5273 lines
58 KiB
Markdown
5273 lines
58 KiB
Markdown
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Version -10.0.0
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Each function, combinator, or definition should be documented here.
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--------------
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## &
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See [and](#and).
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------------------------------------------------------------------------
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## &&
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Basis Function Combinator
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nulco \[nullary \[false\]\] dip branch
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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--------------
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## *
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See [mul](#mul).
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--------------
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## •
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See [id](#id).
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## ^
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See [xor](#xor).
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--------------
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## =
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See [eq](#eq).
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--------------
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## !=
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See [ne](#ne).
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------------------------------------------------------------------------
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## !-
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Basis Function Combinator
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0 \>=
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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--------------
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## >
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See [gt](#gt).
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--------------
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## >=
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See [ge](#ge).
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--------------
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## >>
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See [rshift](#rshift).
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--------------
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## -
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See [sub](#sub).
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--------------
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## --
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See [pred](#pred).
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--------------
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## <
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See [lt](#lt).
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--------------
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## <=
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See [le](#le).
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--------------
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## <>
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See [ne](#ne).
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------------------------------------------------------------------------
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## \<{}
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Basis Function Combinator
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\[\] swap
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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--------------
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## <<
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See [lshift](#lshift).
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------------------------------------------------------------------------
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## \<\<{}
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Basis Function Combinator
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\[\] rollup
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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--------------
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## %
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See [mod](#mod).
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--------------
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## +
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See [add](#add).
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--------------
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## ++
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See [succ](#succ).
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------------------------------------------------------------------------
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## ?
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Basis Function Combinator
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dup bool
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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--------------
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## /
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See [floordiv](#floordiv).
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--------------
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## //
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See [floordiv](#floordiv).
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--------------
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## /floor
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See [floordiv](#floordiv).
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------------------------------------------------------------------------
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## \|\|
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Basis Function Combinator
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nulco \[nullary\] dip \[true\] branch
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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------------------------------------------------------------------------
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## abs
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Basis Function Combinator
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Return the absolute value of the argument.
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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------------------------------------------------------------------------
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## add
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Basis Function Combinator
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Same as a + b.
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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------------------------------------------------------------------------
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## anamorphism
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Basis Function Combinator
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\[pop \[\]\] swap \[dip swons\] genrec
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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------------------------------------------------------------------------
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## and
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Basis Function Combinator
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Same as a & b.
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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--------------------
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## app1
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"apply one"
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(Combinator)
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Given a quoted program on TOS and anything as the second stack item run
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the program without disturbing the stack and replace the two args with
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the first result of the program.
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... x [Q] app1
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---------------------------------
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... [x ...] [Q] infra first
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### Definition
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nullary popd
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### Discussion
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Just a specialization of `nullary` really. Its parallelizable cousins
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are more useful.
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------------------------------------------------------------------------
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## app2
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Basis Function Combinator
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Like app1 with two items.
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: ... y x [Q] . app2
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-----------------------------------
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... [y ...] [Q] . infra first
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[x ...] [Q] infra first
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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------------------------------------------------------------------------
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## app3
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Basis Function Combinator
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Like app1 with three items.
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: ... z y x [Q] . app3
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-----------------------------------
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... [z ...] [Q] . infra first
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[y ...] [Q] infra first
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[x ...] [Q] infra first
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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------------------------------------------------------------------------
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## appN
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Basis Function Combinator
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\[grabN\] codi map disenstacken
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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--------------
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## at
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See [getitem](#getitem).
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------------------------------------------------------------------------
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## average
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Basis Function Combinator
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\[sum\] \[size\] cleave /
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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--------------------
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## b
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(Combinator)
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Run two quoted programs
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[P] [Q] b
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---------------
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P Q
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### Definition
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[i] dip i
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### Derivation
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[P] [Q] b
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[P] [Q] [i] dip i
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[P] i [Q] i
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P [Q] i
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P Q
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### Discussion
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This combinator comes in handy.
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### Crosslinks
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[dupdip](#dupdip)
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[ii](#ii)
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--------------------
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## binary
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(Combinator)
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Run a quoted program using exactly two stack values and leave the first
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item of the result on the stack.
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... y x [P] binary
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-----------------------
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... A
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### Definition
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unary popd
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### Discussion
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Runs any other quoted function and returns its first result while
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consuming exactly two items from the stack.
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### Crosslinks
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[nullary](#nullary)
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[ternary](#ternary)
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[unary](#unary)
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------------------------------------------------------------------------
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## bool
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Basis Function Combinator
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bool(x) -\> bool
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Returns True when the argument x is true, False otherwise. The builtins
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True and False are the only two instances of the class bool. The class
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bool is a subclass of the class int, and cannot be subclassed.
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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------------------------------------------------------------------------
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## branch
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Basis Function Combinator
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Use a Boolean value to select one of two quoted programs to run.
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branch == roll< choice i
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False [F] [T] branch
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--------------------------
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F
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True [F] [T] branch
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-------------------------
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T
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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------------------------------------------------------------------------
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## ccccons
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Basis Function Combinator
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ccons ccons
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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--------------------
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## ccons
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(Function)
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Given two items and a list, append the items to the list to make a new list.
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B A [...] ccons
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---------------------
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[B A ...]
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### Definition
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cons cons
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### Discussion
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Does `cons` twice.
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### Crosslinks
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[cons](#cons)
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------------------------------------------------------------------------
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## choice
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Basis Function Combinator
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Use a Boolean value to select one of two items. :
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A B false choice
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----------------------
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A
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A B true choice
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---------------------
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B
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Currently Python semantics are used to evaluate the \"truthiness\" of
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the Boolean value (so empty string, zero, etc. are counted as false,
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etc.)
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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------------------------------------------------------------------------
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## clear
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Basis Function Combinator
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Clear everything from the stack.
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: clear == stack [pop stack] loop
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... clear
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---------------
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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### Crosslinks
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Lorem ipsum.
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------------------------------------------------------------------------
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## cleave
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Basis Function Combinator
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fork popdd
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## clop
|
|
|
|
Basis Function Combinator
|
|
|
|
cleave popdd
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## codi
|
|
|
|
Basis Function Combinator
|
|
|
|
cons dip
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## codireco
|
|
|
|
Basis Function Combinator
|
|
|
|
codi reco
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------
|
|
|
|
## div
|
|
|
|
See [floordiv](#floordiv).
|
|
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## down_to_zero
|
|
|
|
Basis Function Combinator
|
|
|
|
\[0 \>\] \[dup \--\] while
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## dup
|
|
|
|
Basis Function Combinator
|
|
|
|
(a1 -- a1 a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## dupd
|
|
|
|
Basis Function Combinator
|
|
|
|
(a2 a1 -- a2 a2 a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## dupdipd
|
|
|
|
Basis Function Combinator
|
|
|
|
dup dipd
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## enstacken
|
|
|
|
Basis Function Combinator
|
|
|
|
stack \[clear\] dip
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## eq
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a == b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## first
|
|
|
|
Basis Function Combinator
|
|
|
|
([a1 ...1] -- a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## first_two
|
|
|
|
Basis Function Combinator
|
|
|
|
([a1 a2 ...1] -- a1 a2)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## flatten
|
|
|
|
Basis Function Combinator
|
|
|
|
\<{} \[concat\] step
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## floordiv
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a // b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## fork
|
|
|
|
Basis Function Combinator
|
|
|
|
\[i\] app2
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## fourth
|
|
|
|
Basis Function Combinator
|
|
|
|
([a1 a2 a3 a4 ...1] -- a4)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## gcd2
|
|
|
|
Basis Function Combinator
|
|
|
|
Compiled GCD function.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## ge
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a \>= b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## grabN
|
|
|
|
Basis Function Combinator
|
|
|
|
\<{} \[cons\] times
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## grba
|
|
|
|
Basis Function Combinator
|
|
|
|
\[stack popd\] dip
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## gt
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a \> b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## hypot
|
|
|
|
Basis Function Combinator
|
|
|
|
\[sqr\] ii + sqrt
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## ii
|
|
|
|
Basis Function Combinator
|
|
|
|
... a [Q] ii
|
|
------------------
|
|
... Q a Q
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## le
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a \<= b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## lshift
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a \<\< b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## lt
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a \< b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## make_generator
|
|
|
|
Basis Function Combinator
|
|
|
|
\[codireco\] ccons
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## max
|
|
|
|
Basis Function Combinator
|
|
|
|
Given a list find the maximum.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## min
|
|
|
|
Basis Function Combinator
|
|
|
|
Given a list find the minimum.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## mod
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a % b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------
|
|
|
|
## modulus
|
|
|
|
See [mod](#mod).
|
|
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## mul
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a \* b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## ne
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a != b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## neg
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as -a.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## not
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as not a.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------------
|
|
|
|
## !-
|
|
|
|
"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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## or
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a \| b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## over
|
|
|
|
Basis Function Combinator
|
|
|
|
(a2 a1 -- a2 a1 a2)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## pam
|
|
|
|
Basis Function Combinator
|
|
|
|
\[i\] map
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------
|
|
|
|
## pick
|
|
|
|
See [getitem](#getitem).
|
|
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## pop
|
|
|
|
Basis Function Combinator
|
|
|
|
(a1 --)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## popd
|
|
|
|
Basis Function Combinator
|
|
|
|
(a2 a1 -- a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## popdd
|
|
|
|
Basis Function Combinator
|
|
|
|
(a3 a2 a1 -- a2 a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## popop
|
|
|
|
Basis Function Combinator
|
|
|
|
(a2 a1 --)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## popopd
|
|
|
|
Basis Function Combinator
|
|
|
|
(a3 a2 a1 -- a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## popopdd
|
|
|
|
Basis Function Combinator
|
|
|
|
(a4 a3 a2 a1 -- a2 a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## popopop
|
|
|
|
Basis Function Combinator
|
|
|
|
pop popop
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## pow
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a \*\* b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## pred
|
|
|
|
Basis Function Combinator
|
|
|
|
Decrement TOS.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## product
|
|
|
|
Basis Function Combinator
|
|
|
|
1 swap \[\*\] step
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## quoted
|
|
|
|
Basis Function Combinator
|
|
|
|
\[unit\] dip
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## range
|
|
|
|
Basis Function Combinator
|
|
|
|
\[0 \<=\] \[1 - dup\] anamorphism
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## reco
|
|
|
|
Basis Function Combinator
|
|
|
|
rest cons
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------
|
|
|
|
## rem
|
|
|
|
See [mod](#mod).
|
|
|
|
|
|
--------------
|
|
|
|
## remainder
|
|
|
|
See [mod](#mod).
|
|
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## rest
|
|
|
|
Basis Function Combinator
|
|
|
|
([a1 ...0] -- [...0])
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## rolldown
|
|
|
|
Basis Function Combinator
|
|
|
|
(a1 a2 a3 -- a2 a3 a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## rollup
|
|
|
|
Basis Function Combinator
|
|
|
|
(a1 a2 a3 -- a3 a1 a2)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------
|
|
|
|
## roll>
|
|
|
|
See [rollup](#rollup).
|
|
|
|
|
|
--------------
|
|
|
|
## roll<
|
|
|
|
See [rolldown](#rolldown).
|
|
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## rrest
|
|
|
|
Basis Function Combinator
|
|
|
|
([a1 a2 ...1] -- [...1])
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## rshift
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a \>\> b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## run
|
|
|
|
Basis Function Combinator
|
|
|
|
\<{} infra
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## second
|
|
|
|
Basis Function Combinator
|
|
|
|
([a1 a2 ...1] -- a2)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## sharing
|
|
|
|
Basis Function Combinator
|
|
|
|
Print redistribution information.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## shift
|
|
|
|
Basis Function Combinator
|
|
|
|
uncons \[swons\] dip
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## size
|
|
|
|
Basis Function Combinator
|
|
|
|
\[pop ++\] step_zero
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## sort
|
|
|
|
Basis Function Combinator
|
|
|
|
Given a list return it sorted.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## split_at
|
|
|
|
Basis Function Combinator
|
|
|
|
\[drop\] \[take\] clop
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## split_list
|
|
|
|
Basis Function Combinator
|
|
|
|
\[take reverse\] \[drop\] clop
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## sqr
|
|
|
|
Basis Function Combinator
|
|
|
|
dup \*
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## stack
|
|
|
|
Basis Function Combinator
|
|
|
|
(... -- ... [...])
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## stackd
|
|
|
|
Basis Function Combinator
|
|
|
|
\[stack\] dip
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## step_zero
|
|
|
|
Basis Function Combinator
|
|
|
|
0 roll> step
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## stuncons
|
|
|
|
Basis Function Combinator
|
|
|
|
(... a1 -- ... a1 a1 [...])
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## stununcons
|
|
|
|
Basis Function Combinator
|
|
|
|
(... a2 a1 -- ... a2 a1 a1 a2 [...])
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## sub
|
|
|
|
Basis Function Combinator
|
|
|
|
Same as a - b.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## succ
|
|
|
|
Basis Function Combinator
|
|
|
|
Increment TOS.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## swaack
|
|
|
|
Basis Function Combinator
|
|
|
|
([...1] -- [...0])
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## swap
|
|
|
|
Basis Function Combinator
|
|
|
|
(a1 a2 -- a2 a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## swapd
|
|
|
|
Basis Function Combinator
|
|
|
|
\[swap\] dip
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## swoncat
|
|
|
|
Basis Function Combinator
|
|
|
|
swap concat
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## swons
|
|
|
|
Basis Function Combinator
|
|
|
|
([...1] a1 -- [a1 ...1])
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## tailrec
|
|
|
|
Basis Function Combinator
|
|
|
|
\[i\] genrec
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------
|
|
|
|
## truthy
|
|
|
|
See [bool](#bool).
|
|
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## tuck
|
|
|
|
Basis Function Combinator
|
|
|
|
(a2 a1 -- a1 a2 a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## unit
|
|
|
|
Basis Function Combinator
|
|
|
|
(a1 -- [a1 ])
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## unquoted
|
|
|
|
Basis Function Combinator
|
|
|
|
\[i\] dip
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## unswons
|
|
|
|
Basis Function Combinator
|
|
|
|
([a1 ...1] -- [...1] a1)
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## warranty
|
|
|
|
Basis Function Combinator
|
|
|
|
Print warranty information.
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## while
|
|
|
|
Basis Function Combinator
|
|
|
|
swap nulco dupdipd concat loop
|
|
|
|
Gentzen diagram.
|
|
|
|
### Definition
|
|
|
|
if not basis.
|
|
|
|
### Derivation
|
|
|
|
if not basis.
|
|
|
|
### Source
|
|
|
|
if basis
|
|
|
|
### Discussion
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
--------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|
|
|
|
------------------------------------------------------------------------
|
|
|
|
## 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
|
|
|
|
Lorem ipsum.
|
|
|
|
### Crosslinks
|
|
|
|
Lorem ipsum.
|