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author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/algebra/ystream.spad.pamphlet | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/algebra/ystream.spad.pamphlet')
-rw-r--r-- | src/algebra/ystream.spad.pamphlet | 96 |
1 files changed, 96 insertions, 0 deletions
diff --git a/src/algebra/ystream.spad.pamphlet b/src/algebra/ystream.spad.pamphlet new file mode 100644 index 00000000..0a443168 --- /dev/null +++ b/src/algebra/ystream.spad.pamphlet @@ -0,0 +1,96 @@ +\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} |