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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{src/algebra ystream.spad}
\author{William Burge, Stephen M. Watt, Clifton J. Williamson}
\maketitle
\begin{abstract}
\end{abstract}
\tableofcontents
\eject
\section{package YSTREAM ParadoxicalCombinatorsForStreams}
<<package YSTREAM ParadoxicalCombinatorsForStreams>>=
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
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
-- - Redistributions of source code must retain the above copyright
-- notice, this list of conditions and the following disclaimer.
--
-- - Redistributions in binary form must reproduce the above copyright
-- notice, this list of conditions and the following disclaimer in
-- the documentation and/or other materials provided with the
-- distribution.
--
-- - Neither the name of The Numerical ALgorithms Group Ltd. nor the
-- names of its contributors may be used to endorse or promote products
-- derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@
<<*>>=
<<license>>
<<package YSTREAM ParadoxicalCombinatorsForStreams>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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