/usr/lib/open-axiom/src/algebra/ystream.spad is in open-axiom-source 1.4.1+svn~2626-2ubuntu2.
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import Type
import Stream
)abbrev package YSTREAM ParadoxicalCombinatorsForStreams
++ Computation of fixed points of mappings on streams
++ Author: Burge, Watt (revised by Williamson)
++ Date Created: 1986
++ Date Last Updated: 21 October 1989
++ Keywords: stream, fixed point
++ Examples:
++ References:
ParadoxicalCombinatorsForStreams(A):Exports == Implementation where
++ This package implements fixed-point computations on streams.
A : Type
ST ==> Stream
L ==> List
I ==> Integer
Exports ==> with
Y: (ST A -> ST A) -> ST A
++ Y(f) computes a fixed point of the function f.
Y: (L ST A -> L ST A,I) -> L ST A
++ Y(g,n) computes a fixed point of the function g, where g takes
++ a list of n streams and returns a list of n streams.
Implementation ==> add
import %head: ST A -> A from Foreign Builtin
import %tail: ST A -> ST A from Foreign Builtin
Y f ==
y : ST A := %pair(0$I,0$I)$Foreign(Builtin)
j := f y
%store(%head y,frst j)$Foreign(Builtin)
%store(%tail y,rst j)$Foreign(Builtin)
y
Y(g,n) ==
x : L ST A := [%pair(0$I,0$I)$Foreign(Builtin) for i in 1..n]
j := g x
for xi in x for ji in j repeat
%store(%head xi,frst ji)$Foreign(Builtin)
%store(%tail xi,rst ji)$Foreign(Builtin)
x
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