diff --git a/docs/reference/LESS-THAN-SIGN•LEFT-CURLY-BRACKET•RIGHT-CURLY-BRACKET.md b/docs/reference/LESS-THAN-SIGN•LEFT-CURLY-BRACKET•RIGHT-CURLY-BRACKET.md index 28d1ef9..57fe699 100644 --- a/docs/reference/LESS-THAN-SIGN•LEFT-CURLY-BRACKET•RIGHT-CURLY-BRACKET.md +++ b/docs/reference/LESS-THAN-SIGN•LEFT-CURLY-BRACKET•RIGHT-CURLY-BRACKET.md @@ -1,23 +1,24 @@ ------------------------------------------------------------------------ -## \<{} +## \<\{\} Function - ... a \<{} + ... a <{} ---------------- ... [] a ### Definition - \[\] swap + [] swap ### Discussion -Lorem ipsum. +Tuck an empty list just under the first item on the stack. ### Crosslinks -Lorem ipsum. +[<<{}](#section-18) + diff --git a/docs/reference/LESS-THAN-SIGN•LESS-THAN-SIGN•LEFT-CURLY-BRACKET•RIGHT-CURLY-BRACKET.md b/docs/reference/LESS-THAN-SIGN•LESS-THAN-SIGN•LEFT-CURLY-BRACKET•RIGHT-CURLY-BRACKET.md index 6d887fc..78cfb09 100644 --- a/docs/reference/LESS-THAN-SIGN•LESS-THAN-SIGN•LEFT-CURLY-BRACKET•RIGHT-CURLY-BRACKET.md +++ b/docs/reference/LESS-THAN-SIGN•LESS-THAN-SIGN•LEFT-CURLY-BRACKET•RIGHT-CURLY-BRACKET.md @@ -1,29 +1,25 @@ ------------------------------------------------------------------------ -## \<\<{} +## \<\<\{\} -Basis Function Combinator +Function -\[\] rollup -Gentzen diagram. + ... b a <{} + ----------------- + ... [] b a + ### Definition -if not basis. + [] rollup -### Derivation - -if not basis. - -### Source - -if basis ### Discussion -Lorem ipsum. +Tuck an empty list just under the first two items on the stack. ### Crosslinks -Lorem ipsum. +[<{}](#section-16) + diff --git a/docs/reference/QUESTION-MARK.md b/docs/reference/QUESTION-MARK.md index d132f07..949ea90 100644 --- a/docs/reference/QUESTION-MARK.md +++ b/docs/reference/QUESTION-MARK.md @@ -2,28 +2,20 @@ ## ? -Basis Function Combinator +Function -dup bool - -Gentzen diagram. +Is the item on the top of the stack "truthy"? ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> [dup](#dup) [bool](#bool) ### Discussion -Lorem ipsum. +You often want to test the truth value of an item on the stack without +consuming the item. ### Crosslinks -Lorem ipsum. +[bool](#bool) + diff --git a/docs/reference/VERTICAL-LINE•VERTICAL-LINE.md b/docs/reference/VERTICAL-LINE•VERTICAL-LINE.md index 5adb253..5408aa9 100644 --- a/docs/reference/VERTICAL-LINE•VERTICAL-LINE.md +++ b/docs/reference/VERTICAL-LINE•VERTICAL-LINE.md @@ -2,28 +2,31 @@ ## \|\| -Basis Function Combinator +Combinator -nulco \[nullary\] dip \[true\] branch +Short-circuiting Boolean OR -Gentzen diagram. ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> [nulco](#nulco) \[[nullary](#nullary)\] [dip](#dip) \[true\] [branch](#branch) ### Discussion -Lorem ipsum. +Accept two quoted programs, run the first and expect a Boolean value, if +it’s `false` pop it and run the second program (which should also return a +Boolean value) otherwise pop the second program (leaving `true` on the +stack.) + + [A] [B] || + ---------------- A -> false + B + + + [A] [B] || + ---------------- A -> true + true ### Crosslinks -Lorem ipsum. +[&&](#section-1) diff --git a/docs/reference/abs.md b/docs/reference/abs.md index 48ae162..9308ff5 100644 --- a/docs/reference/abs.md +++ b/docs/reference/abs.md @@ -2,28 +2,11 @@ ## abs -Basis Function Combinator +Function Return the absolute value of the argument. -Gentzen diagram. - ### Definition -if not basis. +> \[0 <\] \[0 [swap](#swap) -\] \[\] [ifte](#ifte) -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. - -### Crosslinks - -Lorem ipsum. diff --git a/docs/reference/add.md b/docs/reference/add.md index beeb282..dfd769b 100644 --- a/docs/reference/add.md +++ b/docs/reference/add.md @@ -2,28 +2,7 @@ ## add -Basis Function Combinator +Basis Function -Same as a + b. +Add two numbers together: a + b. -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. - -### Crosslinks - -Lorem ipsum. diff --git a/docs/reference/anamorphism.md b/docs/reference/anamorphism.md index d873b3c..159120c 100644 --- a/docs/reference/anamorphism.md +++ b/docs/reference/anamorphism.md @@ -2,28 +2,26 @@ ## anamorphism -Basis Function Combinator +Combinator -\[pop \[\]\] swap \[dip swons\] genrec +Build a list of values from a generator program `G` and a stopping +predicate `P`. -Gentzen diagram. + [P] [G] anamorphism + ----------------------------------------- + [P] [pop []] [G] [dip swons] genrec ### Definition -if not basis. +> \[[pop](#pop) \[\]\] [swap](#swap) \[[dip](#dip) [swons](#swons)\] [genrec](#genrec) -### Derivation +### Example -if not basis. +The `range` function generates a list of the integers from 0 to n - 1: -### Source - -if basis +> \[0 <=\] \[\-\- dup\] anamorphism ### Discussion -Lorem ipsum. +See the [Recursion Combinators notebook](https://joypy.osdn.io/notebooks/Recursion_Combinators.html). -### Crosslinks - -Lorem ipsum. diff --git a/docs/reference/and.md b/docs/reference/and.md index 551bd71..56c4522 100644 --- a/docs/reference/and.md +++ b/docs/reference/and.md @@ -2,27 +2,10 @@ ## and -Basis Function Combinator +Basis Function -Same as a & b. +Logical bit-wise AND. -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. ### Crosslinks diff --git a/docs/reference/mkref/FuncRef.html b/docs/reference/mkref/FuncRef.html index f4df306..41c37ec 100644 --- a/docs/reference/mkref/FuncRef.html +++ b/docs/reference/mkref/FuncRef.html @@ -171,9 +171,9 @@
See ne.
Function
- ... a \<{}
+ ... a <{}
----------------
... [] a
Definition
-\[\] swap
+[] swap
Discussion
-Lorem ipsum.
+Tuck an empty list just under the first item on the stack.
Crosslinks
-Lorem ipsum.
+
<<
See lshift.
-<<
-Basis Function Combinator
-[] rollup
-Gentzen diagram.
+<<{}
+Function
+ ... b a <{}
+-----------------
+ ... [] b a
Definition
-if not basis.
-Derivation
-if not basis.
-Source
-if basis
+[] rollup
Discussion
-Lorem ipsum.
+Tuck an empty list just under the first two items on the stack.
Crosslinks
-Lorem ipsum.
+
%
See mod.
@@ -469,19 +466,16 @@
See succ.
?
-Basis Function Combinator
-dup bool
-Gentzen diagram.
+Function
+Is the item on the top of the stack “truthy”?
Definition
-if not basis.
-Derivation
-if not basis.
-Source
-if basis
+
+
+
Discussion
-Lorem ipsum.
+You often want to test the truth value of an item on the stack without consuming the item.
Crosslinks
-Lorem ipsum.
+
/
See floordiv.
@@ -493,78 +487,59 @@
See floordiv.
||
-Basis Function Combinator
-nulco [nullary] dip [true] branch
-Gentzen diagram.
+Combinator
+Short-circuiting Boolean OR
Definition
-if not basis.
-Derivation
-if not basis.
-Source
-if basis
+
+
+
Discussion
-Lorem ipsum.
+Accept two quoted programs, run the first and expect a Boolean value, if it’s false pop it and run the second program (which should also return a Boolean value) otherwise pop the second program (leaving true on the stack.)
+ [A] [B] ||
+---------------- A -> false
+ B
+
+
+ [A] [B] ||
+---------------- A -> true
+ true
Crosslinks
-Lorem ipsum.
+
abs
-Basis Function Combinator
+Function
Return the absolute value of the argument.
-Gentzen diagram.
Definition
-if not basis.
-Derivation
-if not basis.
-Source
-if basis
-Discussion
-Lorem ipsum.
-Crosslinks
-Lorem ipsum.
+
+
+
add
-Basis Function Combinator
-Same as a + b.
-Gentzen diagram.
-Definition
-if not basis.
-Derivation
-if not basis.
-Source
-if basis
-Discussion
-Lorem ipsum.
-Crosslinks
-Lorem ipsum.
+Basis Function
+Add two numbers together: a + b.
anamorphism
-Basis Function Combinator
-[pop []] swap [dip swons] genrec
-Gentzen diagram.
-Definition
-if not basis.
-Derivation
-if not basis.
-Source
-if basis
-Discussion
-Lorem ipsum.
-Crosslinks
-Lorem ipsum.
+Combinator
+Build a list of values from a generator program G and a stopping predicate P.
+ [P] [G] anamorphism
+-----------------------------------------
+ [P] [pop []] [G] [dip swons] genrec
+Definition
+
+
+
+Example
+The range function generates a list of the integers from 0 to n - 1:
+
+[0 <=] [-- dup] anamorphism
+
+Discussion
+See the Recursion Combinators notebook.
and
-Basis Function Combinator
-Same as a & b.
-Gentzen diagram.
-Definition
-if not basis.
-Derivation
-if not basis.
-Source
-if basis
-Discussion
-Lorem ipsum.
-Crosslinks
+Basis Function
+Logical bit-wise AND.
+Crosslinks
Lorem ipsum.
app1
@@ -574,9 +549,9 @@
... x [Q] app1
---------------------------------
... [x ...] [Q] infra first
-Definition
+Definition
nullary popd
-Discussion
+Discussion
Just a specialization of nullary really. Its parallelizable cousins are more useful.
app2
@@ -587,15 +562,15 @@
Gentzen diagram.
-Definition
+Definition
if not basis.
-Derivation
+Derivation
if not basis.
-Source
+Source
if basis
-Discussion
+Discussion
Lorem ipsum.
-Crosslinks
+Crosslinks
Lorem ipsum.
app3
@@ -606,30 +581,30 @@
Gentzen diagram.
-Definition
+Definition
if not basis.
-Derivation
+Derivation
if not basis.
-Source
+Source
if basis
-Discussion
+Discussion
Lorem ipsum.
-Crosslinks
+Crosslinks
Lorem ipsum.
appN
Basis Function Combinator
[grabN] codi map disenstacken
Gentzen diagram.
-Definition
+Definition
if not basis.
-Derivation
+Derivation
if not basis.
-Source
+Source
if basis
-Discussion
+Discussion
Lorem ipsum.
-Crosslinks
+Crosslinks
Lorem ipsum.
at
@@ -639,15 +614,15 @@
Basis Function Combinator
[sum] [size] cleave /
Gentzen diagram.
-Definition
+Definition
if not basis.
-Derivation
+Derivation
if not basis.
-Source
+Source
if basis
-Discussion
+Discussion
Lorem ipsum.
-Crosslinks
+Crosslinks
Lorem ipsum.
b
@@ -656,17 +631,17 @@
[P] [Q] b
---------------
P Q
-Definition
+Definition
[i] dip i
-Derivation
+Derivation
[P] [Q] b
[P] [Q] [i] dip i
[P] i [Q] i
P [Q] i
P Q
-Discussion
+Discussion
This combinator comes in handy.
-Crosslinks
+Crosslinks
binary
@@ -675,11 +650,11 @@
... y x [P] binary
-----------------------
... A
-Definition
+Definition
unary popd
-Discussion
+Discussion
Runs any other quoted function and returns its first result while consuming exactly two items from the stack.
-Crosslinks
+Crosslinks
bool
@@ -687,15 +662,15 @@
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
+Definition
if not basis.
-Derivation
+Derivation
if not basis.
-Source
+Source
if basis
-Discussion
+Discussion
Lorem ipsum.
-Crosslinks
+Crosslinks
Lorem ipsum.
branch
@@ -711,30 +686,30 @@ True [F] [T] branch
-------------------------
T
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
ccons ccons
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
B A [...] ccons
---------------------
[B A ...]
-cons cons
-Does cons twice.
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.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
fork popdd
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
cleave popdd
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
cons dip
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
codi reco
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
A [...] cons
------------------
[A ...]
-func(cons, [list(A), B|S], [list([B|A])|S]).
-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.
Basis Function Combinator
dip infrst
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
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.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
divmod(x, y) -> (quotient, remainder)
Return the tuple (x//y, x%y). Invariant: q * y + r == x.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[0 >] [dup --] while
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a1 -- a1 a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a2 a1 -- a2 a2 a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a3 a2 a1 -- a3 a3 a2 a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
dup dipd
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
stack [clear] dip
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a == b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
([a1 ...1] -- a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
([a1 a2 ...1] -- a1 a2)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
<{} [concat] step
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Return the floor of x as an Integral.
This is the largest integer <= x.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a // b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[i] app2
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
([a1 a2 a3 a4 ...1] -- a4)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
true [tuck mod dup 0 >] loop pop
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Compiled GCD function.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a >= b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
<{} [cons] times
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[stack popd] dip
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a > b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Accepts a quoted symbol on the top of the stack and prints its docs.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[sqr] ii + sqrt
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
[Q] i
-----------
Q
-combo(i, [list(P)|S], S, Ei, Eo) :- append(P, Ei, Eo).
-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.)
Basis Function Combinator
The identity function.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Has the effect of grabbing a copy of the stack on which to run the if-part using infra.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
... [a b c] [Q] infra
---------------------------
c b a Q [...] swaack
-swons swaack [i] dip swaack
-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.
Basis Function Combinator
infra first
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
[sqr dup mul] inscribe
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a <= b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a << b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a < b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[codireco] ccons
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
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.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Given a list find the maximum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Given a list find the minimum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a % b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a * b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a != b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as -a.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as not a.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
0 >=
Basis Function Combinator
[nullary] cons
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
... [P] nullary
---------------------
... A
-[stack] dip infra first
-... [P] nullary
... [P] [stack] dip infra first
... stack [P] infra first
... [...] [P] infra first
... [A ...] first
... A
-A very useful function that runs any other quoted function and returns it’s first result without disturbing the stack (under the quoted program.)
-Basis Function Combinator
swap at
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a | b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a2 a1 -- a2 a1 a2)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[i] map
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a1 --)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a2 a1 -- a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a3 a2 a1 -- a2 a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a2 a1 --)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a3 a2 a1 -- a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a4 a3 a2 a1 -- a2 a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
pop popop
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a ** b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Decrement TOS.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
1 swap [*] step
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[unit] dip
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[0 <=] [1 - dup] anamorphism
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
unit [down_to_zero] infra
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
rest cons
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
([a1 ...0] -- [...0])
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Reverse the list on the top of the stack. :
reverse == [] swap shunt
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a1 a2 a3 -- a2 a3 a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a1 a2 a3 -- a3 a1 a2)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
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.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
([a1 a2 ...1] -- [...1])
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a >> b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
<{} infra
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
([a1 a2 ...1] -- a2)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
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.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Print redistribution information.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
uncons [swons] dip
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[pop ++] step_zero
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Given a list return it sorted.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[drop] [take] clop
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[take reverse] [drop] clop
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
dup *
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Return the square root of the number a. Negative numbers return complex roots.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(... -- ... [...])
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[stack] dip
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
The step combinator executes the quotation on each member of the list on top of the stack.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
0 roll> step
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(... a1 -- ... a1 a1 [...])
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(... a2 a1 -- ... a2 a1 a1 a2 [...])
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Same as a - b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Increment TOS.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Given a quoted sequence of numbers return the sum. :
sum == 0 swap [+] step
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
([...1] -- [...0])
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a1 a2 -- a2 a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[swap] dip
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
swap concat
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
([...1] a1 -- [a1 ...1])
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[i] genrec
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
... z y x [P] unary
-------------------------
... A
-binary popd
-Runs any other quoted function and returns its first result while consuming exactly three items from the stack.
-Basis Function Combinator
([a1 a2 a3 ...1] -- a3)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a2 a1 -- a1 a2 a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
... x [P] unary
---------------------
... A
-nullary popd
-Runs any other quoted function and returns its first result while consuming exactly one item from the stack.
- [A ...] uncons
--------------------
A [...]
-func(uncons, Si, So) :- func(cons, So, Si).
-This is the inverse of cons.
Basis Function Combinator
Given a list remove duplicate items.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
(a1 -- [a1 ])
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
[i] dip
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
([a1 ...1] -- [...1] a1)
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
True if the form on TOS is void otherwise False.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Print warranty information.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
swap nulco dupdipd concat loop
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Print all the words in alphabetical order.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
[F] x
-----------
[F] F
-dup i
-The x combinator …
Basis Function Combinator
Same as a ^ b.
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
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.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.