diff --git a/docs/reference/b.md b/docs/reference/b.md index 37647a1..49b7d0a 100644 --- a/docs/reference/b.md +++ b/docs/reference/b.md @@ -2,7 +2,7 @@ ## b -(Combinator) +Combinator Run two quoted programs @@ -12,19 +12,11 @@ Run two quoted programs ### Definition - [i] dip i - -### Derivation - - [P] [Q] b - [P] [Q] [i] dip i - [P] i [Q] i - P [Q] i - P Q +> \[[i]\] [dip] [i] ### Discussion -This combinator comes in handy. +This combinator may seem trivial but it comes in handy. ### Crosslinks diff --git a/docs/reference/binary.md b/docs/reference/binary.md index 182da5b..eab0aae 100644 --- a/docs/reference/binary.md +++ b/docs/reference/binary.md @@ -2,18 +2,18 @@ ## binary -(Combinator) +Combinator Run a quoted program using exactly two stack values and leave the first item of the result on the stack. ... y x [P] binary ----------------------- - ... A + ... a ### Definition - unary popd +> [unary] [popd] ### Discussion diff --git a/docs/reference/bool.md b/docs/reference/bool.md index 55a3288..e683717 100644 --- a/docs/reference/bool.md +++ b/docs/reference/bool.md @@ -2,32 +2,16 @@ ## bool -Basis Function Combinator +Basis Function -bool(x) -\> bool - -Returns True when the argument x is true, False otherwise. The builtins -True and False are the only two instances of the class bool. The class -bool is a subclass of the class int, and cannot be subclassed. - -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +Convert the item on the top of the stack to a Boolean value. ### Discussion -Lorem ipsum. +For integers 0 is `false` and any other number is `true`; for lists the +empty list is `false` and all other lists are `true`. ### Crosslinks -Lorem ipsum. +[not] + diff --git a/docs/reference/branch.md b/docs/reference/branch.md index 7fe9e83..a88eb4f 100644 --- a/docs/reference/branch.md +++ b/docs/reference/branch.md @@ -2,38 +2,33 @@ ## branch -Basis Function Combinator +Basis Combinator -Use a Boolean value to select one of two quoted programs to run. +Use a Boolean value to select and run one of two quoted programs. - branch == roll< choice i - False [F] [T] branch + false [F] [T] branch -------------------------- - F + F - True [F] [T] branch + true [F] [T] branch ------------------------- - T + T -Gentzen diagram. ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> [rolldown] [choice] [i] ### Discussion -Lorem ipsum. +This is one of the fundamental operations (although it can be defined in +terms of [choice] as above). The more common "if..then..else" construct +[ifte] adds a predicate function that is evaluated [nullary]. ### Crosslinks -Lorem ipsum. +[choice] +[ifte] +[select] + diff --git a/docs/reference/mkref/FuncRef.html b/docs/reference/mkref/FuncRef.html index 496cbb5..413045f 100644 --- a/docs/reference/mkref/FuncRef.html +++ b/docs/reference/mkref/FuncRef.html @@ -627,86 +627,71 @@

As an exercise in Functional Programming in Joy it would be fun to convert this into a catamorphism. See the Recursion Combinators notebook.

b

-

(Combinator)

+

Combinator

Run two quoted programs

   [P] [Q] b
 ---------------
       P Q

Definition

-
[i] dip i
-

Derivation

-
[P] [Q] b
-[P] [Q] [i] dip i
-[P] i [Q] i
- P    [Q] i
- P     Q
+
+

[i] dip i

+

Discussion

-

This combinator comes in handy.

+

This combinator may seem trivial but it comes in handy.

dupdip ii

binary

-

(Combinator)

+

Combinator

Run a quoted program using exactly two stack values and leave the first item of the result on the stack.

   ... y x [P] binary
 -----------------------
-        ... A
+ ... a

Definition

-
unary popd
+
+

unary popd

+

Discussion

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

nullary ternary unary

bool

-

Basis Function Combinator

-

bool(x) -> bool

-

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

-

Gentzen diagram.

-

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

+

Basis Function

+

Convert the item on the top of the stack to a Boolean value.

Discussion

-

Lorem ipsum.

+

For integers 0 is false and any other number is true; for lists the empty list is false and all other lists are true.

-

Lorem ipsum.

+

not

branch

-

Basis Function Combinator

-

Use a Boolean value to select one of two quoted programs to run.

-
branch == roll< choice i
-
-False [F] [T] branch
+
Basis Combinator

+
Use a Boolean value to select and run one of two quoted programs.

+
   false [F] [T] branch
 --------------------------
-   F
+          F
 
-True [F] [T] branch
+   true [F] [T] branch
 -------------------------
-      T

-
Gentzen diagram.

-
Definition

-
if not basis.

-
Derivation

-
if not basis.

-
Source

-
if basis

+             T
+

Definition

+
+

rolldown choice i

+

Discussion

-

Lorem ipsum.

+

This is one of the fundamental operations (although it can be defined in terms of choice as above). The more common “if..then..else” construct ifte adds a predicate function that is evaluated nullary.

-

Lorem ipsum.

+

choice ifte select

ccccons

Basis Function Combinator

ccons ccons

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -719,7 +704,7 @@ True [F] [T] branch 
   B A [...] ccons
 ---------------------
       [B A ...]
-

Definition

+

Definition

cons cons

Discussion

Does cons twice.

@@ -739,11 +724,11 @@ 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.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -760,11 +745,11 @@ A B true choice

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -775,11 +760,11 @@ A B true choice

Basis Function Combinator

fork popdd

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -790,11 +775,11 @@ A B true choice

Basis Function Combinator

cleave popdd

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -816,11 +801,11 @@ a b [G] [E] [L] cmp ------------------------- a < b L

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -831,11 +816,11 @@ a b [G] [E] [L] cmp

Basis Function Combinator

cons dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -846,11 +831,11 @@ a b [G] [E] [L] cmp

Basis Function Combinator

codi reco

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -864,11 +849,11 @@ 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

Lorem ipsum.

@@ -883,11 +868,11 @@ 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

Lorem ipsum.

@@ -900,7 +885,7 @@ a b [G] [E] [L] cmp 
   A [...] cons
 ------------------
      [A ...]
-

Source

+

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.

@@ -911,11 +896,11 @@ 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

Lorem ipsum.

@@ -929,11 +914,11 @@ 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

Lorem ipsum.

@@ -947,11 +932,11 @@ 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

Lorem ipsum.

@@ -965,11 +950,11 @@ 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

Lorem ipsum.

@@ -980,11 +965,11 @@ 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

Lorem ipsum.

@@ -999,11 +984,11 @@ 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

Lorem ipsum.

@@ -1014,11 +999,11 @@ 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

Lorem ipsum.

@@ -1033,11 +1018,11 @@ 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

Lorem ipsum.

@@ -1048,11 +1033,11 @@ 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

Lorem ipsum.

@@ -1063,11 +1048,11 @@ 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

Lorem ipsum.

@@ -1078,11 +1063,11 @@ 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

Lorem ipsum.

@@ -1098,11 +1083,11 @@ 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

Lorem ipsum.

@@ -1113,11 +1098,11 @@ 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

Lorem ipsum.

@@ -1128,11 +1113,11 @@ 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

Lorem ipsum.

@@ -1143,11 +1128,11 @@ 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

Lorem ipsum.

@@ -1158,11 +1143,11 @@ 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

Lorem ipsum.

@@ -1173,11 +1158,11 @@ 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

Lorem ipsum.

@@ -1188,11 +1173,11 @@ 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

Lorem ipsum.

@@ -1204,11 +1189,11 @@ 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

Lorem ipsum.

@@ -1219,11 +1204,11 @@ 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

Lorem ipsum.

@@ -1234,11 +1219,11 @@ 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

Lorem ipsum.

@@ -1249,11 +1234,11 @@ 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

Lorem ipsum.

@@ -1264,11 +1249,11 @@ 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

Lorem ipsum.

@@ -1279,11 +1264,11 @@ 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

Lorem ipsum.

@@ -1294,11 +1279,11 @@ 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

Lorem ipsum.

@@ -1325,11 +1310,11 @@ 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

Lorem ipsum.

@@ -1344,11 +1329,11 @@ a b [G] [E] [L] cmp ------------------------- a

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -1359,11 +1344,11 @@ 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

Lorem ipsum.

@@ -1374,11 +1359,11 @@ 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

Lorem ipsum.

@@ -1389,11 +1374,11 @@ 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

Lorem ipsum.

@@ -1404,11 +1389,11 @@ 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

Lorem ipsum.

@@ -1419,11 +1404,11 @@ 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

Lorem ipsum.

@@ -1436,7 +1421,7 @@ a b [G] [E] [L] cmp 
   [Q] i
 -----------
     Q
-

Source

+

Source

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

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.)

@@ -1445,11 +1430,11 @@ a b [G] [E] [L] cmp

Basis Function Combinator

The identity function.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -1471,11 +1456,11 @@ 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

Lorem ipsum.

@@ -1488,11 +1473,11 @@ 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

Lorem ipsum.

@@ -1505,7 +1490,7 @@ a b [G] [E] [L] cmp 
   ... [a b c] [Q] infra
 ---------------------------
     c b a Q [...] swaack
-

Definition

+

Definition

swons swaack [i] dip swaack

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.

@@ -1516,11 +1501,11 @@ 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

Lorem ipsum.

@@ -1534,11 +1519,11 @@ 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

Lorem ipsum.

@@ -1549,11 +1534,11 @@ 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

Lorem ipsum.

@@ -1571,11 +1556,11 @@ a b [G] [E] [L] cmp ------------------------ ...

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -1586,11 +1571,11 @@ 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

Lorem ipsum.

@@ -1601,11 +1586,11 @@ 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

Lorem ipsum.

@@ -1616,11 +1601,11 @@ 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

Lorem ipsum.

@@ -1631,11 +1616,11 @@ 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

Lorem ipsum.

@@ -1646,11 +1631,11 @@ 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

Lorem ipsum.

@@ -1661,11 +1646,11 @@ 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

Lorem ipsum.

@@ -1676,11 +1661,11 @@ 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

Lorem ipsum.

@@ -1694,11 +1679,11 @@ 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

Lorem ipsum.

@@ -1709,11 +1694,11 @@ 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

Lorem ipsum.

@@ -1724,11 +1709,11 @@ 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

Lorem ipsum.

@@ -1739,11 +1724,11 @@ 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

Lorem ipsum.

@@ -1761,18 +1746,18 @@ 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

Lorem ipsum.

@@ -1785,9 +1770,9 @@ 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
@@ -1803,11 +1788,11 @@ 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

 
Lorem ipsum.

@@ -1818,11 +1803,11 @@ 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

 
Lorem ipsum.

@@ -1833,11 +1818,11 @@ 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

 
Lorem ipsum.

@@ -1848,11 +1833,11 @@ 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

 
Lorem ipsum.

@@ -1869,11 +1854,11 @@ 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

Lorem ipsum.

@@ -1884,11 +1869,11 @@ 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

Lorem ipsum.

@@ -1899,11 +1884,11 @@ 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

Lorem ipsum.

@@ -1914,11 +1899,11 @@ 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

Lorem ipsum.

@@ -1929,11 +1914,11 @@ 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

Lorem ipsum.

@@ -1944,11 +1929,11 @@ 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

Lorem ipsum.

@@ -1959,11 +1944,11 @@ 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

Lorem ipsum.

@@ -1974,11 +1959,11 @@ 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

Lorem ipsum.

@@ -1989,11 +1974,11 @@ 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

Lorem ipsum.

@@ -2004,11 +1989,11 @@ 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

Lorem ipsum.

@@ -2031,11 +2016,11 @@ 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

Lorem ipsum.

@@ -2046,11 +2031,11 @@ 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

Lorem ipsum.

@@ -2061,11 +2046,11 @@ 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

Lorem ipsum.

@@ -2076,11 +2061,11 @@ 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

Lorem ipsum.

@@ -2091,11 +2076,11 @@ 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

Lorem ipsum.

@@ -2106,11 +2091,11 @@ 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

Lorem ipsum.

@@ -2130,11 +2115,11 @@ a+b a-b ------------------------ [2 3 1]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -2145,11 +2130,11 @@ 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

Lorem ipsum.

@@ -2161,11 +2146,11 @@ 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

Lorem ipsum.

@@ -2176,11 +2161,11 @@ 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

Lorem ipsum.

@@ -2191,11 +2176,11 @@ 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

Lorem ipsum.

@@ -2213,11 +2198,11 @@ 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

Lorem ipsum.

@@ -2228,11 +2213,11 @@ 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

Lorem ipsum.

@@ -2243,11 +2228,11 @@ 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

Lorem ipsum.

@@ -2258,11 +2243,11 @@ 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

Lorem ipsum.

@@ -2273,11 +2258,11 @@ 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

Lorem ipsum.

@@ -2297,11 +2282,11 @@ 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

Lorem ipsum.

@@ -2312,11 +2297,11 @@ 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

Lorem ipsum.

@@ -2327,11 +2312,11 @@ 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

Lorem ipsum.

@@ -2347,11 +2332,11 @@ 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

Lorem ipsum.

@@ -2362,11 +2347,11 @@ 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

Lorem ipsum.

@@ -2377,11 +2362,11 @@ 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

Lorem ipsum.

@@ -2392,11 +2377,11 @@ 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

Lorem ipsum.

@@ -2407,11 +2392,11 @@ 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

Lorem ipsum.

@@ -2422,11 +2407,11 @@ 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

Lorem ipsum.

@@ -2437,11 +2422,11 @@ 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

Lorem ipsum.

@@ -2452,11 +2437,11 @@ 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

Lorem ipsum.

@@ -2467,11 +2452,11 @@ a+b a-b

Basis Function Combinator

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

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -2482,11 +2467,11 @@ 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

Lorem ipsum.

@@ -2511,11 +2496,11 @@ 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

Lorem ipsum.

@@ -2526,11 +2511,11 @@ 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

Lorem ipsum.

@@ -2541,11 +2526,11 @@ 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

Lorem ipsum.

@@ -2556,11 +2541,11 @@ 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

Lorem ipsum.

@@ -2571,11 +2556,11 @@ 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

Lorem ipsum.

@@ -2586,11 +2571,11 @@ 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

Lorem ipsum.

@@ -2602,11 +2587,11 @@ 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

Lorem ipsum.

@@ -2617,11 +2602,11 @@ 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

Lorem ipsum.

@@ -2632,11 +2617,11 @@ 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

Lorem ipsum.

@@ -2647,11 +2632,11 @@ 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

Lorem ipsum.

@@ -2662,11 +2647,11 @@ 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

Lorem ipsum.

@@ -2677,11 +2662,11 @@ 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

Lorem ipsum.

@@ -2692,11 +2677,11 @@ 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

Lorem ipsum.

@@ -2710,11 +2695,11 @@ a+b a-b ---------------------- [b a]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

Discussion

Lorem ipsum.

@@ -2727,7 +2712,7 @@ a+b a-b 
   ... z y x [P] unary
 -------------------------
          ... A
-

Definition

+

Definition

binary popd

Discussion

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

@@ -2738,11 +2723,11 @@ 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

Lorem ipsum.

@@ -2766,11 +2751,11 @@ 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

Lorem ipsum.

@@ -2784,11 +2769,11 @@ 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

Lorem ipsum.

@@ -2801,7 +2786,7 @@ a+b a-b 
   ... x [P] unary
 ---------------------
        ... A
-

Definition

+

Definition

nullary popd

Discussion

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

@@ -2814,7 +2799,7 @@ a+b a-b 
   [A ...] uncons
 --------------------
       A [...]
-

Source

+

Source

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

Discussion

This is the inverse of cons.

@@ -2825,11 +2810,11 @@ 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

Lorem ipsum.

@@ -2840,11 +2825,11 @@ 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

Lorem ipsum.

@@ -2855,11 +2840,11 @@ 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

Lorem ipsum.

@@ -2870,11 +2855,11 @@ 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

Lorem ipsum.

@@ -2885,11 +2870,11 @@ 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

Lorem ipsum.

@@ -2900,11 +2885,11 @@ 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

Lorem ipsum.

@@ -2915,11 +2900,11 @@ 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

Lorem ipsum.

@@ -2930,11 +2915,11 @@ 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

Lorem ipsum.

@@ -2946,7 +2931,7 @@ a+b a-b 
   [F] x
 -----------
    [F] F
-

Definition

+

Definition

dup i

Discussion

The x combinator …

@@ -2955,11 +2940,11 @@ 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

Lorem ipsum.

@@ -2970,11 +2955,11 @@ 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

Lorem ipsum.

diff --git a/docs/reference/mkref/Functor-Reference.md b/docs/reference/mkref/Functor-Reference.md index a8d9fb1..f1d79ba 100644 --- a/docs/reference/mkref/Functor-Reference.md +++ b/docs/reference/mkref/Functor-Reference.md @@ -563,7 +563,7 @@ See the [Recursion Combinators notebook](https://joypy.osdn.io/notebooks/Recursi ## b -(Combinator) +Combinator Run two quoted programs @@ -573,19 +573,11 @@ Run two quoted programs ### Definition - [i] dip i - -### Derivation - - [P] [Q] b - [P] [Q] [i] dip i - [P] i [Q] i - P [Q] i - P Q +> \[[i]\] [dip] [i] ### Discussion -This combinator comes in handy. +This combinator may seem trivial but it comes in handy. ### Crosslinks @@ -597,18 +589,18 @@ This combinator comes in handy. ## binary -(Combinator) +Combinator Run a quoted program using exactly two stack values and leave the first item of the result on the stack. ... y x [P] binary ----------------------- - ... A + ... a ### Definition - unary popd +> [unary] [popd] ### Discussion @@ -626,75 +618,54 @@ consuming exactly two items from the stack. ## bool -Basis Function Combinator +Basis Function -bool(x) -\> bool - -Returns True when the argument x is true, False otherwise. The builtins -True and False are the only two instances of the class bool. The class -bool is a subclass of the class int, and cannot be subclassed. - -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +Convert the item on the top of the stack to a Boolean value. ### Discussion -Lorem ipsum. +For integers 0 is `false` and any other number is `true`; for lists the +empty list is `false` and all other lists are `true`. ### Crosslinks -Lorem ipsum. +[not] + ------------------------------------------------------------------------ ## branch -Basis Function Combinator +Basis Combinator -Use a Boolean value to select one of two quoted programs to run. +Use a Boolean value to select and run one of two quoted programs. - branch == roll< choice i - False [F] [T] branch + false [F] [T] branch -------------------------- - F + F - True [F] [T] branch + true [F] [T] branch ------------------------- - T + T -Gentzen diagram. ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> [rolldown] [choice] [i] ### Discussion -Lorem ipsum. +This is one of the fundamental operations (although it can be defined in +terms of [choice] as above). The more common "if..then..else" construct +[ifte] adds a predicate function that is evaluated [nullary]. ### Crosslinks -Lorem ipsum. +[choice] +[ifte] +[select] + ------------------------------------------------------------------------