on</span> <span class="n">TOS</span> <span class="ow">and</span> <span class="n">anything</span> <span class="k">as</span> <span class="n">the</span> <span class="n">second</span> <span class="n">stack</span> <span class="n">item</span> <span class="n">run</span>
@ -761,19 +761,19 @@ reduces them to their … least common factors or whatever.</p>
<span class="o">...</span> <span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span> <span class="o">...</span> <span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;10 4 [sqr *] app1&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;10 4 [sqr *] app1&#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> <span class="mi">160</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span> <span class="mi">160</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;10 3 4 [sqr *] app2&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;10 3 4 [sqr *] app2&#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> <span class="mi">90</span> <span class="mi">160</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span> <span class="mi">90</span> <span class="mi">160</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[app2] help&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[app2] 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">Like</span> <span class="n">app1</span> <span class="k">with</span> <span class="n">two</span> <span class="n">items</span><span class="o">.</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Like</span> <span class="n">app1</span> <span class="k">with</span> <span class="n">two</span> <span class="n">items</span><span class="o">.</span>
@ -784,7 +784,7 @@ reduces them to their … least common factors or whatever.</p>
<span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;10 2 3 4 [sqr *] app3&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;10 2 3 4 [sqr *] app3&#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> <span class="mi">40</span> <span class="mi">90</span> <span class="mi">160</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span> <span class="mi">40</span> <span class="mi">90</span> <span class="mi">160</span>
@ -804,7 +804,7 @@ function <code class="docutils literal notranslate"><span class="pre">[G]</span>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">range</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="mi">1</span> <span class="o">-</span> <span class="n">dup</span><span class="p">]</span> <span class="n">anamorphism</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">range</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="mi">1</span> <span class="o">-</span> <span class="n">dup</span><span class="p">]</span> <span class="n">anamorphism</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;3 [0 &lt;=] [1 - dup] anamorphism&#39;) <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 &lt;=] [1 - dup] anamorphism&#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">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">2</span> <span class="mi">1</span> <span class="mi">0</span><span class="p">]</span>
@ -813,13 +813,13 @@ function <code class="docutils literal notranslate"><span class="pre">[G]</span>
</section> </section>
<section id="branch"> <section id="branch">
<h3><code class="docutils literal notranslate"><span class="pre">branch</span></code><a class="headerlink" href="#branch" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">branch</span></code><a class="headerlink" href="#branch" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;3 4 1 [+] [*] branch&#39;) <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 4 1 [+] [*] branch&#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">12</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">12</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;3 4 0 [+] [*] branch&#39;) <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 4 0 [+] [*] branch&#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">7</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">7</span>
@ -846,7 +846,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">cleave</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">cleave</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;10 2 [+] [-] cleave&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;10 2 [+] [-] cleave&#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> <span class="mi">12</span> <span class="mi">8</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span> <span class="mi">12</span> <span class="mi">8</span>
@ -855,19 +855,19 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
</section> </section>
<section id="dip-dipd-dipdd"> <section id="dip-dipd-dipdd">
<h3><code class="docutils literal notranslate"><span class="pre">dip</span></code> <code class="docutils literal notranslate"><span class="pre">dipd</span></code> <code class="docutils literal notranslate"><span class="pre">dipdd</span></code><a class="headerlink" href="#dip-dipd-dipdd" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">dip</span></code> <code class="docutils literal notranslate"><span class="pre">dipd</span></code> <code class="docutils literal notranslate"><span class="pre">dipdd</span></code><a class="headerlink" href="#dip-dipd-dipdd" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 4 5 [+] dip&#39;) <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 5 [+] dip&#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">1</span> <span class="mi">2</span> <span class="mi">7</span> <span class="mi">5</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">7</span> <span class="mi">5</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 4 5 [+] dipd&#39;) <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 5 [+] dipd&#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">1</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">5</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">5</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 4 5 [+] dipdd&#39;) <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 5 [+] dipdd&#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="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span>
@ -881,7 +881,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">==</span> <span class="n">n</span> <span class="n">Q</span> <span class="n">n</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">==</span> <span class="n">n</span> <span class="n">Q</span> <span class="n">n</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;23 [++] dupdip *&#39;) # N(N + 1) <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 [++] dupdip *&#39;</span><span class="p">)</span> <span class="c1"># N(N + 1)</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">23</span> <span class="p">[</span><span class="o">++</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">*</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">23</span> <span class="p">[</span><span class="o">++</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">*</span>
@ -896,7 +896,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
</section> </section>
<section id="genrec-primrec"> <section id="genrec-primrec">
<h3><code class="docutils literal notranslate"><span class="pre">genrec</span></code> <code class="docutils literal notranslate"><span class="pre">primrec</span></code><a class="headerlink" href="#genrec-primrec" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">genrec</span></code> <code class="docutils literal notranslate"><span class="pre">primrec</span></code><a class="headerlink" href="#genrec-primrec" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[genrec] help&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[genrec] 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">General</span> <span class="n">Recursion</span> <span class="n">Combinator</span><span class="o">.</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">General</span> <span class="n">Recursion</span> <span class="n">Combinator</span><span class="o">.</span>
@ -945,7 +945,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
<span class="p">)</span> <span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;3 [1 &lt;=] [] [dup --] [i *] genrec&#39;) <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 &lt;=] [] [dup --] [i *] genrec&#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>
@ -954,7 +954,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
</section> </section>
<section id="i"> <section id="i">
<h3><code class="docutils literal notranslate"><span class="pre">i</span></code><a class="headerlink" href="#i" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">i</span></code><a class="headerlink" href="#i" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;1 2 3 [+ +] i&#39;) <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 [+ +] i&#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="mi">2</span> <span class="mi">3</span> <span class="p">[</span><span class="o">+</span> <span class="o">+</span><span class="p">]</span> <span class="n">i</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="p">[</span><span class="o">+</span> <span class="o">+</span><span class="p">]</span> <span class="n">i</span>
@ -973,13 +973,13 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">predicate</span><span class="p">]</span> <span class="p">[</span><span class="n">then</span><span class="p">]</span> <span class="p">[</span><span class="k">else</span><span class="p">]</span> <span class="n">ifte</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">predicate</span><span class="p">]</span> <span class="p">[</span><span class="n">then</span><span class="p">]</span> <span class="p">[</span><span class="k">else</span><span class="p">]</span> <span class="n">ifte</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 [1] [+] [*] ifte&#39;) <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 [1] [+] [*] ifte&#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> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 [0] [+] [*] ifte&#39;) <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 [0] [+] [*] ifte&#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> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span>
@ -988,7 +988,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
</section> </section>
<section id="infra"> <section id="infra">
<h3><code class="docutils literal notranslate"><span class="pre">infra</span></code><a class="headerlink" href="#infra" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">infra</span></code><a class="headerlink" href="#infra" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;1 2 3 [4 5 6] [* +] infra&#39;) <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 5 6] [* +] 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="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span><span class="p">]</span> <span class="p">[</span><span class="o">*</span> <span class="o">+</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="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span><span class="p">]</span> <span class="p">[</span><span class="o">*</span> <span class="o">+</span><span class="p">]</span> <span class="n">infra</span>
@ -1007,7 +1007,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
</section> </section>
<section id="loop"> <section id="loop">
<h3><code class="docutils literal notranslate"><span class="pre">loop</span></code><a class="headerlink" href="#loop" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">loop</span></code><a class="headerlink" href="#loop" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[loop] help&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[loop] 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">Basic</span> <span class="n">loop</span> <span class="n">combinator</span><span class="o">.</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Basic</span> <span class="n">loop</span> <span class="n">combinator</span><span class="o">.</span>
@ -1021,7 +1021,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
<span class="o">...</span> <span class="o">...</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;3 dup [1 - dup] loop&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;3 dup [1 - dup] loop&#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">3</span> <span class="n">dup</span> <span class="p">[</span><span class="mi">1</span> <span class="o">-</span> <span class="n">dup</span><span class="p">]</span> <span class="n">loop</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">3</span> <span class="n">dup</span> <span class="p">[</span><span class="mi">1</span> <span class="o">-</span> <span class="n">dup</span><span class="p">]</span> <span class="n">loop</span>
@ -1049,13 +1049,13 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
</section> </section>
<section id="map-pam"> <section id="map-pam">
<h3><code class="docutils literal notranslate"><span class="pre">map</span></code> <code class="docutils literal notranslate"><span class="pre">pam</span></code><a class="headerlink" href="#map-pam" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">map</span></code> <code class="docutils literal notranslate"><span class="pre">pam</span></code><a class="headerlink" href="#map-pam" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;10 [1 2 3] [*] map&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;10 [1 2 3] [*] 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="mi">10</span> <span class="p">[</span><span class="mi">10</span> <span class="mi">20</span> <span class="mi">30</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span> <span class="p">[</span><span class="mi">10</span> <span class="mi">20</span> <span class="mi">30</span><span class="p">]</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;10 5 [[*][/][+][-]] pam&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;10 5 [[*][/][+][-]] pam&#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> <span class="mi">5</span> <span class="p">[</span><span class="mi">50</span> <span class="mf">2.0</span> <span class="mi">15</span> <span class="mi">5</span><span class="p">]</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span> <span class="mi">5</span> <span class="p">[</span><span class="mi">50</span> <span class="mf">2.0</span> <span class="mi">15</span> <span class="mi">5</span><span class="p">]</span>
@ -1066,25 +1066,25 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
<h3><code class="docutils literal notranslate"><span class="pre">nullary</span></code> <code class="docutils literal notranslate"><span class="pre">unary</span></code> <code class="docutils literal notranslate"><span class="pre">binary</span></code> <code class="docutils literal notranslate"><span class="pre">ternary</span></code><a class="headerlink" href="#nullary-unary-binary-ternary" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">nullary</span></code> <code class="docutils literal notranslate"><span class="pre">unary</span></code> <code class="docutils literal notranslate"><span class="pre">binary</span></code> <code class="docutils literal notranslate"><span class="pre">ternary</span></code><a class="headerlink" href="#nullary-unary-binary-ternary" title="Permalink to this headline"></a></h3>
<p>Run a quoted program enforcing <p>Run a quoted program enforcing
<a class="reference external" href="https://en.wikipedia.org/wiki/Arity">arity</a>.</p> <a class="reference external" href="https://en.wikipedia.org/wiki/Arity">arity</a>.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 4 5 [+] nullary&#39;) <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 5 [+] nullary&#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">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">9</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></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="mi">9</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 4 5 [+] unary&#39;) <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 5 [+] unary&#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">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">9</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">9</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 4 5 [+] binary&#39;) # + has arity 2 so this is technically pointless... <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 5 [+] binary&#39;</span><span class="p">)</span> <span class="c1"># + has arity 2 so this is technically pointless...</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">9</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">9</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 2 3 4 5 [+] ternary&#39;) <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 5 [+] ternary&#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">1</span> <span class="mi">2</span> <span class="mi">9</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">9</span>
@ -1093,7 +1093,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
</section> </section>
<section id="step"> <section id="step">
<h3><code class="docutils literal notranslate"><span class="pre">step</span></code><a class="headerlink" href="#step" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">step</span></code><a class="headerlink" href="#step" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[step] help&#39;) <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>
</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>
@ -1116,7 +1116,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;0 [1 2 3] [+] step&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;0 [1 2 3] [+] 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="o">.</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">step</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">step</span>
@ -1141,7 +1141,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
</section> </section>
<section id="times"> <section id="times">
<h3><code class="docutils literal notranslate"><span class="pre">times</span></code><a class="headerlink" href="#times" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">times</span></code><a class="headerlink" href="#times" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;3 2 1 2 [+] times&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;3 2 1 2 [+] times&#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">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">2</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">times</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">2</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">times</span>
@ -1161,7 +1161,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
</section> </section>
<section id="b"> <section id="b">
<h3><code class="docutils literal notranslate"><span class="pre">b</span></code><a class="headerlink" href="#b" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">b</span></code><a class="headerlink" href="#b" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[b] help&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[b] 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">b</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">dip</span> <span class="n">i</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">dip</span> <span class="n">i</span>
@ -1170,7 +1170,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
<span class="o">...</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">b</span> <span class="o">==</span> <span class="o">...</span> <span class="n">P</span> <span class="n">Q</span> <span class="o">...</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">b</span> <span class="o">==</span> <span class="o">...</span> <span class="n">P</span> <span class="n">Q</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;1 2 [3] [4] b&#39;) <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] b&#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="mi">2</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="n">b</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">1</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">4</span><span class="p">]</span> <span class="n">b</span>
@ -1189,7 +1189,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">predicate</span><span class="p">]</span> <span class="p">[</span><span class="n">body</span><span class="p">]</span> <span class="k">while</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">predicate</span><span class="p">]</span> <span class="p">[</span><span class="n">body</span><span class="p">]</span> <span class="k">while</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;3 [0 &gt;] [dup --] while&#39;) <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 &gt;] [dup --] while&#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="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="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span>
@ -1198,7 +1198,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
</section> </section>
<section id="x"> <section id="x">
<h3><code class="docutils literal notranslate"><span class="pre">x</span></code><a class="headerlink" href="#x" title="Permalink to this headline"></a></h3> <h3><code class="docutils literal notranslate"><span class="pre">x</span></code><a class="headerlink" href="#x" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[x] help&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[x] 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">x</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">i</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">i</span>
@ -1208,7 +1208,7 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
<span class="o">...</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">x</span> <span class="o">=</span> <span class="o">...</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">Q</span> <span class="o">...</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">x</span> <span class="o">=</span> <span class="o">...</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">Q</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;1 [2] [i 3] x&#39;) # Kind of a pointless example. <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] [i 3] x&#39;</span><span class="p">)</span> <span class="c1"># Kind of a pointless example.</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="p">]</span> <span class="p">[</span><span class="n">i</span> <span class="mi">3</span><span class="p">]</span> <span class="n">x</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="p">]</span> <span class="p">[</span><span class="n">i</span> <span class="mi">3</span><span class="p">]</span> <span class="n">x</span>
@ -1231,25 +1231,25 @@ in terms of <code class="docutils literal notranslate"><span class="pre">app2</s
*arithmetic*</a> *arithmetic*</a>
over quote-only datastructures (that is, datastructures that consist over quote-only datastructures (that is, datastructures that consist
soley of containers, without strings or numbers or anything else.)</p> soley of containers, without strings or numbers or anything else.)</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] void&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] void&#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="kc">False</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kc">False</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[]] void&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[]] void&#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="kc">True</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kc">True</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[][[]]] void&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[][[]]] void&#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="kc">True</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kc">True</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[[]][[][]]] void&#39;) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[[]][[][]]] void&#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="kc">False</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kc">False</span>

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@ -96,15 +96,15 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>from functools import partial as curry <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>
from itertools import product <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-ipython2 notranslate"><div class="highlight"><pre><span></span>phi = frozenset() # ϕ <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>
y = frozenset({&#39;&#39;}) # λ <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>
</section> </section>
@ -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-ipython2 notranslate"><div class="highlight"><pre><span></span>syms = O, l = frozenset({&#39;0&#39;}), frozenset({&#39;1&#39;}) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>AND, CONS, KSTAR, NOT, OR = &#39;and cons * not or&#39;.split() # Tags are just strings. <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>
</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
@ -141,36 +141,36 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>def stringy(re): <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>
&#39;&#39;&#39; <span class="sd">&#39;&#39;&#39;</span>
Return a nice string repr for a regular expression datastructure. <span class="sd"> Return a nice string repr for a regular expression datastructure.</span>
&#39;&#39;&#39; <span class="sd"> &#39;&#39;&#39;</span>
if re == I: return &#39;.&#39; <span class="k">if</span> <span class="n">re</span> <span class="o">==</span> <span class="n">I</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;.&#39;</span>
if re in syms: return next(iter(re)) <span class="k">if</span> <span class="n">re</span> <span class="ow">in</span> <span class="n">syms</span><span class="p">:</span> <span class="k">return</span> <span class="nb">next</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">re</span><span class="p">))</span>
if re == y: return &#39;^&#39; <span class="k">if</span> <span class="n">re</span> <span class="o">==</span> <span class="n">y</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;^&#39;</span>
if re == phi: return &#39;X&#39; <span class="k">if</span> <span class="n">re</span> <span class="o">==</span> <span class="n">phi</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;X&#39;</span>
assert isinstance(re, tuple), repr(re) <span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">re</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">),</span> <span class="nb">repr</span><span class="p">(</span><span class="n">re</span><span class="p">)</span>
tag = re[0] <span class="n">tag</span> <span class="o">=</span> <span class="n">re</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
if tag == KSTAR: <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
body = stringy(re[1]) <span class="n">body</span> <span class="o">=</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
if not body: return body <span class="k">if</span> <span class="ow">not</span> <span class="n">body</span><span class="p">:</span> <span class="k">return</span> <span class="n">body</span>
if len(body) &gt; 1: return &#39;(&#39; + body + &quot;)*&quot; <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">body</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;(&#39;</span> <span class="o">+</span> <span class="n">body</span> <span class="o">+</span> <span class="s2">&quot;)*&quot;</span>
return body + &#39;*&#39; <span class="k">return</span> <span class="n">body</span> <span class="o">+</span> <span class="s1">&#39;*&#39;</span>
if tag == NOT: <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
body = stringy(re[1]) <span class="n">body</span> <span class="o">=</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
if not body: return body <span class="k">if</span> <span class="ow">not</span> <span class="n">body</span><span class="p">:</span> <span class="k">return</span> <span class="n">body</span>
if len(body) &gt; 1: return &#39;(&#39; + body + &quot;)&#39;&quot; <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">body</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;(&#39;</span> <span class="o">+</span> <span class="n">body</span> <span class="o">+</span> <span class="s2">&quot;)&#39;&quot;</span>
return body + &quot;&#39;&quot; <span class="k">return</span> <span class="n">body</span> <span class="o">+</span> <span class="s2">&quot;&#39;&quot;</span>
r, s = stringy(re[1]), stringy(re[2]) <span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
if tag == CONS: return r + s <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">CONS</span><span class="p">:</span> <span class="k">return</span> <span class="n">r</span> <span class="o">+</span> <span class="n">s</span>
if tag == OR: return &#39;%s | %s&#39; % (r, s) <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">OR</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="n">r</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
if tag == AND: return &#39;(%s) &amp; (%s)&#39; % (r, s) <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">AND</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;(</span><span class="si">%s</span><span class="s1">) &amp; (</span><span class="si">%s</span><span class="s1">)&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
raise ValueError <span class="k">raise</span> <span class="ne">ValueError</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -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-ipython2 notranslate"><div class="highlight"><pre><span></span>I = (KSTAR, (OR, O, l)) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print stringy(I) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>a = (CONS, I, (CONS, l, (CONS, l, (CONS, l, I)))) <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>
b = (CONS, I, (CONS, O, l)) <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>
c = (CONS, l, (KSTAR, l)) <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>
it = (AND, a, (NOT, (OR, b, c))) <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-ipython2 notranslate"><div class="highlight"><pre><span></span>print stringy(it) <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>
</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>
@ -214,36 +214,36 @@ it = (AND, a, (NOT, (OR, b, c)))
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>def nully(R): <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>
&#39;&#39;&#39; <span class="sd">&#39;&#39;&#39;</span>
δ - Return λ if λ ⊆ R otherwise ϕ. <span class="sd"> δ - Return λ if λ ⊆ R otherwise ϕ.</span>
&#39;&#39;&#39; <span class="sd"> &#39;&#39;&#39;</span>
# δ(a) → ϕ <span class="c1"># δ(a) → ϕ</span>
# δ(ϕ) → ϕ <span class="c1"># δ(ϕ) → ϕ</span>
if R in syms or R == phi: <span class="k">if</span> <span class="n">R</span> <span class="ow">in</span> <span class="n">syms</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span><span class="p">:</span>
return phi <span class="k">return</span> <span class="n">phi</span>
# δ(λ) → λ <span class="c1"># δ(λ) → λ</span>
if R == y: <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">y</span><span class="p">:</span>
return y <span class="k">return</span> <span class="n">y</span>
tag = R[0] <span class="n">tag</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
# δ(R*) → λ <span class="c1"># δ(R*) → λ</span>
if tag == KSTAR: <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
return y <span class="k">return</span> <span class="n">y</span>
# δ(¬R) δ(R)≟ϕ → λ <span class="c1"># δ(¬R) δ(R)≟ϕ → λ</span>
# δ(¬R) δ(R)≟λ → ϕ <span class="c1"># δ(¬R) δ(R)≟λ → ϕ</span>
if tag == NOT: <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
return phi if nully(R[1]) else y <span class="k">return</span> <span class="n">phi</span> <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="k">else</span> <span class="n">y</span>
# δ(R∘S) → δ(R) ∧ δ(S) <span class="c1"># δ(R∘S) → δ(R) ∧ δ(S)</span>
# δ(R ∧ S) → δ(R) ∧ δ(S) <span class="c1"># δ(R ∧ S) → δ(R) ∧ δ(S)</span>
# δ(R ∨ S) → δ(R) ∨ δ(S) <span class="c1"># δ(R ∨ S) → δ(R) ∨ δ(S)</span>
r, s = nully(R[1]), nully(R[2]) <span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">nully</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">nully</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
return r &amp; s if tag in {AND, CONS} else r | s <span class="k">return</span> <span class="n">r</span> <span class="o">&amp;</span> <span class="n">s</span> <span class="k">if</span> <span class="n">tag</span> <span class="ow">in</span> <span class="p">{</span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">}</span> <span class="k">else</span> <span class="n">r</span> <span class="o">|</span> <span class="n">s</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -252,71 +252,71 @@ it = (AND, a, (NOT, (OR, b, c)))
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>def D(symbol): <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>
def derv(R): <span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
# ∂a(a) → λ <span class="c1"># ∂a(a) → λ</span>
if R == {symbol}: <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="p">{</span><span class="n">symbol</span><span class="p">}:</span>
return y <span class="k">return</span> <span class="n">y</span>
# ∂a(λ) → ϕ <span class="c1"># ∂a(λ) → ϕ</span>
# ∂a(ϕ) → ϕ <span class="c1"># ∂a(ϕ) → ϕ</span>
# ∂a(¬a) → ϕ <span class="c1"># ∂a(¬a) → ϕ</span>
if R == y or R == phi or R in syms: <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">y</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span> <span class="ow">or</span> <span class="n">R</span> <span class="ow">in</span> <span class="n">syms</span><span class="p">:</span>
return phi <span class="k">return</span> <span class="n">phi</span>
tag = R[0] <span class="n">tag</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
# ∂a(R*) → ∂a(R)∘R* <span class="c1"># ∂a(R*) → ∂a(R)∘R*</span>
if tag == KSTAR: <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
return (CONS, derv(R[1]), R) <span class="k">return</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">R</span><span class="p">)</span>
# ∂a(¬R) → ¬∂a(R) <span class="c1"># ∂a(¬R) → ¬∂a(R)</span>
if tag == NOT: <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
return (NOT, derv(R[1])) <span class="k">return</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
r, s = R[1:] <span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
# ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S) <span class="c1"># ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)</span>
if tag == CONS: <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">CONS</span><span class="p">:</span>
A = (CONS, derv(r), s) # A = ∂a(R)∘S <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">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">s</span><span class="p">)</span> <span class="c1"># A = ∂a(R)∘S</span>
# A ∨ δ(R) ∘ ∂a(S) <span class="c1"># A ∨ δ(R) ∘ ∂a(S)</span>
# A ∨ λ ∘ ∂a(S) → A ∨ ∂a(S) <span class="c1"># A ∨ λ ∘ ∂a(S) → A ∨ ∂a(S)</span>
# A ∨ ϕ ∘ ∂a(S) → A ∨ ϕ → A <span class="c1"># A ∨ ϕ ∘ ∂a(S) → A ∨ ϕ → A</span>
return (OR, A, derv(s)) if nully(r) else A <span class="k">return</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">A</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">))</span> <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">r</span><span class="p">)</span> <span class="k">else</span> <span class="n">A</span>
# ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S) <span class="c1"># ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)</span>
# ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S) <span class="c1"># ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)</span>
return (tag, derv(r), derv(s)) <span class="k">return</span> <span class="p">(</span><span class="n">tag</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">))</span>
return derv <span class="k">return</span> <span class="n">derv</span>
</pre></div> </pre></div>
</div> </div>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>def _compaction_rule(relation, one, zero, a, b): <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>
return ( <span class="k">return</span> <span class="p">(</span>
b if a == one else # R*1 = 1*R = R <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>
a if b == one else <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>
zero if a == zero or b == zero else # R*0 = 0*R = 0 <span class="n">zero</span> <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">zero</span> <span class="ow">or</span> <span class="n">b</span> <span class="o">==</span> <span class="n">zero</span> <span class="k">else</span> <span class="c1"># R*0 = 0*R = 0</span>
(relation, a, b) <span class="p">(</span><span class="n">relation</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="p">)</span>
</pre></div> </pre></div>
</div> </div>
<p>An elegant symmetry.</p> <p>An elegant symmetry.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span># R ∧ I = I ∧ R = R <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># R ∧ I = I ∧ R = R</span>
# R ∧ ϕ = ϕ ∧ R = ϕ <span class="c1"># R ∧ ϕ = ϕ ∧ R = ϕ</span>
_and = curry(_compaction_rule, AND, I, phi) <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>
# R ∨ ϕ = ϕ ∨ R = R <span class="c1"># R ∨ ϕ = ϕ ∨ R = R</span>
# R ∨ I = I ∨ R = I <span class="c1"># R ∨ I = I ∨ R = I</span>
_or = curry(_compaction_rule, OR, phi, I) <span class="n">_or</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">OR</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">I</span><span class="p">)</span>
# R∘λ = λ∘R = R <span class="c1"># R∘λ = λ∘R = R</span>
# R∘ϕ = ϕ∘R = ϕ <span class="c1"># R∘ϕ = ϕ∘R = ϕ</span>
_cons = curry(_compaction_rule, CONS, y, phi) <span class="n">_cons</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">CONS</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -325,21 +325,21 @@ _cons = curry(_compaction_rule, CONS, y, phi)
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>class Memo(object): <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>
def __init__(self, f): <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>
self.f = f <span class="bp">self</span><span class="o">.</span><span class="n">f</span> <span class="o">=</span> <span class="n">f</span>
self.calls = self.hits = 0 <span class="bp">self</span><span class="o">.</span><span class="n">calls</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hits</span> <span class="o">=</span> <span class="mi">0</span>
self.mem = {} <span class="bp">self</span><span class="o">.</span><span class="n">mem</span> <span class="o">=</span> <span class="p">{}</span>
def __call__(self, key): <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">):</span>
self.calls += 1 <span class="bp">self</span><span class="o">.</span><span class="n">calls</span> <span class="o">+=</span> <span class="mi">1</span>
try: <span class="k">try</span><span class="p">:</span>
result = self.mem[key] <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mem</span><span class="p">[</span><span class="n">key</span><span class="p">]</span>
self.hits += 1 <span class="bp">self</span><span class="o">.</span><span class="n">hits</span> <span class="o">+=</span> <span class="mi">1</span>
except KeyError: <span class="k">except</span> <span class="ne">KeyError</span><span class="p">:</span>
result = self.mem[key] = self.f(key) <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mem</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">f</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
return result <span class="k">return</span> <span class="n">result</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -347,47 +347,47 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>def D_compaction(symbol): <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>
@Memo <span class="nd">@Memo</span>
def derv(R): <span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
# ∂a(a) → λ <span class="c1"># ∂a(a) → λ</span>
if R == {symbol}: <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="p">{</span><span class="n">symbol</span><span class="p">}:</span>
return y <span class="k">return</span> <span class="n">y</span>
# ∂a(λ) → ϕ <span class="c1"># ∂a(λ) → ϕ</span>
# ∂a(ϕ) → ϕ <span class="c1"># ∂a(ϕ) → ϕ</span>
# ∂a(¬a) → ϕ <span class="c1"># ∂a(¬a) → ϕ</span>
if R == y or R == phi or R in syms: <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">y</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span> <span class="ow">or</span> <span class="n">R</span> <span class="ow">in</span> <span class="n">syms</span><span class="p">:</span>
return phi <span class="k">return</span> <span class="n">phi</span>
tag = R[0] <span class="n">tag</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
# ∂a(R*) → ∂a(R)∘R* <span class="c1"># ∂a(R*) → ∂a(R)∘R*</span>
if tag == KSTAR: <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
return _cons(derv(R[1]), R) <span class="k">return</span> <span class="n">_cons</span><span class="p">(</span><span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">R</span><span class="p">)</span>
# ∂a(¬R) → ¬∂a(R) <span class="c1"># ∂a(¬R) → ¬∂a(R)</span>
if tag == NOT: <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
return (NOT, derv(R[1])) <span class="k">return</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
r, s = R[1:] <span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
# ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S) <span class="c1"># ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)</span>
if tag == CONS: <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">CONS</span><span class="p">:</span>
A = _cons(derv(r), s) # A = ∂a(r)∘s <span class="n">A</span> <span class="o">=</span> <span class="n">_cons</span><span class="p">(</span><span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">s</span><span class="p">)</span> <span class="c1"># A = ∂a(r)∘s</span>
# A ∨ δ(R) ∘ ∂a(S) <span class="c1"># A ∨ δ(R) ∘ ∂a(S)</span>
# A ∨ λ ∘ ∂a(S) → A ∨ ∂a(S) <span class="c1"># A ∨ λ ∘ ∂a(S) → A ∨ ∂a(S)</span>
# A ∨ ϕ ∘ ∂a(S) → A ∨ ϕ → A <span class="c1"># A ∨ ϕ ∘ ∂a(S) → A ∨ ϕ → A</span>
return _or(A, derv(s)) if nully(r) else A <span class="k">return</span> <span class="n">_or</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">))</span> <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">r</span><span class="p">)</span> <span class="k">else</span> <span class="n">A</span>
# ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S) <span class="c1"># ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)</span>
# ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S) <span class="c1"># ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)</span>
dr, ds = derv(r), derv(s) <span class="n">dr</span><span class="p">,</span> <span class="n">ds</span> <span class="o">=</span> <span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
return _and(dr, ds) if tag == AND else _or(dr, ds) <span class="k">return</span> <span class="n">_and</span><span class="p">(</span><span class="n">dr</span><span class="p">,</span> <span class="n">ds</span><span class="p">)</span> <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">AND</span> <span class="k">else</span> <span class="n">_or</span><span class="p">(</span><span class="n">dr</span><span class="p">,</span> <span class="n">ds</span><span class="p">)</span>
return derv <span class="k">return</span> <span class="n">derv</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -395,26 +395,26 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>o, z = D_compaction(&#39;0&#39;), D_compaction(&#39;1&#39;) <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>
REs = set() <span class="n">REs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
N = 5 <span class="n">N</span> <span class="o">=</span> <span class="mi">5</span>
names = list(product(*(N * [(0, 1)]))) <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>
dervs = list(product(*(N * [(o, z)]))) <span class="n">dervs</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="n">o</span><span class="p">,</span> <span class="n">z</span><span class="p">)])))</span>
for name, ds in zip(names, dervs): <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">ds</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">names</span><span class="p">,</span> <span class="n">dervs</span><span class="p">):</span>
R = it <span class="n">R</span> <span class="o">=</span> <span class="n">it</span>
ds = list(ds) <span class="n">ds</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">ds</span><span class="p">)</span>
while ds: <span class="k">while</span> <span class="n">ds</span><span class="p">:</span>
R = ds.pop()(R) <span class="n">R</span> <span class="o">=</span> <span class="n">ds</span><span class="o">.</span><span class="n">pop</span><span class="p">()(</span><span class="n">R</span><span class="p">)</span>
if R == phi or R == I: <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">I</span><span class="p">:</span>
break <span class="k">break</span>
REs.add(R) <span class="n">REs</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">R</span><span class="p">)</span>
print stringy(it) ; print <span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</span><span class="p">)</span> <span class="p">;</span> <span class="nb">print</span>
print o.hits, &#39;/&#39;, o.calls <span class="nb">print</span> <span class="n">o</span><span class="o">.</span><span class="n">hits</span><span class="p">,</span> <span class="s1">&#39;/&#39;</span><span class="p">,</span> <span class="n">o</span><span class="o">.</span><span class="n">calls</span>
print z.hits, &#39;/&#39;, z.calls <span class="nb">print</span> <span class="n">z</span><span class="o">.</span><span class="n">hits</span><span class="p">,</span> <span class="s1">&#39;/&#39;</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">calls</span>
print <span class="nb">print</span>
for s in sorted(map(stringy, REs), key=lambda n: (len(n), n)): <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">stringy</span><span class="p">,</span> <span class="n">REs</span><span class="p">),</span> <span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">n</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">n</span><span class="p">)):</span>
print s <span class="nb">print</span> <span class="n">s</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>
@ -555,45 +555,45 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>from collections import defaultdict <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>
from pprint import pprint <span class="kn">from</span> <span class="nn">pprint</span> <span class="kn">import</span> <span class="n">pprint</span>
from string import ascii_lowercase <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-ipython2 notranslate"><div class="highlight"><pre><span></span>d0, d1 = D_compaction(&#39;0&#39;), D_compaction(&#39;1&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>def explore(re): <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>
# Don&#39;t have more than 26 states... <span class="c1"># Don&#39;t have more than 26 states...</span>
names = defaultdict(iter(ascii_lowercase).next) <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>
table, accepting = dict(), set() <span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(),</span> <span class="nb">set</span><span class="p">()</span>
to_check = {re} <span class="n">to_check</span> <span class="o">=</span> <span class="p">{</span><span class="n">re</span><span class="p">}</span>
while to_check: <span class="k">while</span> <span class="n">to_check</span><span class="p">:</span>
re = to_check.pop() <span class="n">re</span> <span class="o">=</span> <span class="n">to_check</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
state_name = names[re] <span class="n">state_name</span> <span class="o">=</span> <span class="n">names</span><span class="p">[</span><span class="n">re</span><span class="p">]</span>
if (state_name, 0) in table: <span class="k">if</span> <span class="p">(</span><span class="n">state_name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="ow">in</span> <span class="n">table</span><span class="p">:</span>
continue <span class="k">continue</span>
if nully(re): <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
accepting.add(state_name) <span class="n">accepting</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">state_name</span><span class="p">)</span>
o, i = d0(re), d1(re) <span class="n">o</span><span class="p">,</span> <span class="n">i</span> <span class="o">=</span> <span class="n">d0</span><span class="p">(</span><span class="n">re</span><span class="p">),</span> <span class="n">d1</span><span class="p">(</span><span class="n">re</span><span class="p">)</span>
table[state_name, 0] = names[o] ; to_check.add(o) <span class="n">table</span><span class="p">[</span><span class="n">state_name</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">names</span><span class="p">[</span><span class="n">o</span><span class="p">]</span> <span class="p">;</span> <span class="n">to_check</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">o</span><span class="p">)</span>
table[state_name, 1] = names[i] ; to_check.add(i) <span class="n">table</span><span class="p">[</span><span class="n">state_name</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">names</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">;</span> <span class="n">to_check</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
return table, accepting <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-ipython2 notranslate"><div class="highlight"><pre><span></span>table, accepting = explore(it) <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>
table <span class="n">table</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="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">&#39;b&#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;a&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span>
@ -618,7 +618,7 @@ table
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>accepting <div class="highlight-python 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>
@ -629,31 +629,31 @@ table
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>_template = &#39;&#39;&#39;\ <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>
digraph finite_state_machine { <span class="s1">digraph finite_state_machine {</span>
rankdir=LR; <span class="s1"> rankdir=LR;</span>
size=&quot;8,5&quot; <span class="s1"> size=&quot;8,5&quot;</span>
node [shape = doublecircle]; %s; <span class="s1"> node [shape = doublecircle]; </span><span class="si">%s</span><span class="s1">;</span>
node [shape = circle]; <span class="s1"> node [shape = circle];</span>
%s <span class="si">%s</span><span class="s1"></span>
} <span class="s1">}</span>
&#39;&#39;&#39; <span class="s1">&#39;&#39;&#39;</span>
def link(fr, nm, label): <span class="k">def</span> <span class="nf">link</span><span class="p">(</span><span class="n">fr</span><span class="p">,</span> <span class="n">nm</span><span class="p">,</span> <span class="n">label</span><span class="p">):</span>
return &#39; %s -&gt; %s [ label = &quot;%s&quot; ];&#39; % (fr, nm, label) <span class="k">return</span> <span class="s1">&#39; </span><span class="si">%s</span><span class="s1"> -&gt; </span><span class="si">%s</span><span class="s1"> [ label = &quot;</span><span class="si">%s</span><span class="s1">&quot; ];&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">fr</span><span class="p">,</span> <span class="n">nm</span><span class="p">,</span> <span class="n">label</span><span class="p">)</span>
def make_graph(table, accepting): <span class="k">def</span> <span class="nf">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>
return _template % ( <span class="k">return</span> <span class="n">_template</span> <span class="o">%</span> <span class="p">(</span>
&#39; &#39;.join(accepting), <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">accepting</span><span class="p">),</span>
&#39;\n&#39;.join( <span class="s1">&#39;</span><span class="se">\n</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span>
link(from_, to, char) <span class="n">link</span><span class="p">(</span><span class="n">from_</span><span class="p">,</span> <span class="n">to</span><span class="p">,</span> <span class="n">char</span><span class="p">)</span>
for (from_, char), (to) in sorted(table.iteritems()) <span class="k">for</span> <span class="p">(</span><span class="n">from_</span><span class="p">,</span> <span class="n">char</span><span class="p">),</span> <span class="p">(</span><span class="n">to</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">table</span><span class="o">.</span><span class="n">iteritems</span><span class="p">())</span>
) <span class="p">)</span>
) <span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print make_graph(table, accepting) <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>
</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>
@ -699,14 +699,14 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>def trampoline(input_, jump_from, accepting): <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>
I = iter(input_) <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>
while True: <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
try: <span class="k">try</span><span class="p">:</span>
bounce_to = jump_from(I) <span class="n">bounce_to</span> <span class="o">=</span> <span class="n">jump_from</span><span class="p">(</span><span class="n">I</span><span class="p">)</span>
except StopIteration: <span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
return jump_from in accepting <span class="k">return</span> <span class="n">jump_from</span> <span class="ow">in</span> <span class="n">accepting</span>
jump_from = bounce_to <span class="n">jump_from</span> <span class="o">=</span> <span class="n">bounce_to</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -714,17 +714,17 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>getch = lambda I: int(next(I)) <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>
def _1(I): <span class="k">def</span> <span class="nf">_1</span><span class="p">(</span><span class="n">I</span><span class="p">):</span>
&#39;&#39;&#39;Loop on ones.&#39;&#39;&#39; <span class="sd">&#39;&#39;&#39;Loop on ones.&#39;&#39;&#39;</span>
while getch(I): pass <span class="k">while</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">):</span> <span class="k">pass</span>
def _0(I): <span class="k">def</span> <span class="nf">_0</span><span class="p">(</span><span class="n">I</span><span class="p">):</span>
&#39;&#39;&#39;Loop on zeros.&#39;&#39;&#39; <span class="sd">&#39;&#39;&#39;Loop on zeros.&#39;&#39;&#39;</span>
while not getch(I): pass <span class="k">while</span> <span class="ow">not</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">):</span> <span class="k">pass</span>
</pre></div> </pre></div>
</div> </div>
</section> </section>
@ -735,28 +735,28 @@ def _0(I):
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-ipython2 notranslate"><div class="highlight"><pre><span></span>a = lambda I: c if getch(I) else b <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>
b = lambda I: _0(I) or d <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>
c = lambda I: e if getch(I) else b <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>
d = lambda I: f if getch(I) else b <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>
e = lambda I: g if getch(I) else b <span class="n">e</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">g</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>
f = lambda I: h if getch(I) else b <span class="n">f</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">h</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>
g = lambda I: _1(I) or i <span class="n">g</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_1</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">i</span>
h = lambda I: _1(I) or i <span class="n">h</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_1</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">i</span>
i = lambda I: _0(I) or j <span class="n">i</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">j</span>
j = lambda I: h if getch(I) else i <span class="n">j</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">h</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">i</span>
</pre></div> </pre></div>
</div> </div>
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>def acceptable(input_): <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>
return trampoline(input_, a, {h, i}) <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-ipython2 notranslate"><div class="highlight"><pre><span></span>for n in range(2**5): <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>
s = bin(n)[2:] <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>
print &#39;%05s&#39; % s, acceptable(s) <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>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="mi">0</span> <span class="kc">False</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="mi">0</span> <span class="kc">False</span>

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@ -157,33 +157,33 @@ like that.</p>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>joy.parser.text_to_expression(&#39;1 2 3 4 5&#39;) # A simple sequence. <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;1 2 3 4 5&#39;</span><span class="p">)</span> <span class="c1"># A simple sequence.</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">2</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">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</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">1</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">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="p">())))))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>joy.parser.text_to_expression(&#39;[1 2 3] 4 5&#39;) # Three items, the first is a list with three items <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[1 2 3] 4 5&#39;</span><span class="p">)</span> <span class="c1"># Three items, the first is a list with three 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">1</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">3</span><span class="p">,</span> <span class="p">()))),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</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">1</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">3</span><span class="p">,</span> <span class="p">()))),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="p">())))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>joy.parser.text_to_expression(&#39;1 23 [&quot;four&quot; [-5.0] cons] 8888&#39;) # A mixed bag. cons is <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;1 23 [&quot;four&quot; [-5.0] cons] 8888&#39;</span><span class="p">)</span> <span class="c1"># A mixed bag. cons is</span>
# a Symbol, no lookup at <span class="c1"># a Symbol, no lookup at</span>
# parse-time. Haiku docs. <span class="c1"># parse-time. Haiku docs.</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">23</span><span class="p">,</span> <span class="p">((</span><span class="s1">&#39;four&#39;</span><span class="p">,</span> <span class="p">((</span><span class="o">-</span><span class="mf">5.0</span><span class="p">,</span> <span class="p">()),</span> <span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="p">()))),</span> <span class="p">(</span><span class="mi">8888</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">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">23</span><span class="p">,</span> <span class="p">((</span><span class="s1">&#39;four&#39;</span><span class="p">,</span> <span class="p">((</span><span class="o">-</span><span class="mf">5.0</span><span class="p">,</span> <span class="p">()),</span> <span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="p">()))),</span> <span class="p">(</span><span class="mi">8888</span><span class="p">,</span> <span class="p">()))))</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>joy.parser.text_to_expression(&#39;[][][][][]&#39;) # Five empty lists. <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[][][][][]&#39;</span><span class="p">)</span> <span class="c1"># Five empty lists.</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="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="p">((),</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-ipython2 notranslate"><div class="highlight"><pre><span></span>joy.parser.text_to_expression(&#39;[[[[[]]]]]&#39;) # Five nested lists. <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[[[[[]]]]]&#39;</span><span class="p">)</span> <span class="c1"># Five nested lists.</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="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="p">()),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">())</span>
@ -199,7 +199,7 @@ the Joy system. There are simple functions such as addition <code class="docutil
<code class="docutils literal notranslate"><span class="pre">+</span></code>, the library module supports aliases), and combinators which <code class="docutils literal notranslate"><span class="pre">+</span></code>, the library module supports aliases), and combinators which
provide control-flow and higher-order operations.</p> provide control-flow and higher-order operations.</p>
<p>Many of the functions are defined in Python, like <code class="docutils literal notranslate"><span class="pre">dip</span></code>:</p> <p>Many of the functions are defined in Python, like <code class="docutils literal notranslate"><span class="pre">dip</span></code>:</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print inspect.getsource(joy.library.dip) <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getsource</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>
</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">dip</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-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">dip</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>
@ -212,7 +212,7 @@ provide control-flow and higher-order operations.</p>
When the interpreter executes a definition function that function just When the interpreter executes a definition function that function just
pushes its body expression onto the pending expression (the pushes its body expression onto the pending expression (the
continuation) and returns control to the interpreter.</p> continuation) and returns control to the interpreter.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print joy.library.definitions <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">definitions</span>
</pre></div> </pre></div>
</div> </div>
<pre class="literal-block">second == rest first <pre class="literal-block">second == rest first

178
docs/sphinx_docs/_build/html/notebooks/Ordered_Binary_Trees.html
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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-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, J, V, define, DefinitionWrapper <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Tree-new == swap [[] []] cons cons&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;&quot;v&quot; &quot;k&quot; Tree-new&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;P == pop roll&gt; pop first&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;old_key&quot; 23 [] []] 17 &quot;new_key&quot; [&quot;...&quot;] P&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;T == cons cons [dipdd] cons infra&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#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;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;E == [P &lt;] [Te] [Ee] ifte&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Te == cons cons [dipd] cons infra&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#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;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Ee == pop swap roll&lt; rest rest cons cons&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#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;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P &gt;] [T] [E] ifte] genrec&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] 23 &quot;b&quot; Tree-add&#39;) # Initial <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;b&quot; 23 [] []] 88 &quot;c&quot; Tree-add&#39;) # Greater than <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;b&quot; 23 [] []] 88 &quot;a&quot; Tree-add&#39;) # Less than <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;b&quot; 23 [] []] 88 &quot;b&quot; Tree-add&#39;) # Equal to <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;) # Series. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] [[23 &quot;b&quot;] [88 &quot;a&quot;] [44 &quot;c&quot;]] [i Tree-add] step&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;1 0 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;1 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;0 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;P == over [popop popop first] nullary&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;) # Still works. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Tree-iter == [not] [pop] roll&lt; [dupdip rest rest] cons [step] genrec&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] [foo] Tree-iter&#39;) # It doesn&#39;t matter what F is as it won&#39;t be used. <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [first] Tree-iter&quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [second] Tree-iter&quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;to_set == [] swap [0 swap Tree-add] step&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[3 9 5 2 8 6 7 8 4] to_set&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;unique == [to_set [first] Tree-iter] cons run&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique&#39;) # Filter duplicate items. <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>
</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>
@ -679,23 +679,23 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>#define(&#39;Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec&#39;) <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>
DefinitionWrapper.add_definitions(&#39;&#39;&#39; <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>
fourth == rest rest rest first <span class="s1">fourth == rest rest rest first</span>
proc_left == [cons dip] dupdip <span class="s1">proc_left == [cons dip] dupdip</span>
proc_current == [[first] dupdip] dip <span class="s1">proc_current == [[first] dupdip] dip</span>
proc_right == [fourth] dip i <span class="s1">proc_right == [fourth] dip i</span>
Tree-iter-order == [not] [pop] [dup third] [proc_left proc_current proc_right] genrec <span class="s1">Tree-iter-order == [not] [pop] [dup third] [proc_left proc_current proc_right] genrec</span>
&#39;&#39;&#39;, D) <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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order&#39;) <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>
</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>
@ -835,54 +835,54 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span># I don&#39;t want to deal with name conflicts with the above so I&#39;m inlining everything here. <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>
# The original Joy system has &quot;hide&quot; which is a meta-command which allows you to use named <span class="c1"># The original Joy system has &quot;hide&quot; which is a meta-command which allows you to use named</span>
# definitions that are only in scope for a given definition. I don&#39;t want to implement <span class="c1"># definitions that are only in scope for a given definition. I don&#39;t want to implement</span>
# that (yet) so... <span class="c1"># that (yet) so...</span>
define(&#39;&#39;&#39; <span class="n">define</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
Tree-get == [pop not] swap [] [ <span class="s1">Tree-get == [pop not] swap [] [</span>
over [pop popop first] nullary <span class="s1"> over [pop popop first] nullary</span>
[[fourth] dipd i] <span class="s1"> [[fourth] dipd i]</span>
[popop second] <span class="s1"> [popop second]</span>
[[third] dipd i] <span class="s1"> [[third] dipd i]</span>
cmp <span class="s1"> cmp</span>
] genrec <span class="s1"> ] genrec</span>
&#39;&#39;&#39;) <span class="s1">&#39;&#39;&#39;</span><span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;gary&quot; 23 [] []] &quot;mike&quot; [popd &quot; not in tree&quot; +] Tree-get&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;gary&quot; 23 [] []] &quot;gary&quot; [popop &quot;err&quot;] Tree-get&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;&#39;&#39; <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>
[] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step <span class="s1"> [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step</span>
&#39;c&#39; [popop &#39;not found&#39;] Tree-get <span class="s1"> &#39;c&#39; [popop &#39;not found&#39;] Tree-get</span>
&#39;&#39;&#39;) <span class="s1">&#39;&#39;&#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> <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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;&#39;&#39; <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>
[] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step <span class="s1"> [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step</span>
&#39;d&#39; [popop &#39;not found&#39;] Tree-get <span class="s1"> &#39;d&#39; [popop &#39;not found&#39;] Tree-get</span>
&#39;&#39;&#39;) <span class="s1">&#39;&#39;&#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;not found&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;not found&#39;</span>
@ -1175,61 +1175,61 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>DefinitionWrapper.add_definitions(&#39;&#39;&#39; <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>
first_two == uncons uncons pop <span class="s1">first_two == uncons uncons pop</span>
fourth == rest rest rest first <span class="s1">fourth == rest rest rest first</span>
?fourth == [] [fourth] [] ifte <span class="s1">?fourth == [] [fourth] [] ifte</span>
W.rightmost == [?fourth] [fourth] while <span class="s1">W.rightmost == [?fourth] [fourth] while</span>
E.clear_stuff == roll&gt; popop rest <span class="s1">E.clear_stuff == roll&gt; popop rest</span>
E.delete == cons dipd <span class="s1">E.delete == cons dipd</span>
W == dup W.rightmost first_two over <span class="s1">W == dup W.rightmost first_two over</span>
E.0 == E.clear_stuff [W] dip E.delete swap <span class="s1">E.0 == E.clear_stuff [W] dip E.delete swap</span>
E == [[[pop third not] pop fourth] [[pop fourth not] pop third] [[E.0] cons infra]] cond <span class="s1">E == [[[pop third not] pop fourth] [[pop fourth not] pop third] [[E.0] cons infra]] cond</span>
T&gt; == [dipd] cons infra <span class="s1">T&gt; == [dipd] cons infra</span>
T&lt; == [dipdd] cons infra <span class="s1">T&lt; == [dipdd] cons infra</span>
R0 == over first swap dup <span class="s1">R0 == over first swap dup</span>
R1 == cons roll&gt; [T&gt;] [E] [T&lt;] cmp <span class="s1">R1 == cons roll&gt; [T&gt;] [E] [T&lt;] cmp</span>
Tree-Delete == [pop not] [pop] [R0] [R1] genrec <span class="s1">Tree-Delete == [pop not] [pop] [R0] [R1] genrec</span>
&#39;&#39;&#39;, D) <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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;c&#39; Tree-Delete &quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;b&#39; Tree-Delete &quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;a&#39; Tree-Delete &quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;der&#39; Tree-Delete &quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete &quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete &quot;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<p>Let’s try it out:</p> <p>Let’s try it out:</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;3 1 1 quadratic&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;-5 1 4 quadratic&#39;) <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>
</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>

66
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@ -33,7 +33,7 @@
<div class="body" role="main"> <div class="body" role="main">
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, DefinitionWrapper, J, V, define <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>
</pre></div> </pre></div>
</div> </div>
<section id="recursion-combinators"> <section id="recursion-combinators">
@ -101,18 +101,18 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>def hylomorphism(c, F, P, G): <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>
&#39;&#39;&#39;Return a hylomorphism function H.&#39;&#39;&#39; <span class="sd">&#39;&#39;&#39;Return a hylomorphism function H.&#39;&#39;&#39;</span>
def H(a): <span class="k">def</span> <span class="nf">H</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
if P(a): <span class="k">if</span> <span class="n">P</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
result = c <span class="n">result</span> <span class="o">=</span> <span class="n">c</span>
else: <span class="k">else</span><span class="p">:</span>
b, aa = G(a) <span class="n">b</span><span class="p">,</span> <span class="n">aa</span> <span class="o">=</span> <span class="n">G</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
result = F(b, H(aa)) # b is stored in the stack frame during recursive call to H(). <span class="n">result</span> <span class="o">=</span> <span class="n">F</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">H</span><span class="p">(</span><span class="n">aa</span><span class="p">))</span> <span class="c1"># b is stored in the stack frame during recursive call to H().</span>
return result <span class="k">return</span> <span class="n">result</span>
return H <span class="k">return</span> <span class="n">H</span>
</pre></div> </pre></div>
</div> </div>
<p>Cf. <a class="reference external" href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125">“Bananas, Lenses, &amp; Barbed <p>Cf. <a class="reference external" href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125">“Bananas, Lenses, &amp; Barbed
@ -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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;triangular_number == [1 &lt;=] 0 [-- dup] [+] hylomorphism&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<p>Let’s try it:</p> <p>Let’s try it:</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 triangular_number&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[0 1 2 3 4 5 6] [triangular_number] map&#39;) <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>
</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>
@ -372,10 +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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;range == [0 &lt;=] [] [-- dup] [swons] hylomorphism&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 range&#39;) <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>
</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>
@ -388,10 +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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;range_reverse == [] swap [0 &lt;=] [pop] [-- dup [swons] dip] primrec&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 range_reverse&#39;) <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>
</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>
@ -404,10 +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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;ranger == [0 &lt;=] [pop []] [[--] dupdip] [dip swons] genrec&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 ranger&#39;) <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>
</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>
@ -420,10 +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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;ranger_reverse == [] swap [0 &lt;=] [pop] [[swons] dupdip --] primrec&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 ranger_reverse&#39;) <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>
</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>
@ -444,17 +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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;swuncons == uncons swap&#39;) # Awkward name. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;sum == [not] 0 [swuncons] [+] hylomorphism&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[5 4 3 2 1] sum&#39;) <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>
</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>
@ -464,7 +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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[step] help&#39;) <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>
</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>
@ -488,10 +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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;sum == 0 swap [+] step&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[5 4 3 2 1] sum&#39;) <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>
</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>
@ -512,10 +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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;factorial == 1 swap [1 &lt;=] [pop] [[*] dupdip --] primrec&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 factorial&#39;) <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>
</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>
@ -544,10 +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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;tails == [] swap [not] [pop] [rest dup [swons] dip] primrec&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3] tails&#39;) <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>
</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>

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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-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, J, V <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[23 18] average&#39;) <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>
</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>
@ -105,30 +105,30 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>from joy.library import SimpleFunctionWrapper <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>
from joy.utils.stack import iter_stack <span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">iter_stack</span>
@SimpleFunctionWrapper <span class="nd">@SimpleFunctionWrapper</span>
def size(stack): <span class="k">def</span> <span class="nf">size</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
&#39;&#39;&#39;Return the size of the sequence on the stack.&#39;&#39;&#39; <span class="sd">&#39;&#39;&#39;Return the size of the sequence on the stack.&#39;&#39;&#39;</span>
sequence, stack = stack <span class="n">sequence</span><span class="p">,</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">stack</span>
n = 0 <span class="n">n</span> <span class="o">=</span> <span class="mi">0</span>
for _ in iter_stack(sequence): <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">iter_stack</span><span class="p">(</span><span class="n">sequence</span><span class="p">):</span>
n += 1 <span class="n">n</span> <span class="o">+=</span> <span class="mi">1</span>
return n, stack <span class="k">return</span> <span class="n">n</span><span class="p">,</span> <span class="n">stack</span>
</pre></div> </pre></div>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>D[&#39;size&#39;] = size <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[23 18] average&#39;) <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>
</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>

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docs/sphinx_docs/_build/html/notebooks/Treestep.html
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@ -148,17 +148,17 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, J, V, define, DefinitionWrapper <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>DefinitionWrapper.add_definitions(&#39;&#39;&#39; <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>
_treestep_0 == [[not] swap] dip <span class="s1"> _treestep_0 == [[not] swap] dip</span>
_treestep_1 == [dip] cons [uncons] swoncat <span class="s1"> _treestep_1 == [dip] cons [uncons] swoncat</span>
treegrind == [_treestep_1 _treestep_0] dip genrec <span class="s1"> treegrind == [_treestep_1 _treestep_0] dip genrec</span>
treestep == [map] swoncat treegrind <span class="s1"> treestep == [map] swoncat treegrind</span>
&#39;&#39;&#39;, D) <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>
</section> </section>
@ -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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;sumtree == [pop 0] [] [sum +] treestep&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] sumtree&#39;) # Empty tree. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23] sumtree&#39;) # No child trees. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 []] sumtree&#39;) # Child tree, empty. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [4]] [3]] sumtree&#39;) # Non-empty child trees. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] sumtree&#39;) # Etc... <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep&#39;) # Alternate &quot;spelling&quot;. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep&#39;) # Replace each node. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep&#39;) # Combine replace and sum into one function. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep&#39;) # Combine replace and sum into one function. <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] [&quot;B&quot;] [first] [i] treestep&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#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;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[&quot;key&quot; &quot;value&quot;] [&quot;left&quot;] [&quot;right&quot;] ] [&quot;B&quot;] [&quot;N&quot;] [&quot;C&quot;] treegrind&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [&quot;N&quot;] [step] treegrind&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind&#39;) <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>
</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>
@ -449,37 +449,37 @@ 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-ipython2 notranslate"><div class="highlight"><pre><span></span>DefinitionWrapper.add_definitions(&#39;&#39;&#39; <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>
T&gt; == pop [first] dip i <span class="s1"> T&gt; == pop [first] dip i</span>
T&lt; == pop [second] dip i <span class="s1"> T&lt; == pop [second] dip i</span>
E == roll&gt; popop first <span class="s1"> E == roll&gt; popop first</span>
P == roll&lt; [roll&lt; uncons swap] dip <span class="s1"> P == roll&lt; [roll&lt; uncons swap] dip</span>
Tree-get == [P [T&gt;] [E] [T&lt;] cmp] treegrind <span class="s1"> Tree-get == [P [T&gt;] [E] [T&lt;] cmp] treegrind</span>
&#39;&#39;&#39;, D) <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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;&#39;&#39;\ <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>
[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]] <span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
[] [5] Tree-get <span class="s1">[] [5] Tree-get</span>
&#39;&#39;&#39;) <span class="s1">&#39;&#39;&#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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;&#39;&#39;\ <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>
[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]] <span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
[pop &quot;nope&quot;] [25] Tree-get <span class="s1">[pop &quot;nope&quot;] [25] Tree-get</span>
&#39;&#39;&#39;) <span class="s1">&#39;&#39;&#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;nope&#39;</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;nope&#39;</span>

78
docs/sphinx_docs/_build/html/notebooks/TypeChecking.html
View File

@ -35,33 +35,33 @@
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>import logging, sys <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>
logging.basicConfig( <span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span>
format=&#39;%(message)s&#39;, <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>
stream=sys.stdout, <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>
level=logging.INFO, <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="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from joy.utils.types import ( <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>
doc_from_stack_effect, <span class="n">doc_from_stack_effect</span><span class="p">,</span>
infer, <span class="n">infer</span><span class="p">,</span>
reify, <span class="n">reify</span><span class="p">,</span>
unify, <span class="n">unify</span><span class="p">,</span>
FUNCTIONS, <span class="n">FUNCTIONS</span><span class="p">,</span>
JoyTypeError, <span class="n">JoyTypeError</span><span class="p">,</span>
) <span class="p">)</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>D = FUNCTIONS.copy() <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>
del D[&#39;product&#39;] <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>
globals().update(D) <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-ipython2 notranslate"><div class="highlight"><pre><span></span>fi, fo = infer(pop, swap, rolldown, rrest, ccons)[0] <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>
</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
@ -72,32 +72,32 @@ globals().update(D)
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-ipython2 notranslate"><div class="highlight"><pre><span></span>print doc_from_stack_effect(fi, fo) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>from joy.parser import text_to_expression <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>
from joy.utils.stack import stack_to_string <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-ipython2 notranslate"><div class="highlight"><pre><span></span>e = text_to_expression(&#39;0 1 2 [3 4]&#39;) # reverse order <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>
print stack_to_string(e) <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-ipython2 notranslate"><div class="highlight"><pre><span></span>u = unify(e, fi)[0] <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>
u <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-ipython2 notranslate"><div class="highlight"><pre><span></span>g = reify(u, (fi, fo)) <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>
print doc_from_stack_effect(*g) <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>
<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="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> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="mi">1</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="o">...</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> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="p">])</span>
@ -106,18 +106,18 @@ print doc_from_stack_effect(*g)
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>e = text_to_expression(&#39;[2 3]&#39;) <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>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>u = unify(e, fo)[0] # output side, not input side <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>
u <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-ipython2 notranslate"><div class="highlight"><pre><span></span>g = reify(u, (fi, fo)) <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>
print doc_from_stack_effect(*g) <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>
<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">a4</span> <span class="n">a5</span> <span class="p">]</span> <span class="mi">3</span> <span class="mi">2</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</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="o">...</span> <span class="p">[</span><span class="n">a4</span> <span class="n">a5</span> <span class="p">]</span> <span class="mi">3</span> <span class="mi">2</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="p">])</span>
@ -126,7 +126,7 @@ print doc_from_stack_effect(*g)
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>fi, fo = infer(dup, mul)[0] <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>
</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
@ -135,17 +135,17 @@ print doc_from_stack_effect(*g)
31 (i1 -- i2) ∘ 31 (i1 -- i2) ∘
</pre></div> </pre></div>
</div> </div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>e = text_to_expression(&#39;&quot;two&quot;&#39;) <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>
print stack_to_string(e) <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-ipython2 notranslate"><div class="highlight"><pre><span></span>try: <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
unify(e, fi) <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>
except JoyTypeError, err: <span class="k">except</span> <span class="n">JoyTypeError</span><span class="p">,</span> <span class="n">err</span><span class="p">:</span>
print err <span class="nb">print</span> <span class="n">err</span>
</pre></div> </pre></div>
</div> </div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Cannot</span> <span class="n">unify</span> <span class="s1">&#39;two&#39;</span> <span class="ow">and</span> <span class="n">f1</span><span class="o">.</span> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Cannot</span> <span class="n">unify</span> <span class="s1">&#39;two&#39;</span> <span class="ow">and</span> <span class="n">f1</span><span class="o">.</span>

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@ -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-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 [2 [3 4 25 6] 7] 8]&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;z-down == [] swap uncons swap&#39;) <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>
define(&#39;z-up == swons swap shunt&#39;) <span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-up == swons swap shunt&#39;</span><span class="p">)</span>
define(&#39;z-right == [swons] cons dip uncons swap&#39;) <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>
define(&#39;z-left == swons [uncons swap] dip swap&#39;) <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-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[1 [2 [3 4 25 6] 7] 8] z-down&#39;) <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>
</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 @@ define(&#39;z-left == swons [uncons swap] dip swap&#39;)
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[] [[2 [3 4 25 6] 7] 8] 1 z-right&#39;) <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>
</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 @@ define(&#39;z-left == swons [uncons swap] dip swap&#39;)
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2 [3 4 25 6] 7] z-down&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [] [[3 4 25 6] 7] 2 z-right&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2] [7] [3 4 25 6] z-down&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2] [7] [] [4 25 6] 3 z-right&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2] [7] [3] [25 6] 4 z-right&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2] [7] [4 3] [6] 25 sqr&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[1] [8] [2] [7] [4 3] [6] 625 z-up&#39;) <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>
</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 @@ define(&#39;z-left == swons [uncons swap] dip swap&#39;)
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2] [7] [3 4 625 6] z-up&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2 [3 4 625 6] 7] z-up&#39;) <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>
</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 @@ define(&#39;z-left == swons [uncons swap] dip swap&#39;)
<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-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Z == [[] cons cons] step i&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;1 [2 3 4] Z&#39;) <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>
</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-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z&#39;) <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>
</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>

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:: ipython3 .. code:: python
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:: ipython3 .. code:: python
define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator') define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
.. code:: ipython3 .. code:: python
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:: ipython3 .. code:: python
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:: ipython3 .. code:: python
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:: ipython3 .. code:: python
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:: ipython3 .. code:: python
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:: ipython3 .. code:: python
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:: ipython3 .. code:: python
J('36 sqrt') J('36 sqrt')
@ -216,7 +216,7 @@ Try it out...
6.0 6.0
.. code:: ipython3 .. code:: python
J('23 sqrt') J('23 sqrt')
@ -228,7 +228,7 @@ Try it out...
Check it. Check it.
.. code:: ipython3 .. code:: python
4.795831523312719**2 4.795831523312719**2
@ -241,7 +241,7 @@ Check it.
.. code:: ipython3 .. code:: python
from math import sqrt from math import sqrt