From 6a71bfb0036b6ec8e3cac4f1b50b5e9c9da2c12d Mon Sep 17 00:00:00 2001 From: Simon Forman Date: Thu, 24 Mar 2022 13:35:37 -0700 Subject: [PATCH] The rest of the C's. --- docs/reference/codireco.md | 25 +- docs/reference/concat.md | 47 +- docs/reference/cond.md | 41 +- docs/reference/cons.md | 18 +- docs/reference/mkref/FuncRef.html | 1078 ++++++++++++++--------------- docs/reference/mkref/Functor-Reference.md | 135 ++-- 6 files changed, 650 insertions(+), 694 deletions(-) diff --git a/docs/reference/codireco.md b/docs/reference/codireco.md index 9551e34..4b5598c 100644 --- a/docs/reference/codireco.md +++ b/docs/reference/codireco.md @@ -2,28 +2,23 @@ ## codireco -Basis Function Combinator +Combinator -codi reco - -Gentzen diagram. +This is part of the [make_generator] function. You would not use this +combinator directly. ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> [codi] [reco] ### Discussion -Lorem ipsum. +See [make_generator] and the +["Using `x` to Generate Values" notebook](https://joypy.osdn.io/notebooks/Generator_Programs.html#an-interesting-variation) +as well as +[Recursion Theory and Joy](https://www.kevinalbrecht.com/code/joy-mirror/j05cmp.html) by Manfred von Thun. ### Crosslinks -Lorem ipsum. +[make_generator] + diff --git a/docs/reference/concat.md b/docs/reference/concat.md index e59e6b1..d1bdcd6 100644 --- a/docs/reference/concat.md +++ b/docs/reference/concat.md @@ -2,32 +2,33 @@ ## concat -Basis Function Combinator +Function -Concatinate the two lists on the top of the stack. : +Concatinate two lists. - [a b c] [d e f] concat + [a b c] [d e f] concat ---------------------------- - [a b c d e f] - -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. + [a b c d e f] ### Crosslinks -Lorem ipsum. +[first] +[first_two] +[flatten] +[fourth] +[getitem] +[remove] +[rest] +[reverse] +[rrest] +[second] +[shift] +[shunt] +[size] +[sort] +[split_at] +[split_list] +[swaack] +[third] +[zip] + diff --git a/docs/reference/cond.md b/docs/reference/cond.md index 47f77fc..b3d26e4 100644 --- a/docs/reference/cond.md +++ b/docs/reference/cond.md @@ -2,39 +2,34 @@ ## cond -Basis Function Combinator +Combinator This combinator works like a case statement. It expects a single quote on the stack that must contain zero or more condition quotes and a -default quote. Each condition clause should contain a quoted predicate +default quote. Each condition quote should contain a quoted predicate followed by the function expression to run if that predicate returns -true. If no predicates return true the default function runs. +`true`. If no predicates return `true` the default function runs. + + [ + [ [Predicate0] Function0 ] + [ [Predicate1] Function1 ] + ... + [ [PredicateN] FunctionN ] + [Default] + ] + cond + +### Discussion It works by rewriting into a chain of nested [ifte]{.title-ref} expressions, e.g.: - [[[B0] T0] [[B1] T1] [D]] cond + [[[B0] T0] [[B1] T1] [D]] cond ----------------------------------------- - [B0] [T0] [[B1] [T1] [D] ifte] ifte - -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation + [B0] [T0] [[B1] [T1] [D] ifte] ifte -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. ### Crosslinks -Lorem ipsum. +[ifte] + diff --git a/docs/reference/cons.md b/docs/reference/cons.md index cfc19aa..6534b64 100644 --- a/docs/reference/cons.md +++ b/docs/reference/cons.md @@ -2,26 +2,20 @@ ## cons -(Basis Function) +Basis Function Given an item and a list, append the item to the list to make a new list. - A [...] cons + a [...] cons ------------------ - [A ...] - -### Source - - func(cons, [list(A), B|S], [list([B|A])|S]). + [a ...] ### Discussion -Cons is a venerable old function from Lisp. It doesn't inspect the item -but it will not cons onto a non-list. It's inverse operation is called -`uncons`. +Cons is a [venerable old function from Lisp](https://en.wikipedia.org/wiki/Cons#Lists). +Its inverse operation is [uncons]. ### Crosslinks -[ccons](#ccons) -[uncons](#uncons) +[uncons] diff --git a/docs/reference/mkref/FuncRef.html b/docs/reference/mkref/FuncRef.html index 16d0a74..c9d424d 100644 --- a/docs/reference/mkref/FuncRef.html +++ b/docs/reference/mkref/FuncRef.html @@ -815,81 +815,67 @@

appN codireco

codireco

-

Basis Function Combinator

-

codi reco

-

Gentzen diagram.

+

Combinator

+

This is part of the make_generator function. You would not use this combinator directly.

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

+
+

codi reco

+

Discussion

-

Lorem ipsum.

+

See make_generator and the “Using x to Generate Values” notebook as well as Recursion Theory and Joy by Manfred von Thun.

-

Lorem ipsum.

+

make_generator

concat

-

Basis Function Combinator

-

Concatinate the two lists on the top of the stack. :

-
[a b c] [d e f] concat
+
Function

+
Concatinate two lists.

+
   [a b c] [d e f] concat
 ----------------------------
-    [a b c d e f]

-
Gentzen diagram.

-
Definition

-
if not basis.

-
Derivation

-
if not basis.

-
Source

-
if basis

-
Discussion

-
Lorem ipsum.

+       [a b c d e f]
-

Lorem ipsum.

+

first first_two flatten fourth getitem remove rest reverse rrest second shift shunt size sort split_at split_list swaack third zip

cond

-

Basis Function Combinator

-

This combinator works like a case statement. It expects a single quote on the stack that must contain zero or more condition quotes and a default quote. Each condition clause should contain a quoted predicate followed by the function expression to run if that predicate returns true. If no predicates return true the default function runs.

+

Combinator

+

This combinator works like a case statement. It expects a single quote on the stack that must contain zero or more condition quotes and a default quote. Each condition quote should contain a quoted predicate followed by the function expression to run if that predicate returns true. If no predicates return true the default function runs.

+
[
+    [ [Predicate0] Function0 ]
+    [ [Predicate1] Function1 ]
+    ...
+    [ [PredicateN] FunctionN ]
+    [Default]
+]
+cond
+

Discussion

It works by rewriting into a chain of nested ifte expressions, e.g.:

-
[[[B0] T0] [[B1] T1] [D]] cond
+
      [[[B0] T0] [[B1] T1] [D]] cond
 -----------------------------------------
-[B0] [T0] [[B1] [T1] [D] ifte] ifte

-
Gentzen diagram.

-
Definition

-
if not basis.

-
Derivation

-
if not basis.

-
Source

-
if basis

-
Discussion

-
Lorem ipsum.

+   [B0] [T0] [[B1] [T1] [D] ifte] ifte
-

Lorem ipsum.

+

ifte

cons

-

(Basis Function)

+

Basis Function

Given an item and a list, append the item to the list to make a new list.

-
   A [...] cons
+
   a [...] cons
 ------------------
-     [A ...]

-
Source

-
func(cons, [list(A), B|S], [list([B|A])|S]).

-
Discussion

-
Cons is a venerable old function from Lisp. It doesn’t inspect the item but it will not cons onto a non-list. It’s inverse operation is called uncons.

+     [a ...]
+

Discussion

+

Cons is a venerable old function from Lisp. Its inverse operation is uncons.

-

ccons uncons

+

uncons

dinfrirst

Basis Function Combinator

dip infrst

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -901,13 +887,13 @@ ------------------- ... Q x

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -919,13 +905,13 @@ --------------------- ... Q y x

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -937,13 +923,13 @@ ----------------------- ... Q z y x

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -952,13 +938,13 @@

Basis Function Combinator

The disenstacken operator expects a list on top of the stack and makes that the stack discarding the rest of the stack.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -971,13 +957,13 @@

divmod(x, y) -> (quotient, remainder)

Return the tuple (x//y, x%y). Invariant: q * y + r == x.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -986,13 +972,13 @@

Basis Function Combinator

[0 >] [dup --] while

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1005,13 +991,13 @@ ---------------------- [c d]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1020,13 +1006,13 @@

Basis Function Combinator

(a1 -- a1 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1035,13 +1021,13 @@

Basis Function Combinator

(a2 a1 -- a2 a2 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1050,13 +1036,13 @@

Basis Function Combinator

(a3 a2 a1 -- a3 a3 a2 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1070,13 +1056,13 @@ ... a a [F] dip ... a F a

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1085,13 +1071,13 @@

Basis Function Combinator

dup dipd

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1100,13 +1086,13 @@

Basis Function Combinator

stack [clear] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1115,13 +1101,13 @@

Basis Function Combinator

Same as a == b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1130,13 +1116,13 @@

Basis Function Combinator

([a1 ...1] -- a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1145,13 +1131,13 @@

Basis Function Combinator

([a1 a2 ...1] -- a1 a2)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1160,13 +1146,13 @@

Basis Function Combinator

<{} [concat] step

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1176,13 +1162,13 @@

Return the floor of x as an Integral.

This is the largest integer <= x.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1191,13 +1177,13 @@

Basis Function Combinator

Same as a // b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1206,13 +1192,13 @@

Basis Function Combinator

[i] app2

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1221,13 +1207,13 @@

Basis Function Combinator

([a1 a2 a3 a4 ...1] -- a4)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1236,13 +1222,13 @@

Basis Function Combinator

true [tuck mod dup 0 >] loop pop

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1251,13 +1237,13 @@

Basis Function Combinator

Compiled GCD function.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1266,13 +1252,13 @@

Basis Function Combinator

Same as a >= b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1297,13 +1283,13 @@ == [I] [T] [R [P] i] ifte == [I] [T] [R P] ifte

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1316,13 +1302,13 @@ ------------------------- a

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1331,13 +1317,13 @@

Basis Function Combinator

<{} [cons] times

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1346,13 +1332,13 @@

Basis Function Combinator

[stack popd] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1361,13 +1347,13 @@

Basis Function Combinator

Same as a > b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1376,13 +1362,13 @@

Basis Function Combinator

Accepts a quoted symbol on the top of the stack and prints its docs.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1391,13 +1377,13 @@

Basis Function Combinator

[sqr] ii + sqrt

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1408,22 +1394,22 @@ 
   [Q] i
 -----------
     Q
-

Source

+

Source

combo(i, [list(P)|S], S, Ei, Eo) :- append(P, Ei, Eo).
-

Discussion

+

Discussion

This is probably the fundamental combinator. You wind up using it in all kinds of places (for example, the x combinator can be defined as dup i.)

id

Basis Function Combinator

The identity function.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1443,13 +1429,13 @@ ... [else] [then] [...] [if] infra first choice i

Has the effect of grabbing a copy of the stack on which to run the if-part using infra.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1460,13 +1446,13 @@ ------------------ ... Q a Q

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1477,9 +1463,9 @@ 
   ... [a b c] [Q] infra
 ---------------------------
     c b a Q [...] swaack
-

Definition

+

Definition

swons swaack [i] dip swaack
-

Discussion

+

Discussion

This is one of the more useful combinators. It allows a quoted expression to serve as a stack for a program, effectively running it in a kind of “pocket universe”. If the list represents a datastructure then infra lets you work on its internal structure.

swaack

@@ -1488,13 +1474,13 @@

Basis Function Combinator

infra first

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1506,13 +1492,13 @@

[sqr dup mul] inscribe

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1521,13 +1507,13 @@

Basis Function Combinator

Same as a <= b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1543,13 +1529,13 @@ ------------------------ ...

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1558,13 +1544,13 @@

Basis Function Combinator

Same as a << b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1573,13 +1559,13 @@

Basis Function Combinator

Same as a < b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1588,13 +1574,13 @@

Basis Function Combinator

[codireco] ccons

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1603,13 +1589,13 @@

Basis Function Combinator

Run the quoted program on TOS on the items in the list under it, push a new list with the results in place of the program and original list.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1618,13 +1604,13 @@

Basis Function Combinator

Given a list find the maximum.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1633,13 +1619,13 @@

Basis Function Combinator

Given a list find the minimum.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1648,13 +1634,13 @@

Basis Function Combinator

Same as a % b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1666,13 +1652,13 @@

Basis Function Combinator

Same as a * b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1681,13 +1667,13 @@

Basis Function Combinator

Same as a != b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1696,13 +1682,13 @@

Basis Function Combinator

Same as -a.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1711,13 +1697,13 @@

Basis Function Combinator

Same as not a.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1733,20 +1719,20 @@ N !- ---------- N >= 0 true -

Definition

+

Definition

0 >=

nulco

Basis Function Combinator

[nullary] cons

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1757,16 +1743,16 @@ 
   ... [P] nullary
 ---------------------
         ... A
-

Definition

+

Definition

[stack] dip infra first
-

Derivation

+

Derivation

... [P] nullary
 ... [P] [stack] dip infra first
 ... stack [P] infra first
 ... [...] [P] infra first
 ... [A ...] first
 ...  A
-

Discussion

+

Discussion

A very useful function that runs any other quoted function and returns it’s first result without disturbing the stack (under the quoted program.)

unary binary ternary

@@ -1775,13 +1761,13 @@

Basis Function Combinator

swap at

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1790,13 +1776,13 @@

Basis Function Combinator

Same as a | b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1805,13 +1791,13 @@

Basis Function Combinator

(a2 a1 -- a2 a1 a2)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1820,13 +1806,13 @@

Basis Function Combinator

[i] map

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1841,13 +1827,13 @@ ------------- a+b a-b

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1856,13 +1842,13 @@ a+b a-b

Basis Function Combinator

(a1 --)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1871,13 +1857,13 @@ a+b a-b

Basis Function Combinator

(a2 a1 -- a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1886,13 +1872,13 @@ a+b a-b

Basis Function Combinator

(a3 a2 a1 -- a2 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1901,13 +1887,13 @@ a+b a-b

Basis Function Combinator

(a2 a1 --)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1916,13 +1902,13 @@ a+b a-b

Basis Function Combinator

(a3 a2 a1 -- a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1931,13 +1917,13 @@ a+b a-b

Basis Function Combinator

(a4 a3 a2 a1 -- a2 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1946,13 +1932,13 @@ a+b a-b

Basis Function Combinator

pop popop

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1961,13 +1947,13 @@ a+b a-b

Basis Function Combinator

Same as a ** b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1976,13 +1962,13 @@ a+b a-b

Basis Function Combinator

Decrement TOS.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2003,13 +1989,13 @@ a+b a-b ------------------------------------------ n > 0 n (n-1) [Base] [Recur] primrec Recur

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2018,13 +2004,13 @@ a+b a-b

Basis Function Combinator

1 swap [*] step

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2033,13 +2019,13 @@ a+b a-b

Basis Function Combinator

[unit] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2048,13 +2034,13 @@ a+b a-b

Basis Function Combinator

[0 <=] [1 - dup] anamorphism

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2063,13 +2049,13 @@ a+b a-b

Basis Function Combinator

unit [down_to_zero] infra

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2078,13 +2064,13 @@ a+b a-b

Basis Function Combinator

rest cons

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2102,13 +2088,13 @@ a+b a-b ------------------------ [2 3 1]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2117,13 +2103,13 @@ a+b a-b

Basis Function Combinator

([a1 ...0] -- [...0])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2133,13 +2119,13 @@ a+b a-b

Reverse the list on the top of the stack. :

reverse == [] swap shunt

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2148,13 +2134,13 @@ a+b a-b

Basis Function Combinator

(a1 a2 a3 -- a2 a3 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2163,13 +2149,13 @@ a+b a-b

Basis Function Combinator

(a1 a2 a3 -- a3 a1 a2)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2185,13 +2171,13 @@ a+b a-b

Round a number to a given precision in decimal digits.

The return value is an integer if ndigits is omitted or None. Otherwise the return value has the same type as the number. ndigits may be negative.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2200,13 +2186,13 @@ a+b a-b

Basis Function Combinator

([a1 a2 ...1] -- [...1])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2215,13 +2201,13 @@ a+b a-b

Basis Function Combinator

Same as a >> b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2230,13 +2216,13 @@ a+b a-b

Basis Function Combinator

<{} infra

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2245,13 +2231,13 @@ a+b a-b

Basis Function Combinator

([a1 a2 ...1] -- a2)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2269,13 +2255,13 @@ a+b a-b B

The sequence can contain more than two items but not fewer. Currently Python semantics are used to evaluate the "truthiness" of the Boolean value (so empty string, zero, etc. are counted as false, etc.)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2284,13 +2270,13 @@ a+b a-b

Basis Function Combinator

Print redistribution information.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2299,13 +2285,13 @@ a+b a-b

Basis Function Combinator

uncons [swons] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2319,13 +2305,13 @@ a+b a-b --------------------------- [f e d a b c]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2334,13 +2320,13 @@ a+b a-b

Basis Function Combinator

[pop ++] step_zero

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2349,13 +2335,13 @@ a+b a-b

Basis Function Combinator

Given a list return it sorted.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2364,13 +2350,13 @@ a+b a-b

Basis Function Combinator

[[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2379,13 +2365,13 @@ a+b a-b

Basis Function Combinator

[drop] [take] clop

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2394,13 +2380,13 @@ a+b a-b

Basis Function Combinator

[take reverse] [drop] clop

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2409,13 +2395,13 @@ a+b a-b

Basis Function Combinator

dup *

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2424,13 +2410,13 @@ a+b a-b

Basis Function Combinator

Return the square root of the number a. Negative numbers return complex roots.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2439,13 +2425,13 @@ a+b a-b

Basis Function Combinator

(... -- ... [...])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2454,13 +2440,13 @@ a+b a-b

Basis Function Combinator

[stack] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2483,13 +2469,13 @@ a+b a-b ... a . Q [b c] [Q] step

The step combinator executes the quotation on each member of the list on top of the stack.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2498,13 +2484,13 @@ a+b a-b

Basis Function Combinator

0 roll> step

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2513,13 +2499,13 @@ a+b a-b

Basis Function Combinator

(... a1 -- ... a1 a1 [...])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2528,13 +2514,13 @@ a+b a-b

Basis Function Combinator

(... a2 a1 -- ... a2 a1 a1 a2 [...])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2543,13 +2529,13 @@ a+b a-b

Basis Function Combinator

Same as a - b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2558,13 +2544,13 @@ a+b a-b

Basis Function Combinator

Increment TOS.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2574,13 +2560,13 @@ a+b a-b

Given a quoted sequence of numbers return the sum. :

sum == 0 swap [+] step

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2589,13 +2575,13 @@ a+b a-b

Basis Function Combinator

([...1] -- [...0])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2604,13 +2590,13 @@ a+b a-b

Basis Function Combinator

(a1 a2 -- a2 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2619,13 +2605,13 @@ a+b a-b

Basis Function Combinator

[swap] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2634,13 +2620,13 @@ a+b a-b

Basis Function Combinator

swap concat

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2649,13 +2635,13 @@ a+b a-b

Basis Function Combinator

([...1] a1 -- [a1 ...1])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2664,13 +2650,13 @@ a+b a-b

Basis Function Combinator

[i] genrec

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2682,13 +2668,13 @@ a+b a-b ---------------------- [b a]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2699,9 +2685,9 @@ a+b a-b 
   ... z y x [P] unary
 -------------------------
          ... A
-

Definition

+

Definition

binary popd
-

Discussion

+

Discussion

Runs any other quoted function and returns its first result while consuming exactly three items from the stack.

binary nullary unary

@@ -2710,13 +2696,13 @@ a+b a-b

Basis Function Combinator

([a1 a2 a3 ...1] -- a3)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2738,13 +2724,13 @@ a+b a-b ------------------------------------- w/ n > 1 ... . Q (n - 1) [Q] times

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2756,13 +2742,13 @@ a+b a-b

Basis Function Combinator

(a2 a1 -- a1 a2 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2773,9 +2759,9 @@ a+b a-b 
   ... x [P] unary
 ---------------------
        ... A
-

Definition

+

Definition

nullary popd
-

Discussion

+

Discussion

Runs any other quoted function and returns its first result while consuming exactly one item from the stack.

binary nullary ternary

@@ -2786,9 +2772,9 @@ a+b a-b 
   [A ...] uncons
 --------------------
       A [...]
-

Source

+

Source

func(uncons, Si, So) :- func(cons, So, Si).
-

Discussion

+

Discussion

This is the inverse of cons.

cons

@@ -2797,13 +2783,13 @@ a+b a-b

Basis Function Combinator

Given a list remove duplicate items.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2812,13 +2798,13 @@ a+b a-b

Basis Function Combinator

(a1 -- [a1 ])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2827,13 +2813,13 @@ a+b a-b

Basis Function Combinator

[i] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2842,13 +2828,13 @@ a+b a-b

Basis Function Combinator

([a1 ...1] -- [...1] a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2857,13 +2843,13 @@ a+b a-b

Basis Function Combinator

True if the form on TOS is void otherwise False.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2872,13 +2858,13 @@ a+b a-b

Basis Function Combinator

Print warranty information.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2887,13 +2873,13 @@ a+b a-b

Basis Function Combinator

swap nulco dupdipd concat loop

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2902,13 +2888,13 @@ a+b a-b

Basis Function Combinator

Print all the words in alphabetical order.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2918,22 +2904,22 @@ a+b a-b 
   [F] x
 -----------
    [F] F
-

Definition

+

Definition

dup i
-

Discussion

+

Discussion

The x combinator …

xor

Basis Function Combinator

Same as a ^ b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2942,13 +2928,13 @@ a+b a-b

Basis Function Combinator

Replace the two lists on the top of the stack with a list of the pairs from each list. The smallest list sets the length of the result list.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

diff --git a/docs/reference/mkref/Functor-Reference.md b/docs/reference/mkref/Functor-Reference.md index 64ec5c2..4e9d47e 100644 --- a/docs/reference/mkref/Functor-Reference.md +++ b/docs/reference/mkref/Functor-Reference.md @@ -895,133 +895,118 @@ useful in a few places. ## codireco -Basis Function Combinator +Combinator -codi reco - -Gentzen diagram. +This is part of the [make_generator] function. You would not use this +combinator directly. ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> [codi] [reco] ### Discussion -Lorem ipsum. +See [make_generator] and the +["Using `x` to Generate Values" notebook](https://joypy.osdn.io/notebooks/Generator_Programs.html#an-interesting-variation) +as well as +[Recursion Theory and Joy](https://www.kevinalbrecht.com/code/joy-mirror/j05cmp.html) by Manfred von Thun. ### Crosslinks -Lorem ipsum. +[make_generator] + ------------------------------------------------------------------------ ## concat -Basis Function Combinator +Function -Concatinate the two lists on the top of the stack. : +Concatinate two lists. - [a b c] [d e f] concat + [a b c] [d e f] concat ---------------------------- - [a b c d e f] - -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. - -### Crosslinks + [a b c d e f] + +### Crosslinks + +[first] +[first_two] +[flatten] +[fourth] +[getitem] +[remove] +[rest] +[reverse] +[rrest] +[second] +[shift] +[shunt] +[size] +[sort] +[split_at] +[split_list] +[swaack] +[third] +[zip] -Lorem ipsum. ------------------------------------------------------------------------ ## cond -Basis Function Combinator +Combinator This combinator works like a case statement. It expects a single quote on the stack that must contain zero or more condition quotes and a -default quote. Each condition clause should contain a quoted predicate +default quote. Each condition quote should contain a quoted predicate followed by the function expression to run if that predicate returns -true. If no predicates return true the default function runs. +`true`. If no predicates return `true` the default function runs. + + [ + [ [Predicate0] Function0 ] + [ [Predicate1] Function1 ] + ... + [ [PredicateN] FunctionN ] + [Default] + ] + cond + +### Discussion It works by rewriting into a chain of nested [ifte]{.title-ref} expressions, e.g.: - [[[B0] T0] [[B1] T1] [D]] cond + [[[B0] T0] [[B1] T1] [D]] cond ----------------------------------------- - [B0] [T0] [[B1] [T1] [D] ifte] ifte + [B0] [T0] [[B1] [T1] [D] ifte] ifte -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. ### Crosslinks -Lorem ipsum. +[ifte] + -------------------- ## cons -(Basis Function) +Basis Function Given an item and a list, append the item to the list to make a new list. - A [...] cons + a [...] cons ------------------ - [A ...] - -### Source - - func(cons, [list(A), B|S], [list([B|A])|S]). + [a ...] ### Discussion -Cons is a venerable old function from Lisp. It doesn't inspect the item -but it will not cons onto a non-list. It's inverse operation is called -`uncons`. +Cons is a [venerable old function from Lisp](https://en.wikipedia.org/wiki/Cons#Lists). +Its inverse operation is [uncons]. ### Crosslinks -[ccons](#ccons) -[uncons](#uncons) +[uncons] ------------------------------------------------------------------------ -- 2.11.0