diff --git a/docs/reference/ccccons.md b/docs/reference/ccccons.md index 1196090..ae3f3b2 100644 --- a/docs/reference/ccccons.md +++ b/docs/reference/ccccons.md @@ -2,28 +2,19 @@ ## ccccons -Basis Function Combinator +Function -ccons ccons + a b c d [...] ccccons + --------------------------- + [a b c d ...] -Gentzen diagram. +Do [cons] four times. ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> [ccons] [ccons] ### Crosslinks -Lorem ipsum. +[ccons] [cons] [times] + diff --git a/docs/reference/ccons.md b/docs/reference/ccons.md index 0afb708..5a179b0 100644 --- a/docs/reference/ccons.md +++ b/docs/reference/ccons.md @@ -2,23 +2,20 @@ ## ccons -(Function) +Function -Given two items and a list, append the items to the list to make a new list. - - B A [...] ccons + a b [...] ccons --------------------- - [B A ...] + [a b ...] + +Do [cons] two times. ### Definition - cons cons - -### Discussion - -Does `cons` twice. +> [cons] [cons] ### Crosslinks -[cons](#cons) +[cons] +[ccons] diff --git a/docs/reference/choice.md b/docs/reference/choice.md index 6110001..5122a8f 100644 --- a/docs/reference/choice.md +++ b/docs/reference/choice.md @@ -2,41 +2,29 @@ ## choice -Basis Function Combinator +Basis Function -Use a Boolean value to select one of two items. : +Use a Boolean value to select one of two items. - A B false choice + a b false choice ---------------------- - A + a - - A B true choice + a b true choice --------------------- - B - -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. + b ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> \[[pop]\] \[[popd]\] [branch] ### Discussion -Lorem ipsum. +It's a matter of taste whether you implement this in terms of [branch] or +the other way around. ### Crosslinks -Lorem ipsum. +[branch] +[select] + diff --git a/docs/reference/clear.md b/docs/reference/clear.md index e2a0720..a92e930 100644 --- a/docs/reference/clear.md +++ b/docs/reference/clear.md @@ -2,33 +2,16 @@ ## clear -Basis Function Combinator +Basis Function Clear everything from the stack. -: clear == stack [pop stack] loop - - ... clear - --------------- - -Gentzen diagram. - ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> [stack] [bool] \[[pop] [stack] [bool]\] [loop] ### Crosslinks -Lorem ipsum. +[stack] +[swaack] + diff --git a/docs/reference/cleave.md b/docs/reference/cleave.md index 91169dd..195f67f 100644 --- a/docs/reference/cleave.md +++ b/docs/reference/cleave.md @@ -2,28 +2,32 @@ ## cleave -Basis Function Combinator +Combinator -fork popdd +Run two programs in parallel, consuming one additional item, and put their +results on the stack. -Gentzen diagram. - -### Definition - -if not basis. + ... x [A] [B] cleave + ------------------------ + ... a b ### Derivation -if not basis. +> [fork] [popdd] -### Source +### Example -if basis + 1 2 3 [+] [-] cleave + -------------------------- + 1 2 5 -1 ### Discussion -Lorem ipsum. +One of a handful of useful parallel combinators. ### Crosslinks -Lorem ipsum. +[clop] +[fork] +[map] + diff --git a/docs/reference/clop.md b/docs/reference/clop.md index 6963bbb..6983b6f 100644 --- a/docs/reference/clop.md +++ b/docs/reference/clop.md @@ -2,28 +2,29 @@ ## clop -Basis Function Combinator +Combinator -cleave popdd +Run two programs in parallel, consuming two additional items, and put their results on the stack. -Gentzen diagram. + ... x y [A] [B] clop + -------------------------- + ... a b ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> [cleave] [popdd] ### Discussion -Lorem ipsum. +Like [cleave] but consumes an additional item from the stack. + + 1 2 3 4 [+] [-] clop + -------------------------- + 1 2 7 -1 ### Crosslinks -Lorem ipsum. +[cleave] +[fork] +[map] + diff --git a/docs/reference/cmp.md b/docs/reference/cmp.md index 650ecbe..b992eb1 100644 --- a/docs/reference/cmp.md +++ b/docs/reference/cmp.md @@ -2,41 +2,37 @@ ## cmp -Basis Function Combinator +Combinator -cmp takes two values and three quoted programs on the stack and runs one -of the three depending on the results of comparing the two values: : +Take two values and three quoted programs on the stack and run one +of the three depending on the results of comparing the two values. - a b [G] [E] [L] cmp + a b [G] [E] [L] cmp ------------------------- a > b - G + G - a b [G] [E] [L] cmp + a b [G] [E] [L] cmp ------------------------- a = b - E + E - a b [G] [E] [L] cmp + a b [G] [E] [L] cmp ------------------------- a < b - L - -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - + L ### Discussion -Lorem ipsum. +This is useful sometimes, and you can [dup] or [dupd] with two quoted +programs to handle the cases when you just want to deal with [<=] or [>=] +and not all three possibilities, e.g.: + + [G] [LE] dup cmp + + [GE] [L] dupd cmp + +Or even: + + [GL] [E] over cmp ### Crosslinks -Lorem ipsum. +TODO: link to tree notebooks where this was used. + diff --git a/docs/reference/codi.md b/docs/reference/codi.md index b1f0c13..ed57f8e 100644 --- a/docs/reference/codi.md +++ b/docs/reference/codi.md @@ -2,28 +2,26 @@ ## codi -Basis Function Combinator +Combinator -cons dip - -Gentzen diagram. +Take a quoted program from the stack, [cons] the next item onto it, then +[dip] the whole thing under what was the third item on the stack. + + a b [F] . codi + -------------------- + b . F a ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> [cons] [dip] ### Discussion -Lorem ipsum. +This is one of those weirdly specific functions that turns out to be +useful in a few places. ### Crosslinks -Lorem ipsum. +[appN] +[codireco] + diff --git a/docs/reference/mkref/FuncRef.html b/docs/reference/mkref/FuncRef.html index 413045f..16d0a74 100644 --- a/docs/reference/mkref/FuncRef.html +++ b/docs/reference/mkref/FuncRef.html @@ -684,160 +684,147 @@

choice ifte select

ccccons

-

Basis Function Combinator

-

ccons ccons

-

Gentzen diagram.

+

Function

+
   a b c d [...] ccccons
+---------------------------
+       [a b c d ...]
+

Do cons four times.

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

-

Discussion

-

Lorem ipsum.

+
+

ccons ccons

+
-

Lorem ipsum.

+

ccons cons times

ccons

-

(Function)

-

Given two items and a list, append the items to the list to make a new list.

-
   B A [...] ccons
+
Function

+
   a b [...] ccons
 ---------------------
-      [B A ...]

+      [a b ...]
+

Do cons two times.

Definition

-
cons cons
-

Discussion

-

Does cons twice.

+
+

cons cons

+
-

cons

+

cons ccons

choice

-

Basis Function Combinator

-

Use a Boolean value to select one of two items. :

-
A B false choice
+
Basis Function

+
Use a Boolean value to select one of two items.

+
   a b false choice
 ----------------------
-A
+          a
 
-
-A B true choice
+   a b true choice
 ---------------------
-  B

-
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.

+          b

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

-

Discussion

-

Lorem ipsum.

+
+

[pop] [popd] branch

+
+

Discussion

+

It’s a matter of taste whether you implement this in terms of branch or the other way around.

-

Lorem ipsum.

+

branch select

clear

-

Basis Function Combinator

-
-
Clear everything from the stack.
-

clear == stack [pop stack] loop

-
   ... clear
----------------
-
-
-

Gentzen diagram.

+

Basis Function

+

Clear everything from the stack.

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

-

Discussion

-

Lorem ipsum.

+
+

stack bool [pop stack bool] loop

+
-

Lorem ipsum.

+

stack swaack

cleave

-

Basis Function Combinator

-

fork popdd

-

Gentzen diagram.

-

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

-

Discussion

-

Lorem ipsum.

+

Combinator

+

Run two programs in parallel, consuming one additional item, and put their results on the stack.

+
   ... x [A] [B] cleave
+------------------------
+        ... a b
+

Derivation

+
+

fork popdd

+
+

Example

+
   1 2 3 [+] [-] cleave
+--------------------------
+         1 2 5 -1
+

Discussion

+

One of a handful of useful parallel combinators.

-

Lorem ipsum.

+

clop fork map

clop

-

Basis Function Combinator

-

cleave popdd

-

Gentzen diagram.

-

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

-

Discussion

-

Lorem ipsum.

+

Combinator

+

Run two programs in parallel, consuming two additional items, and put their results on the stack.

+
   ... x y [A] [B] clop
+--------------------------
+        ... a b
+

Definition

+
+

cleave popdd

+
+

Discussion

+

Like cleave but consumes an additional item from the stack.

+
   1 2 3 4 [+] [-] clop
+--------------------------
+         1 2 7 -1
-

Lorem ipsum.

+

cleave fork map

cmp

-

Basis Function Combinator

-

cmp takes two values and three quoted programs on the stack and runs one of the three depending on the results of comparing the two values: :

-
a b [G] [E] [L] cmp
+
Combinator

+
Take two values and three quoted programs on the stack and run one of the three depending on the results of comparing the two values.

+
   a b [G] [E] [L] cmp
 ------------------------- a > b
- G
+        G
 
-a b [G] [E] [L] cmp
+   a b [G] [E] [L] cmp
 ------------------------- a = b
-     E
+            E
 
-a b [G] [E] [L] cmp
+   a b [G] [E] [L] cmp
 ------------------------- a < b
-     L

-
Gentzen diagram.

-
Definition

-
if not basis.

-
Derivation

-
if not basis.

-
Source

-
if basis

-
Discussion

-
Lorem ipsum.

+                L
+

Discussion

+

This is useful sometimes, and you can dup or dupd with two quoted programs to handle the cases when you just want to deal with <= or >= and not all three possibilities, e.g.:

+
[G] [LE] dup cmp
+
+[GE] [L] dupd cmp
+

Or even:

+
[GL] [E] over cmp
-

Lorem ipsum.

+

TODO: link to tree notebooks where this was used.

codi

-

Basis Function Combinator

-

cons dip

-

Gentzen diagram.

-

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

-

Discussion

-

Lorem ipsum.

+

Combinator

+

Take a quoted program from the stack, cons the next item onto it, then dip the whole thing under what was the third item on the stack.

+
   a b [F] . codi
+--------------------
+         b . F a
+

Definition

+
+

cons dip

+
+

Discussion

+

This is one of those weirdly specific functions that turns out to be useful in a few places.

-

Lorem ipsum.

+

appN codireco

codireco

Basis Function Combinator

codi reco

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -849,13 +836,13 @@ a b [G] [E] [L] cmp ---------------------------- [a b c d e f]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -868,13 +855,13 @@ a b [G] [E] [L] cmp ----------------------------------------- [B0] [T0] [[B1] [T1] [D] ifte] ifte

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -885,9 +872,9 @@ a b [G] [E] [L] cmp 
   A [...] cons
 ------------------
      [A ...]
-

Source

+

Source

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

Discussion

+

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.

ccons uncons

@@ -896,13 +883,13 @@ a b [G] [E] [L] cmp

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.

@@ -914,13 +901,13 @@ a b [G] [E] [L] cmp ------------------- ... Q x

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -932,13 +919,13 @@ a b [G] [E] [L] cmp --------------------- ... 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.

@@ -950,13 +937,13 @@ a b [G] [E] [L] cmp ----------------------- ... 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.

@@ -965,13 +952,13 @@ a b [G] [E] [L] cmp

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.

@@ -984,13 +971,13 @@ a b [G] [E] [L] cmp

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.

@@ -999,13 +986,13 @@ a b [G] [E] [L] cmp

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.

@@ -1018,13 +1005,13 @@ a b [G] [E] [L] cmp ---------------------- [c d]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1033,13 +1020,13 @@ a b [G] [E] [L] cmp

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.

@@ -1048,13 +1035,13 @@ a b [G] [E] [L] cmp

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.

@@ -1063,13 +1050,13 @@ a b [G] [E] [L] cmp

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.

@@ -1083,13 +1070,13 @@ a b [G] [E] [L] cmp ... 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.

@@ -1098,13 +1085,13 @@ a b [G] [E] [L] cmp

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.

@@ -1113,13 +1100,13 @@ a b [G] [E] [L] cmp

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.

@@ -1128,13 +1115,13 @@ a b [G] [E] [L] cmp

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.

@@ -1143,13 +1130,13 @@ a b [G] [E] [L] cmp

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.

@@ -1158,13 +1145,13 @@ a b [G] [E] [L] cmp

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.

@@ -1173,13 +1160,13 @@ a b [G] [E] [L] cmp

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.

@@ -1189,13 +1176,13 @@ a b [G] [E] [L] cmp

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.

@@ -1204,13 +1191,13 @@ a b [G] [E] [L] cmp

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.

@@ -1219,13 +1206,13 @@ a b [G] [E] [L] cmp

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.

@@ -1234,13 +1221,13 @@ a b [G] [E] [L] cmp

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.

@@ -1249,13 +1236,13 @@ a b [G] [E] [L] cmp

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.

@@ -1264,13 +1251,13 @@ a b [G] [E] [L] cmp

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.

@@ -1279,13 +1266,13 @@ a b [G] [E] [L] cmp

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.

@@ -1310,13 +1297,13 @@ a b [G] [E] [L] cmp == [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.

@@ -1329,13 +1316,13 @@ a b [G] [E] [L] cmp ------------------------- a

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1344,13 +1331,13 @@ a b [G] [E] [L] cmp

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.

@@ -1359,13 +1346,13 @@ a b [G] [E] [L] cmp

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.

@@ -1374,13 +1361,13 @@ a b [G] [E] [L] cmp

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.

@@ -1389,13 +1376,13 @@ a b [G] [E] [L] cmp

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.

@@ -1404,13 +1391,13 @@ a b [G] [E] [L] cmp

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.

@@ -1421,22 +1408,22 @@ a b [G] [E] [L] cmp 
   [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.

@@ -1456,13 +1443,13 @@ a b [G] [E] [L] cmp ... [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.

@@ -1473,13 +1460,13 @@ a b [G] [E] [L] cmp ------------------ ... 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.

@@ -1490,9 +1477,9 @@ a b [G] [E] [L] cmp 
   ... [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

@@ -1501,13 +1488,13 @@ a b [G] [E] [L] cmp

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.

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@@ -1519,13 +1506,13 @@ a b [G] [E] [L] cmp

[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.

@@ -1534,13 +1521,13 @@ a b [G] [E] [L] cmp

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.

@@ -1556,13 +1543,13 @@ a b [G] [E] [L] cmp ------------------------ ...

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1571,13 +1558,13 @@ a b [G] [E] [L] cmp

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.

@@ -1586,13 +1573,13 @@ a b [G] [E] [L] cmp

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.

@@ -1601,13 +1588,13 @@ a b [G] [E] [L] cmp

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.

@@ -1616,13 +1603,13 @@ a b [G] [E] [L] cmp

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.

@@ -1631,13 +1618,13 @@ a b [G] [E] [L] cmp

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.

@@ -1646,13 +1633,13 @@ a b [G] [E] [L] cmp

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.

@@ -1661,13 +1648,13 @@ a b [G] [E] [L] cmp

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.

@@ -1679,13 +1666,13 @@ a b [G] [E] [L] cmp

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.

@@ -1694,13 +1681,13 @@ a b [G] [E] [L] cmp

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.

@@ -1709,13 +1696,13 @@ a b [G] [E] [L] cmp

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.

@@ -1724,13 +1711,13 @@ a b [G] [E] [L] cmp

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.

@@ -1746,20 +1733,20 @@ a b [G] [E] [L] cmp 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.

@@ -1770,16 +1757,16 @@ a b [G] [E] [L] cmp 
   ... [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

@@ -1788,13 +1775,13 @@ a b [G] [E] [L] cmp

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.

@@ -1803,13 +1790,13 @@ a b [G] [E] [L] cmp

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.

@@ -1818,13 +1805,13 @@ a b [G] [E] [L] cmp

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.

@@ -1833,13 +1820,13 @@ a b [G] [E] [L] cmp

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.

@@ -1854,13 +1841,13 @@ a b [G] [E] [L] cmp ------------- 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.

@@ -1869,13 +1856,13 @@ 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.

@@ -1884,13 +1871,13 @@ 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.

@@ -1899,13 +1886,13 @@ 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.

@@ -1914,13 +1901,13 @@ 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.

@@ -1929,13 +1916,13 @@ 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.

@@ -1944,13 +1931,13 @@ 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.

@@ -1959,13 +1946,13 @@ 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.

@@ -1974,13 +1961,13 @@ 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.

@@ -1989,13 +1976,13 @@ 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.

@@ -2016,13 +2003,13 @@ 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.

@@ -2031,13 +2018,13 @@ 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.

@@ -2046,13 +2033,13 @@ 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.

@@ -2061,13 +2048,13 @@ 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.

@@ -2076,13 +2063,13 @@ 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.

@@ -2091,13 +2078,13 @@ 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.

@@ -2115,13 +2102,13 @@ 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.

@@ -2130,13 +2117,13 @@ 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.

@@ -2146,13 +2133,13 @@ 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.

@@ -2161,13 +2148,13 @@ 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.

@@ -2176,13 +2163,13 @@ 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.

@@ -2198,13 +2185,13 @@ 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.

@@ -2213,13 +2200,13 @@ 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.

@@ -2228,13 +2215,13 @@ 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.

@@ -2243,13 +2230,13 @@ 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.

@@ -2258,13 +2245,13 @@ 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.

@@ -2282,13 +2269,13 @@ 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.

@@ -2297,13 +2284,13 @@ 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.

@@ -2312,13 +2299,13 @@ 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.

@@ -2332,13 +2319,13 @@ 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.

@@ -2347,13 +2334,13 @@ 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.

@@ -2362,13 +2349,13 @@ 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.

@@ -2377,13 +2364,13 @@ 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.

@@ -2392,13 +2379,13 @@ 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.

@@ -2407,13 +2394,13 @@ 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.

@@ -2422,13 +2409,13 @@ 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.

@@ -2437,13 +2424,13 @@ 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.

@@ -2452,13 +2439,13 @@ 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.

@@ -2467,13 +2454,13 @@ 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.

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@@ -2496,13 +2483,13 @@ 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.

@@ -2511,13 +2498,13 @@ 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.

@@ -2526,13 +2513,13 @@ 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.

@@ -2541,13 +2528,13 @@ 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.

@@ -2556,13 +2543,13 @@ 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.

@@ -2571,13 +2558,13 @@ 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.

@@ -2587,13 +2574,13 @@ 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.

@@ -2602,13 +2589,13 @@ 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.

@@ -2617,13 +2604,13 @@ 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.

@@ -2632,13 +2619,13 @@ 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.

@@ -2647,13 +2634,13 @@ 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.

@@ -2662,13 +2649,13 @@ 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.

@@ -2677,13 +2664,13 @@ 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.

@@ -2695,13 +2682,13 @@ 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.

@@ -2712,9 +2699,9 @@ 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

@@ -2723,13 +2710,13 @@ 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.

@@ -2751,13 +2738,13 @@ 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.

@@ -2769,13 +2756,13 @@ 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.

@@ -2786,9 +2773,9 @@ 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

@@ -2799,9 +2786,9 @@ 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

@@ -2810,13 +2797,13 @@ 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.

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@@ -2825,13 +2812,13 @@ 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.

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@@ -2840,13 +2827,13 @@ 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.

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@@ -2855,13 +2842,13 @@ 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.

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@@ -2870,13 +2857,13 @@ 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.

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@@ -2885,13 +2872,13 @@ 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.

@@ -2900,13 +2887,13 @@ 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.

@@ -2915,13 +2902,13 @@ 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.

@@ -2931,22 +2918,22 @@ 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.

@@ -2955,13 +2942,13 @@ 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 f1d79ba..64ec5c2 100644 --- a/docs/reference/mkref/Functor-Reference.md +++ b/docs/reference/mkref/Functor-Reference.md @@ -671,267 +671,225 @@ terms of [choice] as above). The more common "if..then..else" construct ## ccccons -Basis Function Combinator +Function -ccons ccons + a b c d [...] ccccons + --------------------------- + [a b c d ...] -Gentzen diagram. +Do [cons] four times. ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> [ccons] [ccons] ### Crosslinks -Lorem ipsum. +[ccons] [cons] [times] + -------------------- ## ccons -(Function) +Function -Given two items and a list, append the items to the list to make a new list. - - B A [...] ccons + a b [...] ccons --------------------- - [B A ...] + [a b ...] + +Do [cons] two times. ### Definition - cons cons - -### Discussion - -Does `cons` twice. +> [cons] [cons] ### Crosslinks -[cons](#cons) +[cons] +[ccons] ------------------------------------------------------------------------ ## choice -Basis Function Combinator +Basis Function -Use a Boolean value to select one of two items. : +Use a Boolean value to select one of two items. - A B false choice + a b false choice ---------------------- - A + a - - A B true choice + a b true choice --------------------- - B - -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. + b ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> \[[pop]\] \[[popd]\] [branch] ### Discussion -Lorem ipsum. +It's a matter of taste whether you implement this in terms of [branch] or +the other way around. ### Crosslinks -Lorem ipsum. +[branch] +[select] + ------------------------------------------------------------------------ ## clear -Basis Function Combinator +Basis Function Clear everything from the stack. -: clear == stack [pop stack] loop - - ... clear - --------------- - -Gentzen diagram. - ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> [stack] [bool] \[[pop] [stack] [bool]\] [loop] ### Crosslinks -Lorem ipsum. +[stack] +[swaack] + ------------------------------------------------------------------------ ## cleave -Basis Function Combinator +Combinator -fork popdd +Run two programs in parallel, consuming one additional item, and put their +results on the stack. -Gentzen diagram. - -### Definition - -if not basis. + ... x [A] [B] cleave + ------------------------ + ... a b ### Derivation -if not basis. +> [fork] [popdd] -### Source +### Example -if basis + 1 2 3 [+] [-] cleave + -------------------------- + 1 2 5 -1 ### Discussion -Lorem ipsum. +One of a handful of useful parallel combinators. ### Crosslinks -Lorem ipsum. +[clop] +[fork] +[map] + ------------------------------------------------------------------------ ## clop -Basis Function Combinator +Combinator -cleave popdd +Run two programs in parallel, consuming two additional items, and put their results on the stack. -Gentzen diagram. + ... x y [A] [B] clop + -------------------------- + ... a b ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> [cleave] [popdd] ### Discussion -Lorem ipsum. +Like [cleave] but consumes an additional item from the stack. + + 1 2 3 4 [+] [-] clop + -------------------------- + 1 2 7 -1 ### Crosslinks -Lorem ipsum. +[cleave] +[fork] +[map] + ------------------------------------------------------------------------ ## cmp -Basis Function Combinator +Combinator -cmp takes two values and three quoted programs on the stack and runs one -of the three depending on the results of comparing the two values: : +Take two values and three quoted programs on the stack and run one +of the three depending on the results of comparing the two values. - a b [G] [E] [L] cmp + a b [G] [E] [L] cmp ------------------------- a > b - G + G - a b [G] [E] [L] cmp + a b [G] [E] [L] cmp ------------------------- a = b - E + E - a b [G] [E] [L] cmp + a b [G] [E] [L] cmp ------------------------- a < b - L - -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - + L ### Discussion -Lorem ipsum. +This is useful sometimes, and you can [dup] or [dupd] with two quoted +programs to handle the cases when you just want to deal with [<=] or [>=] +and not all three possibilities, e.g.: + + [G] [LE] dup cmp + + [GE] [L] dupd cmp + +Or even: + + [GL] [E] over cmp ### Crosslinks -Lorem ipsum. +TODO: link to tree notebooks where this was used. + ------------------------------------------------------------------------ ## codi -Basis Function Combinator +Combinator -cons dip - -Gentzen diagram. +Take a quoted program from the stack, [cons] the next item onto it, then +[dip] the whole thing under what was the third item on the stack. + + a b [F] . codi + -------------------- + b . F a ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> [cons] [dip] ### Discussion -Lorem ipsum. +This is one of those weirdly specific functions that turns out to be +useful in a few places. ### Crosslinks -Lorem ipsum. +[appN] +[codireco] + ------------------------------------------------------------------------ diff --git a/implementations/Python/joy/library.py b/implementations/Python/joy/library.py index b343c9b..c5d17ce 100644 --- a/implementations/Python/joy/library.py +++ b/implementations/Python/joy/library.py @@ -340,10 +340,9 @@ def choice(stack): --------------------- B - Currently Python semantics are used to evaluate the "truthiness" of the - Boolean value (so empty string, zero, etc. are counted as false, etc.) ''' (if_, (then, (else_, stack))) = stack + assert isinstance(if_, bool), repr(if_) return then if if_ else else_, stack