44 lines
1.5 KiB
Factor
44 lines
1.5 KiB
Factor
! Copyright (c) 2012 Anonymous
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! See http://factorcode.org/license.txt for BSD license.
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USING: combinators fry kernel locals math ;
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IN: rosetta-code.y-combinator
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! http://rosettacode.org/wiki/Y_combinator
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! In strict functional programming and the lambda calculus,
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! functions (lambda expressions) don't have state and are only
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! allowed to refer to arguments of enclosing functions. This rules
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! out the usual definition of a recursive function wherein a
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! function is associated with the state of a variable and this
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! variable's state is used in the body of the function.
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! The Y combinator is itself a stateless function that, when
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! applied to another stateless function, returns a recursive
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! version of the function. The Y combinator is the simplest of the
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! class of such functions, called fixed-point combinators.
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! The task is to define the stateless Y combinator and use it to
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! compute factorials and Fibonacci numbers from other stateless
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! functions or lambda expressions.
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: Y ( quot -- quot )
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'[ [ dup call call ] curry @ ] dup call ; inline
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! factorial sequence
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: almost-fac ( quot -- quot )
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'[ dup zero? [ drop 1 ] [ dup 1 - @ * ] if ] ;
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! fibonacci sequence
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: almost-fib ( quot -- quot )
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'[ dup 2 >= [ 1 2 [ - @ ] bi-curry@ bi + ] when ] ;
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! Ackermann–Péter function
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:: almost-ack ( quot -- quot )
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[
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{
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{ [ over zero? ] [ nip 1 + ] }
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{ [ dup zero? ] [ [ 1 - ] [ drop 1 ] bi* quot call ] }
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[ [ drop 1 - ] [ 1 - quot call ] 2bi quot call ]
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} cond
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] ;
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