Version -10.0.0
Each function, combinator, or definition should be documented here.
Basis Function Combinator
-Same as a & b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See and.
Basis Function Combinator
nulco [nullary [false]] dip branch
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.
+See mul.
Basis Function Combinator
-The identity function.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See id.
Basis Function Combinator
-Same as a ^ b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See xor.
Basis Function Combinator
-Same as a == b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See eq.
Basis Function Combinator
-Same as a != b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See ne.
!-^^^^
+Basis Function Combinator
0 >=
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.
+See gt.
Basis Function Combinator
-Same as a >= b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See ge.
Basis Function Combinator
-Same as a >> b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
-Version -10.0.0
-Each function, combinator, or definition should be documented here.
+See rshift.
-^^^
-Basis Function Combinator
-Same as a - b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See sub.
--^^^^
-Basis Function Combinator
-Decrement TOS.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See pred.
Basis Function Combinator
-Same as a < b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See lt.
Basis Function Combinator
-Same as a <= b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See le.
Basis Function Combinator
-Same as a != b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See ne.
Basis Function Combinator
[] swap
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.
+See lshift.
Basis Function Combinator
[] rollup
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.
+See mod.
Basis Function Combinator
-Same as a + b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See add.
Basis Function Combinator
-Increment TOS.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See succ.
Basis Function Combinator
dup bool
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.
+See floordiv.
Basis Function Combinator
-Same as a // b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See floordiv.
Basis Function Combinator
-Same as a // b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See floordiv.
Basis Function Combinator
nulco [nullary] dip [true] branch
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Return the absolute value of the argument.
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
[pop []] swap [dip swons] genrec
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.
... x [Q] app1
---------------------------------
... [x ...] [Q] infra firstnullary popdJust a specialization of nullary really. Its parallelizable cousins are more useful.
Basis Function Combinator
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
[grabN] codi map disenstacken
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
-getitem == drop firstExpects an integer and a quote on the stack and returns the item at the nth position in the quote counting from 0. :
-[a b c d] 0 getitem
--------------------------
- aGentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See getitem.
Basis Function Combinator
[sum] [size] cleave /
Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
[P] [Q] b
---------------
P Q[i] dip i[P] [Q] b
[P] [Q] [i] dip i
[P] i [Q] i
P [Q] i
P QThis combinator comes in handy.
- ... y x [P] binary
-----------------------
... Aunary popdRuns any other quoted function and returns its first result while consuming exactly two items from the stack.
-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.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Use a Boolean value to select one of two quoted programs to run.
branch == roll< choice i
@@ -2208,30 +708,30 @@ True [F] [T] branch
-------------------------
TGentzen 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 consDoes cons twice.
Basis Function Combinator
Use a Boolean value to select one of two items. :
A B false choice
@@ -2260,18 +760,18 @@ A B true choice
BCurrently 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
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.
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
@@ -2337,66 +837,66 @@ a b [G] [E] [L] cmp
------------------------- a < b
LGentzen 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.
Basis Function Combinator
Concatinate the two lists on the top of the stack. :
[a b c] [d e f] concat
----------------------------
[a b c d e f]Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
This combinator works like a case statement. It expects a single quote on the stack that must contain zero or more condition quotes and a default quote. Each condition clause should contain a quoted predicate followed by the function expression to run if that predicate returns true. If no predicates return true the default function runs.
It works by rewriting into a chain of nested ifte expressions, e.g.:
@@ -2404,15 +904,15 @@ a b [G] [E] [L] cmp ----------------------------------------- [B0] [T0] [[B1] [T1] [D] ifte] ifteGentzen 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.
Basis Function Combinator
The dip combinator expects a quoted program on the stack and below it some item, it hoists the item into the expression and runs the program on the rest of the stack. :
... x [Q] dip
-------------------
... Q xGentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Like dip but expects two items. :
... y x [Q] dip
---------------------
... Q y xGentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
Like dip but expects three items. :
... z y x [Q] dip
-----------------------
... Q z y xGentzen 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.
Basis Function Combinator
-Same as a // b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See floordiv.
Basis Function Combinator
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.
Basis Function Combinator
drop == [rest] timesExpects an integer and a quote on the stack and returns the quote with n items removed off the top. :
@@ -2566,63 +1054,63 @@ a b [G] [E] [L] cmp ---------------------- [c d]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.
Basis Function Combinator
[F] dupdip == dup [F] dip
@@ -2631,214 +1119,214 @@ a b [G] [E] [L] cmp
... a a [F] dip
... a F aGentzen 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.
Basis Function Combinator
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.
Basis Function Combinator
General Recursion Combinator. :
[if] [then] [rec1] [rec2] genrec
@@ -2858,18 +1346,18 @@ a b [G] [E] [L] cmp
== [I] [T] [R [P] i] ifte
== [I] [T] [R P] ifteGentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
Basis Function Combinator
getitem == drop firstExpects an integer and a quote on the stack and returns the item at the nth position in the quote counting from 0. :
@@ -2877,90 +1365,90 @@ a b [G] [E] [L] cmp ------------------------- aGentzen 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
-----------
Qcombo(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.
Basis Function Combinator
If-Then-Else Combinator :
... [if] [then] [else] ifte
@@ -3004,32 +1492,32 @@ a b [G] [E] [L] cmp
... [else] [then] [...] [if] infra first choice iHas 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.
Basis Function Combinator
... a [Q] ii
------------------
... Q a QGentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
... [a b c] [Q] infra
---------------------------
c b a Q [...] swaackswons swaack [i] dip swaackThis 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.
Basis Function Combinator
Create a new Joy function definition in the Joy dictionary. A definition is given as a quote with a name followed by a Joy expression. for example:
[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.
Basis Function Combinator
Basic loop combinator. :
... True [Q] loop
@@ -3104,198 +1592,186 @@ a b [G] [E] [L] cmp
------------------------
...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.
+See mod.
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.
“not negative”
(Function, Boolean Predicate)
Integer on top of stack is replaced by Boolean value indicating whether it is non-negative.
@@ -3306,22 +1782,22 @@ a b [G] [E] [L] cmp N !- ---------- N >= 0 true -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
... AA 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.
Basis Function Combinator
-getitem == drop firstExpects an integer and a quote on the stack and returns the item at the nth position in the quote counting from 0. :
-[a b c d] 0 getitem
--------------------------
- aGentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See getitem.
Basis Function Combinator
Plus or minus :
a b pm
-------------
a+b a-bGentzen 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.
Basis Function Combinator
From the "Overview of the language JOY":
> The primrec combinator expects two quoted programs in addition to a data parameter. For an integer data parameter it works like this: If the data parameter is zero, then the first quotation has to produce the value to be returned. If the data parameter is positive then the second has to combine the data parameter with the result of applying the function to its predecessor.:
@@ -3592,308 +2052,260 @@ a+b a-b ------------------------------------------ n > 0 n (n-1) [Base] [Recur] primrec RecurGentzen 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.
Basis Function Combinator
-Same as a % b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See mod.
Basis Function Combinator
-Same as a % b.
-Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See mod.
Basis Function Combinator
Expects an item on the stack and a quote under it and removes that item from the the quote. The item is only removed once. If the list is empty or the item isn't in the list then the list is unchanged. :
[1 2 3 1] 1 remove
------------------------
[2 3 1]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.
Basis Function Combinator
Reverse the list on the top of the stack. :
reverse == [] swap shuntGentzen 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.
Basis Function Combinator
-(a1 a2 a3 -- a3 a1 a2)Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See rollup.
Basis Function Combinator
-(a1 a2 a3 -- a2 a3 a1)Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See rolldown.
Basis Function Combinator
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.
Basis Function Combinator
Use a Boolean value to select one of two items from a sequence. :
[A B] false select
@@ -3906,48 +2318,48 @@ a+b a-bThe 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.
Basis Function Combinator
Like concat but reverses the top list into the second. :
shunt == [swons] step == reverse swap concat
@@ -3956,153 +2368,153 @@ a+b a-bGentzen 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.
Basis Function Combinator
Run a quoted program on each item in a sequence. :
... [] [Q] . step
@@ -4120,214 +2532,214 @@ a+b a-bThe 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.
Basis Function Combinator
Given a quoted sequence of numbers return the sum. :
sum == 0 swap [+] stepGentzen 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.
Basis Function Combinator
Expects an integer and a quote on the stack and returns the quote with just the top n items in reverse order (because that's easier and you can use reverse if needed.) :
[a b c d] 2 take
----------------------
[b a]Gentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
... z y x [P] unary
-------------------------
... Abinary popdRuns 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.
Basis Function Combinator
times == [-- dip] cons [swap] infra [0 >] swap while pop :
... n [Q] . times
@@ -4375,46 +2787,33 @@ a+b a-bGentzen diagram.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
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.
-if not basis.
-if not basis.
-if basis
-Lorem ipsum.
-Lorem ipsum.
+See bool.
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
---------------------
... Anullary popdRuns 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] Fdup iThe 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.