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
+Basis Function Combinator
+nulco [nullary [false]] dip branch
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a * b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+The identity function.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a ^ b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a == b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a != b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+!-^^^^
+Basis Function Combinator
+0 >=
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a > b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a >= b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a >> b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+--^^^^
+Basis Function Combinator
+Decrement TOS.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a < b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a <= b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a != b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[] swap
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a << b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[] rollup
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a % b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a + b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Increment TOS.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+dup bool
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a // b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a // b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a // b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+nulco [nullary] dip [true] branch
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Return the absolute value of the argument.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a + b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[pop []] swap [dip swons] genrec
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a & b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+“apply one”
(Combinator)
@@ -181,28 +1969,100 @@ ... x [Q] app1
---------------------------------
... [x ...] [Q] infra firstnullary popdJust a specialization of nullary really. Its parallelizable cousins are more useful.
Basis Function Combinator
+… y x [Q] . app2 ———————————– … [y …] [Q] . infra first [x …] [Q] infra first
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+… z y x [Q] . app3 ———————————– … [z …] [Q] . infra first [y …] [Q] infra first [x …] [Q] infra first
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[grabN] codi map disenstacken
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+[sum] [size] cleave /
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+(Combinator)
Run two quoted programs
[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
+Basis Function Combinator
+Use a Boolean value to select one of two quoted programs to run.
+branch == roll< choice i
+
+False [F] [T] branch
+--------------------------
+ F
+
+True [F] [T] branch
+-------------------------
+ TGentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+ccons ccons
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+(Function)
Given two items and a list, append the items to the list to make a new list.
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
+----------------------
+A
+
+
+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
+Basis Function Combinator
+clear == stack [pop stack] loop
+ ... clear
+---------------Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+fork popdd
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+cleave popdd
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+------------------------- a > b
+ G
+
+a b [G] [E] [L] cmp
+------------------------- a = b
+ E
+
+a b [G] [E] [L] cmp
+------------------------- a < b
+ LGentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+cons dip
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+codi reco
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+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.:
+[[[B0] T0] [[B1] T1] [D]] cond
+-----------------------------------------
+[B0] [T0] [[B1] [T1] [D] ifte] ifteGentzen diagram.
+if not basis.
+if not basis.
+if basis
+(Basis Function)
Given an item and a list, append the item to the list to make a new list.
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
+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
+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
+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
+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
+Basis Function Combinator
+Same as a // b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+[0 >] [dup --] while
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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. :
+[a b c d] 2 drop
+----------------------
+ [c d]Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a1 -- a1 a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a2 a1 -- a2 a2 a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a3 a2 a1 -- a3 a3 a2 a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[F] dupdip == dup [F] dip
+
+... a [F] dupdip
+... a dup [F] dip
+... a a [F] dip
+... a F aGentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+dup dipd
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+stack [clear] dip
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a == b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+([a1 ...1] -- a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+([a1 a2 ...1] -- a1 a2)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+<{} [concat] step
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+Same as a // b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[i] app2
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+([a1 a2 a3 a4 ...1] -- a4)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+true [tuck mod dup 0 >] loop pop
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Compiled GCD function.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a >= b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+General Recursion Combinator. :
+[if] [then] [rec1] [rec2] genrec
+---------------------------------------------------------------------
+[if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifteFrom "Recursion Theory and Joy" (j05cmp.html) by Manfred von Thun: "The genrec combinator takes four program parameters in addition to whatever data parameters it needs. Fourth from the top is an if-part, followed by a then-part. If the if-part yields true, then the then-part is executed and the combinator terminates. The other two parameters are the rec1-part and the rec2-part. If the if-part yields false, the rec1-part is executed. Following that the four program parameters and the combinator are again pushed onto the stack bundled up in a quoted form. Then the rec2-part is executed, where it will find the bundled form. Typically it will then execute the bundled form, either with i or with app2, or some other combinator."
+The way to design one of these is to fix your base case [then] and the test [if], and then treat rec1 and rec2 as an else-part "sandwiching" a quotation of the whole function.
+For example, given a (general recursive) function 'F': :
+F == [I] [T] [R1] [R2] genrecIf the [I] if-part fails you must derive R1 and R2 from: :
+... R1 [F] R2Just set the stack arguments in front, and figure out what R1 and R2 have to do to apply the quoted [F] in the proper way. In effect, the genrec combinator turns into an ifte combinator with a quoted copy of the original definition in the else-part: :
+F == [I] [T] [R1] [R2] genrec
+ == [I] [T] [R1 [F] R2] iftePrimitive recursive functions are those where R2 == i. :
+P == [I] [T] [R] tailrec
+ == [I] [T] [R [P] i] ifte
+ == [I] [T] [R P] ifteGentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+<{} [cons] times
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[stack popd] dip
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a > b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+[sqr] ii + sqrt
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+(Basis Combinator)
Append a quoted expression onto the pending expression.
[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
+Basis Function Combinator
+If-Then-Else Combinator :
+... [if] [then] [else] ifte
+---------------------------------------------------
+... [[else] [then]] [...] [if] infra select i
+
+
+
+
+... [if] [then] [else] ifte
+-------------------------------------------------------
+... [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
+Basis Function Combinator
+... a [Q] ii
+------------------
+ ... Q a QGentzen diagram.
+if not basis.
+if not basis.
+if basis
+(Combinator)
Accept a quoted program and a list on the stack and run the program with the list as its stack. Does not affect the stack (below the list.)
... [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
+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
+Basis Function Combinator
+Same as a <= b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Basic loop combinator. :
+... True [Q] loop
+-----------------------
+ ... Q [Q] loop
+
+... False [Q] loop
+------------------------
+ ...Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a << b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a < b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[codireco] ccons
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+Given a list find the maximum.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Given a list find the minimum.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a % b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a % b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a * b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a != b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as -a.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as not a.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+“not negative”
(Function, Boolean Predicate)
Integer on top of stack is replaced by Boolean value indicating whether it is non-negative.
@@ -279,53 +3013,927 @@ N !- ---------- N >= 0 true -0 >=Basis Function Combinator
+[nullary] cons
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+(Combinator)
Run a quoted program without using any stack values and leave the first item of the result on the stack.
... [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
+Basis Function Combinator
+Same as a | b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a2 a1 -- a2 a1 a2)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[i] map
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+Plus or minus :
+a b pm
+-------------
+a+b a-bGentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a1 --)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a2 a1 -- a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a3 a2 a1 -- a2 a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a2 a1 --)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a3 a2 a1 -- a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a4 a3 a2 a1 -- a2 a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+pop popop
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a ** b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Decrement TOS.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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.:
+5 [1] [*] primrec> Then primrec tests whether the top element on the stack (initially the 5) is equal to zero. If it is, it pops it off and executes one of the quotations, the [1] which leaves 1 on the stack as the result. Otherwise it pushes a decremented copy of the top element and recurses. On the way back from the recursion it uses the other quotation, [*], to multiply what is now a factorial on top of the stack by the second element on the stack.:
+n [Base] [Recur] primrec
+
+ 0 [Base] [Recur] primrec
+------------------------------
+ Base
+
+ n [Base] [Recur] primrec
+------------------------------------------ n > 0
+ n (n-1) [Base] [Recur] primrec RecurGentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+1 swap [*] step
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[unit] dip
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[0 <=] [1 - dup] anamorphism
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+unit [down_to_zero] infra
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+rest cons
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a % b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a % b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+([a1 ...0] -- [...0])Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Reverse the list on the top of the stack. :
+reverse == [] swap shuntGentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a1 a2 a3 -- a2 a3 a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a1 a2 a3 -- a3 a1 a2)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a1 a2 a3 -- a3 a1 a2)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a1 a2 a3 -- a2 a3 a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+([a1 a2 ...1] -- [...1])Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a >> b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+<{} infra
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+([a1 a2 ...1] -- a2)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Use a Boolean value to select one of two items from a sequence. :
+[A B] false select
+------------------------
+ A
+
+
+[A B] true select
+-----------------------
+ 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
+Basis Function Combinator
+Print redistribution information.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+uncons [swons] dip
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Like concat but reverses the top list into the second. :
+shunt == [swons] step == reverse swap concat
+
+ [a b c] [d e f] shunt
+---------------------------
+ [f e d a b c] Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[pop ++] step_zero
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Given a list return it sorted.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[drop] [take] clop
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[take reverse] [drop] clop
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+dup *
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+(... -- ... [...])Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[stack] dip
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Run a quoted program on each item in a sequence. :
+... [] [Q] . step
+-----------------------
+ ... .
+
+
+... [a] [Q] . step
+------------------------
+ ... a . Q
+
+
+... [a b c] [Q] . step
+----------------------------------------
+ ... a . Q [b c] [Q] stepThe 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
+Basis Function Combinator
+0 roll> step
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(... a1 -- ... a1 a1 [...])Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(... a2 a1 -- ... a2 a1 a1 a2 [...])Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Same as a - b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Increment TOS.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+([...1] -- [...0])Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+(a1 a2 -- a2 a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[swap] dip
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+swap concat
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+([...1] a1 -- [a1 ...1])Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[i] genrec
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+(Combinator)
Run a quoted program using exactly three stack values and leave the first item of the result on the stack.
... 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
+Basis Function Combinator
+times == [-- dip] cons [swap] infra [0 >] swap while pop :
+... n [Q] . times
+--------------------- w/ n <= 0
+ ... .
+
+
+... 1 [Q] . times
+-----------------------
+ ... . Q
+
+
+... n [Q] . times
+------------------------------------- w/ n > 1
+ ... . Q (n - 1) [Q] timesGentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+Basis Function Combinator
+(a2 a1 -- a1 a2 a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+(Combinator)
Run a quoted program using exactly one stack value and leave the first item of the result on the stack.
... 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
+Basis Function Combinator
+(a1 -- [a1 ])Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+[i] dip
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+([a1 ...1] -- [...1] a1)Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+True if the form on TOS is void otherwise False.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Print warranty information.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+swap nulco dupdipd concat loop
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+Basis Function Combinator
+Print all the words in alphabetical order.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+(Combinator)
[F] x
-----------
[F] Fdup iThe x combinator …
Basis Function Combinator
+Same as a ^ b.
+Gentzen diagram.
+if not basis.
+if not basis.
+if basis
+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
+