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Move the MD files into the reference dir.

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Simon Forman
2022-03-23 10:40:04 -07:00
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docs/yow/AMPERSAND.md
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------------------------------------------------------------------------
# &
Basis Function Combinator
Same as a & b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/AMPERSAND•AMPERSAND.md
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------------------------------------------------------------------------
# &&
Basis Function Combinator
nulco \[nullary \[false\]\] dip branch
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/ASTERISK.md
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------------------------------------------------------------------------
# \*
Basis Function Combinator
Same as a \* b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/BULLET.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# •
Basis Function Combinator
The identity function.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/CIRCUMFLEX-ACCENT.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \^
Basis Function Combinator
Same as a \^ b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/EQUALS-SIGN.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# =
Basis Function Combinator
Same as a == b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/EXCLAMATION-MARK•EQUALS-SIGN.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# !=
Basis Function Combinator
Same as a != b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/EXCLAMATION-MARK•HYPHEN-MINUS.md
-25
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------------------------------------------------------------------------
!-\^\^\^\^
Basis Function Combinator
0 \>=
Gentzen diagram.
# Definition
if not basis.
# Derivation
if not basis.
# Source
if basis
# Discussion
# Crosslinks
docs/yow/GREATER-THAN-SIGN.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \>
Basis Function Combinator
Same as a \> b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/GREATER-THAN-SIGN•EQUALS-SIGN.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \>=
Basis Function Combinator
Same as a \>= b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/GREATER-THAN-SIGN•GREATER-THAN-SIGN.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \>\>
Basis Function Combinator
Same as a \>\> b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/HYPHEN-MINUS.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
-\^\^\^
Basis Function Combinator
Same as a - b.
Gentzen diagram.
# Definition
if not basis.
# Derivation
if not basis.
# Source
if basis
# Discussion
# Crosslinks
docs/yow/HYPHEN-MINUS•HYPHEN-MINUS.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
\--\^\^\^\^
Basis Function Combinator
Decrement TOS.
Gentzen diagram.
# Definition
if not basis.
# Derivation
if not basis.
# Source
if basis
# Discussion
# Crosslinks
docs/yow/LESS-THAN-SIGN.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \<
Basis Function Combinator
Same as a \< b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/LESS-THAN-SIGN•EQUALS-SIGN.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \<=
Basis Function Combinator
Same as a \<= b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/LESS-THAN-SIGN•GREATER-THAN-SIGN.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \<\>
Basis Function Combinator
Same as a != b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/LESS-THAN-SIGN•LEFT-CURLY-BRACKET•RIGHT-CURLY-BRACKET.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \<{}
Basis Function Combinator
\[\] swap
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/LESS-THAN-SIGN•LESS-THAN-SIGN.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \<\<
Basis Function Combinator
Same as a \<\< b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/LESS-THAN-SIGN•LESS-THAN-SIGN•LEFT-CURLY-BRACKET•RIGHT-CURLY-BRACKET.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \<\<{}
Basis Function Combinator
\[\] rollup
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/PERCENT-SIGN.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# %
Basis Function Combinator
Same as a % b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/PLUS-SIGN.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# +
Basis Function Combinator
Same as a + b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/PLUS-SIGN•PLUS-SIGN.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# ++
Basis Function Combinator
Increment TOS.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/QUESTION-MARK.md
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------------------------------------------------------------------------
# ?
Basis Function Combinator
dup bool
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/SOLIDUS.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# /
Basis Function Combinator
Same as a // b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/SOLIDUS•SOLIDUS.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# //
Basis Function Combinator
Same as a // b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/SOLIDUS•floor.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# /floor
Basis Function Combinator
Same as a // b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/VERTICAL-LINE•VERTICAL-LINE.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# \|\|
Basis Function Combinator
nulco \[nullary\] dip \[true\] branch
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/abs.md
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------------------------------------------------------------------------
# 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
docs/yow/add.md
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------------------------------------------------------------------------
# add
Basis Function Combinator
Same as a + b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/anamorphism.md
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------------------------------------------------------------------------
# anamorphism
Basis Function Combinator
\[pop \[\]\] swap \[dip swons\] genrec
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/and.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# and
Basis Function Combinator
Same as a & b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/app2.md
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------------------------------------------------------------------------
# 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
docs/yow/app3.md
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@@ -1,31 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/appN.md
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------------------------------------------------------------------------
# appN
Basis Function Combinator
\[grabN\] codi map disenstacken
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/at.md
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@@ -1,32 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/average.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# average
Basis Function Combinator
\[sum\] \[size\] cleave /
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/bool.md
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@@ -1,29 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/branch.md
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------------------------------------------------------------------------
# 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
docs/yow/ccccons.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# ccccons
Basis Function Combinator
ccons ccons
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/choice.md
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@@ -1,38 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/clear.md
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@@ -1,30 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/cleave.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# cleave
Basis Function Combinator
fork popdd
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/clop.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# clop
Basis Function Combinator
cleave popdd
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/cmp.md
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------------------------------------------------------------------------
# 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
docs/yow/codi.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# codi
Basis Function Combinator
cons dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/codireco.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# codireco
Basis Function Combinator
codi reco
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/concat.md
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@@ -1,29 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/cond.md
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@@ -1,36 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/dinfrirst.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# dinfrirst
Basis Function Combinator
dip infrst
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/dip.md
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@@ -1,31 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/dipd.md
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@@ -1,29 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/dipdd.md
-29
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@@ -1,29 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/disenstacken.md
-26
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@@ -1,26 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/div.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# div
Basis Function Combinator
Same as a // b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/divmod.md
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@@ -1,27 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/down_to_zero.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# down_to_zero
Basis Function Combinator
\[0 \>\] \[dup \--\] while
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/drop.md
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@@ -1,32 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/dup.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# dup
Basis Function Combinator
(a1 -- a1 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/dupd.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# dupd
Basis Function Combinator
(a2 a1 -- a2 a2 a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/dupdd.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/dupdip.md
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@@ -1,30 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/dupdipd.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# dupdipd
Basis Function Combinator
dup dipd
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/enstacken.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# enstacken
Basis Function Combinator
stack \[clear\] dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/eq.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# eq
Basis Function Combinator
Same as a == b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/first.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# first
Basis Function Combinator
([a1 ...1] -- a1)
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/first_two.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/flatten.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# flatten
Basis Function Combinator
\<{} \[concat\] step
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/floor.md
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@@ -1,27 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/floordiv.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# floordiv
Basis Function Combinator
Same as a // b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/fork.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# fork
Basis Function Combinator
\[i\] app2
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/fourth.md
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------------------------------------------------------------------------
# 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
docs/yow/gcd.md
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------------------------------------------------------------------------
# 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
docs/yow/gcd2.md
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------------------------------------------------------------------------
# gcd2
Basis Function Combinator
Compiled GCD function.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/ge.md
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------------------------------------------------------------------------
# ge
Basis Function Combinator
Same as a \>= b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/genrec.md
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------------------------------------------------------------------------
# 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
docs/yow/getitem.md
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------------------------------------------------------------------------
# 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
docs/yow/grabN.md
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------------------------------------------------------------------------
# grabN
Basis Function Combinator
\<{} \[cons\] times
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/grba.md
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------------------------------------------------------------------------
# grba
Basis Function Combinator
\[stack popd\] dip
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/gt.md
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------------------------------------------------------------------------
# gt
Basis Function Combinator
Same as a \> b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/help.md
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------------------------------------------------------------------------
# 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
docs/yow/hypot.md
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------------------------------------------------------------------------
# hypot
Basis Function Combinator
\[sqr\] ii + sqrt
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/id.md
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------------------------------------------------------------------------
# id
Basis Function Combinator
The identity function.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/ifte.md
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------------------------------------------------------------------------
# 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
docs/yow/ii.md
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------------------------------------------------------------------------
# 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
docs/yow/infrst.md
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------------------------------------------------------------------------
# infrst
Basis Function Combinator
infra first
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/inscribe.md
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------------------------------------------------------------------------
# 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
docs/yow/le.md
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------------------------------------------------------------------------
# le
Basis Function Combinator
Same as a \<= b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/loop.md
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------------------------------------------------------------------------
# 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
docs/yow/lshift.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# lshift
Basis Function Combinator
Same as a \<\< b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/lt.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# lt
Basis Function Combinator
Same as a \< b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/make_generator.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# make_generator
Basis Function Combinator
\[codireco\] ccons
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/map.md
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@@ -1,26 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/max.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/min.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# 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
docs/yow/mod.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# mod
Basis Function Combinator
Same as a % b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/modulus.md
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# modulus
Basis Function Combinator
Same as a % b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/mul.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# mul
Basis Function Combinator
Same as a \* b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/ne.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# ne
Basis Function Combinator
Same as a != b.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/neg.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# neg
Basis Function Combinator
Same as -a.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks
docs/yow/not.md
-25
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@@ -1,25 +0,0 @@
------------------------------------------------------------------------
# not
Basis Function Combinator
Same as not a.
Gentzen diagram.
## Definition
if not basis.
## Derivation
if not basis.
## Source
if basis
## Discussion
## Crosslinks

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