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And there are the P's.

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Simon Forman 2022-03-27 13:04:42 -07:00
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@ -2479,31 +2479,31 @@ A fine old word from Forth.
## pam
Basis Function Combinator
Combinator
\[i\] map
Take a list of quoted functions from the stack and replace it with a list
of the [first] results from running those functions (on copies of the
rest of the stack.)
Gentzen diagram.
### Example
5 7 [[+][-][*][/][%]] pam
-------------------------------
5 7 [12 -2 35 0 5]
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
> \[[i]\] [map]
### Discussion
Lorem ipsum.
A specialization of [map] that runs a list of functions in parallel (if
the underlying [map] function is so implemented, of course.)
### Crosslinks
Lorem ipsum.
[map]
--------------
@ -2516,392 +2516,292 @@ See [getitem](#getitem).
## pm
Basis Function Combinator
Function
Plus or minus :
Plus or minus. Replace two numbers with their sum and difference.
a b pm
-------------
a+b a-b
Gentzen diagram.
a b pm
-----------------
(a+b) (a-b)
### Definition
if not basis.
> \[+\] \[-\] [clop]
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.
------------------------------------------------------------------------
## pop
Basis Function Combinator
Basis Function
(a1 --)
Pop the top item from the stack and discard it.
Gentzen diagram.
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
a pop
-----------
### Crosslinks
Lorem ipsum.
[popd]
[popdd]
[popop]
[popopd]
[popopdd]
[popopop]
------------------------------------------------------------------------
## popd
Basis Function Combinator
Function
(a2 a1 -- a1)
[pop] the second item down on the stack.
Gentzen diagram.
a b popd
--------------
b
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [swap] [pop]
### Crosslinks
Lorem ipsum.
[pop]
[popdd]
[popop]
[popopd]
[popopdd]
[popopop]
------------------------------------------------------------------------
## popdd
Basis Function Combinator
Function
(a3 a2 a1 -- a2 a1)
[pop] the third item on the stack.
Gentzen diagram.
a b c popdd
-----------------
b c
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [rolldown] [pop]
### Crosslinks
Lorem ipsum.
[pop]
[popd]
[popop]
[popopd]
[popopdd]
[popopop]
------------------------------------------------------------------------
## popop
Basis Function Combinator
Function
(a2 a1 --)
[pop] two items from the stack.
Gentzen diagram.
a b popop
---------------
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [pop] [pop]
### Crosslinks
Lorem ipsum.
[pop]
[popd]
[popdd]
[popopd]
[popopdd]
[popopop]
------------------------------------------------------------------------
## popopd
Basis Function Combinator
Function
(a3 a2 a1 -- a1)
[pop] the second and third items from the stack.
Gentzen diagram.
a b c popopd
------------------
c
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [rollup] [popop]
### Crosslinks
Lorem ipsum.
[pop]
[popd]
[popdd]
[popop]
[popopdd]
[popopop]
------------------------------------------------------------------------
## popopdd
Basis Function Combinator
Function
(a4 a3 a2 a1 -- a2 a1)
Gentzen diagram.
a b c d popopdd
---------------------
c d
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> \[[popop]\] [dipd]
### Crosslinks
Lorem ipsum.
[pop]
[popd]
[popdd]
[popop]
[popopd]
[popopop]
------------------------------------------------------------------------
## popopop
Basis Function Combinator
Function
pop popop
[pop] three items from the stack.
Gentzen diagram.
a b c popopop
-------------------
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [pop] [popop]
### Crosslinks
Lorem ipsum.
[pop]
[popd]
[popdd]
[popop]
[popopd]
[popopdd]
------------------------------------------------------------------------
## pow
Basis Function Combinator
Basis Function
Same as a \*\* b.
Take two numbers `a` and `b` from the stack and raise `a` to the `n`th
power. (`b` is on the top of the stack.)
Gentzen diagram.
a n pow
-------------
(aⁿ)
### Definition
### Example
if not basis.
2 [2 3 4 5 6 7 8 9] [pow] map
-----------------------------------
2 [4 8 16 32 64 128 256 512]
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.
------------------------------------------------------------------------
## pred
Basis Function Combinator
Function
Decrement TOS.
Gentzen diagram.
Predecessor. Decrement TOS.
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> 1 -
### Crosslinks
Lorem ipsum.
[succ]
------------------------------------------------------------------------
## primrec
Basis Function Combinator
Combinator
From the \"Overview of the language JOY\":
From the ["Overview of the language JOY"](https://www.kevinalbrecht.com/code/joy-mirror/j00ovr.html)
\> The primrec combinator expects two quoted programs in addition to a
data parameter. For an integer data parameter it works like this: If the
data parameter is zero, then the first quotation has to produce the
value to be returned. If the data parameter is positive then the second
has to combine the data parameter with the result of applying the
function to its predecessor.:
> The primrec combinator expects two quoted programs in addition to a
> data parameter. For an integer data parameter it works like this: If
> the data parameter is zero, then the first quotation has to produce the
> value to be returned. If the data parameter is positive then the second
> has to combine the data parameter with the result of applying the
> function to its predecessor.
5 [1] [*] primrec
> 5 \[1\] \[\*\] primrec
\> Then primrec tests whether the top element on the stack (initially
the 5) is equal to zero. If it is, it pops it off and executes one of
the quotations, the \[1\] which leaves 1 on the stack as the result.
Otherwise it pushes a decremented copy of the top element and recurses.
On the way back from the recursion it uses the other quotation, \[\*\],
to multiply what is now a factorial on top of the stack by the second
element on the stack.:
> Then primrec tests whether the top element on the stack (initially the
> 5) is equal to zero. If it is, it pops it off and executes one of the
> quotations, the \[1\] which leaves 1 on the stack as the result.
> Otherwise it pushes a decremented copy of the top element and recurses.
> On the way back from the recursion it uses the other quotation, \[\*\],
> to multiply what is now a factorial on top of the stack by the second
> element on the stack.
n [Base] [Recur] primrec
0 [Base] [Recur] primrec
------------------------------
Base
n [Base] [Recur] primrec
n [Base] [Recur] primrec
------------------------------------------ n > 0
n (n-1) [Base] [Recur] primrec Recur
Gentzen diagram.
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
Simple and useful specialization of the [genrec] combinator from the
[original Joy system](https://www.kevinalbrecht.com/code/joy-mirror/index.html).
### Crosslinks
Lorem ipsum.
[genrec]
[tailrec]
------------------------------------------------------------------------
## product
Basis Function Combinator
Function
1 swap \[\*\] step
Gentzen diagram.
Just as [sum] sums a list of numbers, this function multiplies them
together.
### Definition
if not basis.
> 1 [swap] \[[mul]\] [step]
### Derivation
Or,
if not basis.
> \[1\] \[[mul]\] [primrec]
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.
------------------------------------------------------------------------

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@ -2,28 +2,28 @@
## pam
Basis Function Combinator
Combinator
\[i\] map
Take a list of quoted functions from the stack and replace it with a list
of the [first] results from running those functions (on copies of the
rest of the stack.)
Gentzen diagram.
### Example
5 7 [[+][-][*][/][%]] pam
-------------------------------
5 7 [12 -2 35 0 5]
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
> \[[i]\] [map]
### Discussion
Lorem ipsum.
A specialization of [map] that runs a list of functions in parallel (if
the underlying [map] function is so implemented, of course.)
### Crosslinks
Lorem ipsum.
[map]

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@ -2,32 +2,15 @@
## pm
Basis Function Combinator
Function
Plus or minus :
Plus or minus. Replace two numbers with their sum and difference.
a b pm
-------------
a+b a-b
Gentzen diagram.
a b pm
-----------------
(a+b) (a-b)
### Definition
if not basis.
> \[+\] \[-\] [clop]
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.

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@ -2,28 +2,19 @@
## pop
Basis Function Combinator
Basis Function
(a1 --)
Pop the top item from the stack and discard it.
Gentzen diagram.
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
a pop
-----------
### Crosslinks
Lorem ipsum.
[popd]
[popdd]
[popop]
[popopd]
[popopdd]
[popopop]

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@ -2,28 +2,24 @@
## popd
Basis Function Combinator
Function
(a2 a1 -- a1)
[pop] the second item down on the stack.
Gentzen diagram.
a b popd
--------------
b
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [swap] [pop]
### Crosslinks
Lorem ipsum.
[pop]
[popdd]
[popop]
[popopd]
[popopdd]
[popopop]

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@ -2,28 +2,24 @@
## popdd
Basis Function Combinator
Function
(a3 a2 a1 -- a2 a1)
[pop] the third item on the stack.
Gentzen diagram.
a b c popdd
-----------------
b c
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [rolldown] [pop]
### Crosslinks
Lorem ipsum.
[pop]
[popd]
[popop]
[popopd]
[popopdd]
[popopop]

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@ -2,28 +2,23 @@
## popop
Basis Function Combinator
Function
(a2 a1 --)
[pop] two items from the stack.
Gentzen diagram.
a b popop
---------------
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [pop] [pop]
### Crosslinks
Lorem ipsum.
[pop]
[popd]
[popdd]
[popopd]
[popopdd]
[popopop]

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@ -2,28 +2,24 @@
## popopd
Basis Function Combinator
Function
(a3 a2 a1 -- a1)
[pop] the second and third items from the stack.
Gentzen diagram.
a b c popopd
------------------
c
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [rollup] [popop]
### Crosslinks
Lorem ipsum.
[pop]
[popd]
[popdd]
[popop]
[popopdd]
[popopop]

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@ -2,28 +2,22 @@
## popopdd
Basis Function Combinator
Function
(a4 a3 a2 a1 -- a2 a1)
Gentzen diagram.
a b c d popopdd
---------------------
c d
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> \[[popop]\] [dipd]
### Crosslinks
Lorem ipsum.
[pop]
[popd]
[popdd]
[popop]
[popopd]
[popopop]

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@ -2,28 +2,23 @@
## popopop
Basis Function Combinator
Function
pop popop
[pop] three items from the stack.
Gentzen diagram.
a b c popopop
-------------------
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [pop] [popop]
### Crosslinks
Lorem ipsum.
[pop]
[popd]
[popdd]
[popop]
[popopd]
[popopdd]

30
docs/reference/pow.md
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@ -2,28 +2,18 @@
## pow
Basis Function Combinator
Basis Function
Same as a \*\* b.
Take two numbers `a` and `b` from the stack and raise `a` to the `n`th
power. (`b` is on the top of the stack.)
Gentzen diagram.
a n pow
-------------
(aⁿ)
### Definition
### Example
if not basis.
2 [2 3 4 5 6 7 8 9] [pow] map
-----------------------------------
2 [4 8 16 32 64 128 256 512]
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.

23
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@ -2,28 +2,15 @@
## pred
Basis Function Combinator
Function
Decrement TOS.
Gentzen diagram.
Predecessor. Decrement TOS.
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> 1 -
### Crosslinks
Lorem ipsum.
[succ]

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@ -2,55 +2,43 @@
## primrec
Basis Function Combinator
Combinator
From the \"Overview of the language JOY\":
From the ["Overview of the language JOY"](https://www.kevinalbrecht.com/code/joy-mirror/j00ovr.html)
\> The primrec combinator expects two quoted programs in addition to a
data parameter. For an integer data parameter it works like this: If the
data parameter is zero, then the first quotation has to produce the
value to be returned. If the data parameter is positive then the second
has to combine the data parameter with the result of applying the
function to its predecessor.:
> The primrec combinator expects two quoted programs in addition to a
> data parameter. For an integer data parameter it works like this: If
> the data parameter is zero, then the first quotation has to produce the
> value to be returned. If the data parameter is positive then the second
> has to combine the data parameter with the result of applying the
> function to its predecessor.
5 [1] [*] primrec
> 5 \[1\] \[\*\] primrec
\> Then primrec tests whether the top element on the stack (initially
the 5) is equal to zero. If it is, it pops it off and executes one of
the quotations, the \[1\] which leaves 1 on the stack as the result.
Otherwise it pushes a decremented copy of the top element and recurses.
On the way back from the recursion it uses the other quotation, \[\*\],
to multiply what is now a factorial on top of the stack by the second
element on the stack.:
> Then primrec tests whether the top element on the stack (initially the
> 5) is equal to zero. If it is, it pops it off and executes one of the
> quotations, the \[1\] which leaves 1 on the stack as the result.
> Otherwise it pushes a decremented copy of the top element and recurses.
> On the way back from the recursion it uses the other quotation, \[\*\],
> to multiply what is now a factorial on top of the stack by the second
> element on the stack.
n [Base] [Recur] primrec
0 [Base] [Recur] primrec
------------------------------
Base
n [Base] [Recur] primrec
n [Base] [Recur] primrec
------------------------------------------ n > 0
n (n-1) [Base] [Recur] primrec Recur
Gentzen diagram.
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
Simple and useful specialization of the [genrec] combinator from the
[original Joy system](https://www.kevinalbrecht.com/code/joy-mirror/index.html).
### Crosslinks
Lorem ipsum.
[genrec]
[tailrec]

23
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@ -2,28 +2,17 @@
## product
Basis Function Combinator
Function
1 swap \[\*\] step
Gentzen diagram.
Just as [sum] sums a list of numbers, this function multiplies them
together.
### Definition
if not basis.
> 1 [swap] \[[mul]\] [step]
### Derivation
Or,
if not basis.
> \[1\] \[[mul]\] [primrec]
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.