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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/algebra/ystream.spad.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra ystream.spad}
+\author{William Burge, Stephen M. Watt, Clifton J. Williamson}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{package YSTREAM ParadoxicalCombinatorsForStreams}
+<<package YSTREAM ParadoxicalCombinatorsForStreams>>=
+)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
+
+ Y f ==
+ y : ST A := CONS(0$I,0$I)$Lisp
+ j := f y
+ RPLACA(y,frst j)$Lisp
+ RPLACD(y,rst j)$Lisp
+ y
+
+ Y(g,n) ==
+ x : L ST A := [CONS(0$I,0$I)$Lisp for i in 1..n]
+ j := g x
+ for xi in x for ji in j repeat
+ RPLACA(xi,frst ji)$Lisp
+ RPLACD(xi,rst ji)$Lisp
+ 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}