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# Functor Reference
Version -10.0.0
Each function, combinator, or definition should be documented here.
------------------------------------------------------------------------
# &
Basis Function Combinator
Same as a & b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# &&
Basis Function Combinator
nulco \[nullary \[false\]\] dip branch
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# \*
Basis Function Combinator
Same as a \* b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# •
Basis Function Combinator
The identity function.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# \^
Basis Function Combinator
Same as a \^ b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# =
Basis Function Combinator
Same as a == b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# !=
Basis Function Combinator
Same as a != b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
!-\^\^\^\^
Basis Function Combinator
0 \>=
Gentzen diagram.
# Definition
if not basis.
# Derivation
if not basis.
# Source
if basis
# Discussion
# Crosslinks
------------------------------------------------------------------------
# \>
Basis Function Combinator
Same as a \> b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# \>=
Basis Function Combinator
Same as a \>= b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# \>\>
Basis Function Combinator
Same as a \>\> b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
# Functor Reference
Version -10.0.0
Each function, combinator, or definition should be documented here.
------------------------------------------------------------------------
-\^\^\^
Basis Function Combinator
Same as a - b.
Gentzen diagram.
# Definition
if not basis.
# Derivation
if not basis.
# Source
if basis
# Discussion
# Crosslinks
------------------------------------------------------------------------
\--\^\^\^\^
Basis Function Combinator
Decrement TOS.
Gentzen diagram.
# Definition
if not basis.
# Derivation
if not basis.
# Source
if basis
# Discussion
# Crosslinks
------------------------------------------------------------------------
# \<
Basis Function Combinator
Same as a \< b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# \<=
Basis Function Combinator
Same as a \<= b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# \<\>
Basis Function Combinator
Same as a != b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# \<{}
Basis Function Combinator
\[\] swap
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# \<\<
Basis Function Combinator
Same as a \<\< b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# \<\<{}
Basis Function Combinator
\[\] rollup
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# %
Basis Function Combinator
Same as a % b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# +
Basis Function Combinator
Same as a + b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# ++
Basis Function Combinator
Increment TOS.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# ?
Basis Function Combinator
dup bool
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# /
Basis Function Combinator
Same as a // b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# //
Basis Function Combinator
Same as a // b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# /floor
Basis Function Combinator
Same as a // b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# \|\|
Basis Function Combinator
nulco \[nullary\] dip \[true\] branch
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# abs
Basis Function Combinator
Return the absolute value of the argument.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# add
Basis Function Combinator
Same as a + b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# anamorphism
Basis Function Combinator
\[pop \[\]\] swap \[dip swons\] genrec
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# and
Basis Function Combinator
Same as a & b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## app1
"apply one"
(Combinator)
Given a quoted program on TOS and anything as the second stack item run
the program without disturbing the stack and replace the two args with
the first result of the program.
... x [Q] app1
---------------------------------
... [x ...] [Q] infra first
### Definition
nullary popd
### Discussion
Just a specialization of `nullary` really. Its parallelizable cousins
are more useful.
------------------------------------------------------------------------
# app2
Basis Function Combinator
Like app1 with two items.
: ... y x [Q] . app2
-----------------------------------
... [y ...] [Q] . infra first
[x ...] [Q] infra first
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# app3
Basis Function Combinator
Like app1 with three items.
: ... z y x [Q] . app3
-----------------------------------
... [z ...] [Q] . infra first
[y ...] [Q] infra first
[x ...] [Q] infra first
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# appN
Basis Function Combinator
\[grabN\] codi map disenstacken
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# at
Basis Function Combinator
getitem == drop first
Expects 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
-------------------------
a
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# average
Basis Function Combinator
\[sum\] \[size\] cleave /
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## b
(Combinator)
Run two quoted programs
[P] [Q] b
---------------
P Q
### Definition
[i] dip i
### Derivation
[P] [Q] b
[P] [Q] [i] dip i
[P] i [Q] i
P [Q] i
P Q
### Discussion
This combinator comes in handy.
### Crosslinks
[dupdip](#dupdip)
[ii](#ii)
--------------------
## binary
(Combinator)
Run a quoted program using exactly two stack values and leave the first
item of the result on the stack.
... y x [P] binary
-----------------------
... A
### Definition
unary popd
### Discussion
Runs any other quoted function and returns its first result while
consuming exactly two items from the stack.
### Crosslinks
[nullary](#nullary)
[ternary](#ternary)
[unary](#unary)
------------------------------------------------------------------------
# bool
Basis Function Combinator
bool(x) -\> bool
Returns True when the argument x is true, False otherwise. The builtins
True and False are the only two instances of the class bool. The class
bool is a subclass of the class int, and cannot be subclassed.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# branch
Basis Function Combinator
Use a Boolean value to select one of two quoted programs to run.
branch == roll< choice i
False [F] [T] branch
--------------------------
F
True [F] [T] branch
-------------------------
T
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# ccccons
Basis Function Combinator
ccons ccons
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## ccons
(Function)
Given two items and a list, append the items to the list to make a new list.
B A [...] ccons
---------------------
[B A ...]
### Definition
cons cons
### Discussion
Does `cons` twice.
### Crosslinks
[cons](#cons)
------------------------------------------------------------------------
# choice
Basis Function Combinator
Use a Boolean value to select one of two items. :
A B false choice
----------------------
A
A B true choice
---------------------
B
Currently Python semantics are used to evaluate the \"truthiness\" of
the Boolean value (so empty string, zero, etc. are counted as false,
etc.)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# clear
Basis Function Combinator
Clear everything from the stack.
: clear == stack [pop stack] loop
... clear
---------------
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# cleave
Basis Function Combinator
fork popdd
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# clop
Basis Function Combinator
cleave popdd
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# cmp
Basis Function Combinator
cmp takes two values and three quoted programs on the stack and runs one
of the three depending on the results of comparing the two values: :
a b [G] [E] [L] cmp
------------------------- a > b
G
a b [G] [E] [L] cmp
------------------------- a = b
E
a b [G] [E] [L] cmp
------------------------- a < b
L
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# codi
Basis Function Combinator
cons dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# codireco
Basis Function Combinator
codi reco
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# concat
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.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# cond
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]{.title-ref}
expressions, e.g.:
[[[B0] T0] [[B1] T1] [D]] cond
-----------------------------------------
[B0] [T0] [[B1] [T1] [D] ifte] ifte
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## cons
(Basis Function)
Given an item and a list, append the item to the list to make a new list.
A [...] cons
------------------
[A ...]
### Source
func(cons, [list(A), B|S], [list([B|A])|S]).
### Discussion
Cons is a venerable old function from Lisp. It doesn't inspect the item
but it will not cons onto a non-list. It's inverse operation is called
`uncons`.
### Crosslinks
[ccons](#ccons)
[uncons](#uncons)
------------------------------------------------------------------------
# dinfrirst
Basis Function Combinator
dip infrst
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# dip
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 x
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# dipd
Basis Function Combinator
Like dip but expects two items. :
... y x [Q] dip
---------------------
... Q y x
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# dipdd
Basis Function Combinator
Like dip but expects three items. :
... z y x [Q] dip
-----------------------
... Q z y x
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# disenstacken
Basis Function Combinator
The disenstacken operator expects a list on top of the stack and makes
that the stack discarding the rest of the stack.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# div
Basis Function Combinator
Same as a // b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# divmod
Basis Function Combinator
divmod(x, y) -\> (quotient, remainder)
Return the tuple (x//y, x%y). Invariant: q \* y + r == x.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# down_to_zero
Basis Function Combinator
\[0 \>\] \[dup \--\] while
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# drop
Basis Function Combinator
drop == [rest] times
Expects 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.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# dup
Basis Function Combinator
(a1 -- a1 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# dupd
Basis Function Combinator
(a2 a1 -- a2 a2 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# dupdd
Basis Function Combinator
(a3 a2 a1 -- a3 a3 a2 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# dupdip
Basis Function Combinator
[F] dupdip == dup [F] dip
... a [F] dupdip
... a dup [F] dip
... a a [F] dip
... a F a
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# dupdipd
Basis Function Combinator
dup dipd
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# enstacken
Basis Function Combinator
stack \[clear\] dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# eq
Basis Function Combinator
Same as a == b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# first
Basis Function Combinator
([a1 ...1] -- a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# first_two
Basis Function Combinator
([a1 a2 ...1] -- a1 a2)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# flatten
Basis Function Combinator
\<{} \[concat\] step
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# floor
Basis Function Combinator
Return the floor of x as an Integral.
This is the largest integer \<= x.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# floordiv
Basis Function Combinator
Same as a // b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# fork
Basis Function Combinator
\[i\] app2
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# fourth
Basis Function Combinator
([a1 a2 a3 a4 ...1] -- a4)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# gcd
Basis Function Combinator
true \[tuck mod dup 0 \>\] loop pop
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# gcd2
Basis Function Combinator
Compiled GCD function.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# ge
Basis Function Combinator
Same as a \>= b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# genrec
Basis Function Combinator
General Recursion Combinator. :
[if] [then] [rec1] [rec2] genrec
---------------------------------------------------------------------
[if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte
From \"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] genrec
If the \[I\] if-part fails you must derive R1 and R2 from: :
... R1 [F] R2
Just 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] ifte
Primitive recursive functions are those where R2 == i. :
P == [I] [T] [R] tailrec
== [I] [T] [R [P] i] ifte
== [I] [T] [R P] ifte
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# getitem
Basis Function Combinator
getitem == drop first
Expects 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
-------------------------
a
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# grabN
Basis Function Combinator
\<{} \[cons\] times
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# grba
Basis Function Combinator
\[stack popd\] dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# gt
Basis Function Combinator
Same as a \> b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# help
Basis Function Combinator
Accepts a quoted symbol on the top of the stack and prints its docs.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# hypot
Basis Function Combinator
\[sqr\] ii + sqrt
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## i
(Basis Combinator)
Append a quoted expression onto the pending expression.
[Q] i
-----------
Q
### Source
combo(i, [list(P)|S], S, Ei, Eo) :- append(P, Ei, Eo).
### Discussion
This is probably the fundamental combinator. You wind up using it in all
kinds of places (for example, the `x` combinator can be defined as `dup i`.)
------------------------------------------------------------------------
# id
Basis Function Combinator
The identity function.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# ifte
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 i
Has the effect of grabbing a copy of the stack on which to run the
if-part using infra.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# ii
Basis Function Combinator
... a [Q] ii
------------------
... Q a Q
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## infra
(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 [...] swaack
### Definition
swons swaack [i] dip swaack
### Discussion
This is one of the more useful combinators. It allows a quoted
expression to serve as a stack for a program, effectively running it in a
kind of "pocket universe". If the list represents a datastructure then
`infra` lets you work on its internal structure.
### Crosslinks
[swaack](#swaack)
------------------------------------------------------------------------
# infrst
Basis Function Combinator
infra first
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# inscribe
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.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# le
Basis Function Combinator
Same as a \<= b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# loop
Basis Function Combinator
Basic loop combinator. :
... True [Q] loop
-----------------------
... Q [Q] loop
... False [Q] loop
------------------------
...
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# lshift
Basis Function Combinator
Same as a \<\< b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# lt
Basis Function Combinator
Same as a \< b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# make_generator
Basis Function Combinator
\[codireco\] ccons
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# map
Basis Function Combinator
Run the quoted program on TOS on the items in the list under it, push a
new list with the results in place of the program and original list.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# max
Basis Function Combinator
Given a list find the maximum.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# min
Basis Function Combinator
Given a list find the minimum.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# mod
Basis Function Combinator
Same as a % b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# modulus
Basis Function Combinator
Same as a % b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# mul
Basis Function Combinator
Same as a \* b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# ne
Basis Function Combinator
Same as a != b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# neg
Basis Function Combinator
Same as -a.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# not
Basis Function Combinator
Same as not a.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## !-
"not negative"
(Function, Boolean Predicate)
Integer on top of stack is replaced by Boolean value indicating whether
it is non-negative.
N !-
----------- N < 0
false
N !-
---------- N >= 0
true
### Definition
0 >=
------------------------------------------------------------------------
# nulco
Basis Function Combinator
\[nullary\] cons
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## nullary
(Combinator)
Run a quoted program without using any stack values and leave the first item of the result on the stack.
... [P] nullary
---------------------
... A
### Definition
[stack] dip infra first
### Derivation
... [P] nullary
... [P] [stack] dip infra first
... stack [P] infra first
... [...] [P] infra first
... [A ...] first
... A
### Discussion
A very useful function that runs any other quoted function and returns
it's first result without disturbing the stack (under the quoted
program.)
### Crosslinks
[unary](#unary)
[binary](#binary)
[ternary](#ternary)
------------------------------------------------------------------------
# of
Basis Function Combinator
swap at
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# or
Basis Function Combinator
Same as a \| b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# over
Basis Function Combinator
(a2 a1 -- a2 a1 a2)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# pam
Basis Function Combinator
\[i\] map
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# pick
Basis Function Combinator
getitem == drop first
Expects 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
-------------------------
a
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# pm
Basis Function Combinator
Plus or minus :
a b pm
-------------
a+b a-b
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# pop
Basis Function Combinator
(a1 --)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# popd
Basis Function Combinator
(a2 a1 -- a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# popdd
Basis Function Combinator
(a3 a2 a1 -- a2 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# popop
Basis Function Combinator
(a2 a1 --)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# popopd
Basis Function Combinator
(a3 a2 a1 -- a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# popopdd
Basis Function Combinator
(a4 a3 a2 a1 -- a2 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# popopop
Basis Function Combinator
pop popop
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# pow
Basis Function Combinator
Same as a \*\* b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# pred
Basis Function Combinator
Decrement TOS.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# primrec
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 Recur
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# product
Basis Function Combinator
1 swap \[\*\] step
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# quoted
Basis Function Combinator
\[unit\] dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# range
Basis Function Combinator
\[0 \<=\] \[1 - dup\] anamorphism
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# range_to_zero
Basis Function Combinator
unit \[down_to_zero\] infra
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# reco
Basis Function Combinator
rest cons
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# rem
Basis Function Combinator
Same as a % b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# remainder
Basis Function Combinator
Same as a % b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# remove
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.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# rest
Basis Function Combinator
([a1 ...0] -- [...0])
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# reverse
Basis Function Combinator
Reverse the list on the top of the stack. :
reverse == [] swap shunt
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# rolldown
Basis Function Combinator
(a1 a2 a3 -- a2 a3 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# rollup
Basis Function Combinator
(a1 a2 a3 -- a3 a1 a2)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# roll>
Basis Function Combinator
(a1 a2 a3 -- a3 a1 a2)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# roll\<
Basis Function Combinator
(a1 a2 a3 -- a2 a3 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# round
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.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# rrest
Basis Function Combinator
([a1 a2 ...1] -- [...1])
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# rshift
Basis Function Combinator
Same as a \>\> b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# run
Basis Function Combinator
\<{} infra
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# second
Basis Function Combinator
([a1 a2 ...1] -- a2)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# select
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
-----------------------
B
The sequence can contain more than two items but not fewer. Currently
Python semantics are used to evaluate the \"truthiness\" of the Boolean
value (so empty string, zero, etc. are counted as false, etc.)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# sharing
Basis Function Combinator
Print redistribution information.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# shift
Basis Function Combinator
uncons \[swons\] dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# shunt
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.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# size
Basis Function Combinator
\[pop ++\] step_zero
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# sort
Basis Function Combinator
Given a list return it sorted.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# spiral_next
Basis Function Combinator
\[\[\[abs\] ii \<=\] \[\[\<\>\] \[pop !-\] \|\|\] &&\] \[\[!-\]
\[\[++\]\] \[\[\--\]\] ifte dip\] \[\[pop !-\] \[\--\] \[++\] ifte\]
ifte
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# split_at
Basis Function Combinator
\[drop\] \[take\] clop
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# split_list
Basis Function Combinator
\[take reverse\] \[drop\] clop
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# sqr
Basis Function Combinator
dup \*
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# sqrt
Basis Function Combinator
Return the square root of the number a. Negative numbers return complex
roots.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# stack
Basis Function Combinator
(... -- ... [...])
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# stackd
Basis Function Combinator
\[stack\] dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# step
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] step
The step combinator executes the quotation on each member of the list on
top of the stack.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# step_zero
Basis Function Combinator
0 roll> step
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# stuncons
Basis Function Combinator
(... a1 -- ... a1 a1 [...])
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# stununcons
Basis Function Combinator
(... a2 a1 -- ... a2 a1 a1 a2 [...])
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# sub
Basis Function Combinator
Same as a - b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# succ
Basis Function Combinator
Increment TOS.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# sum
Basis Function Combinator
Given a quoted sequence of numbers return the sum. :
sum == 0 swap [+] step
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# swaack
Basis Function Combinator
([...1] -- [...0])
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# swap
Basis Function Combinator
(a1 a2 -- a2 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# swapd
Basis Function Combinator
\[swap\] dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# swoncat
Basis Function Combinator
swap concat
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# swons
Basis Function Combinator
([...1] a1 -- [a1 ...1])
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# tailrec
Basis Function Combinator
\[i\] genrec
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# take
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.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## ternary
(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
-------------------------
... A
### Definition
binary popd
### Discussion
Runs any other quoted function and returns its first result while
consuming exactly three items from the stack.
### Crosslinks
[binary](#binary)
[nullary](#nullary)
[unary](#unary)
------------------------------------------------------------------------
# third
Basis Function Combinator
([a1 a2 a3 ...1] -- a3)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# times
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] times
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# truthy
Basis Function Combinator
bool(x) -\> bool
Returns True when the argument x is true, False otherwise. The builtins
True and False are the only two instances of the class bool. The class
bool is a subclass of the class int, and cannot be subclassed.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# tuck
Basis Function Combinator
(a2 a1 -- a1 a2 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## unary
(Combinator)
Run a quoted program using exactly one stack value and leave the first item of the result on the stack.
... x [P] unary
---------------------
... A
### Definition
nullary popd
### Discussion
Runs any other quoted function and returns its first result while
consuming exactly one item from the stack.
### Crosslinks
[binary](#binary)
[nullary](#nullary)
[ternary](#ternary)
--------------------
## uncons
(Basis Function)
Removes an item from a list and leaves it on the stack under the rest of
the list. You cannot `uncons` an item from an empty list.
[A ...] uncons
--------------------
A [...]
### Source
func(uncons, Si, So) :- func(cons, So, Si).
### Discussion
This is the inverse of `cons`.
### Crosslinks
[cons](#cons)
------------------------------------------------------------------------
# unique
Basis Function Combinator
Given a list remove duplicate items.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# unit
Basis Function Combinator
(a1 -- [a1 ])
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# unquoted
Basis Function Combinator
\[i\] dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# unswons
Basis Function Combinator
([a1 ...1] -- [...1] a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# void
Basis Function Combinator
True if the form on TOS is void otherwise False.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# warranty
Basis Function Combinator
Print warranty information.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# while
Basis Function Combinator
swap nulco dupdipd concat loop
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# words
Basis Function Combinator
Print all the words in alphabetical order.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
--------------------
## x
(Combinator)
[F] x
-----------
[F] F
### Definition
dup i
### Discussion
The `x` combinator ...
------------------------------------------------------------------------
# xor
Basis Function Combinator
Same as a \^ b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
------------------------------------------------------------------------
# zip
Basis Function Combinator
Replace the two lists on the top of the stack with a list of the pairs
from each list. The smallest list sets the length of the result list.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
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