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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{src/algebra ituple.spad}
\author{Clifton J. Williamson}
\maketitle
\begin{abstract}
\end{abstract}
\tableofcontents
\eject
\section{domain ITUPLE InfiniteTuple}
<<domain ITUPLE InfiniteTuple>>=
import CoercibleTo OutputForm
import Boolean
import Stream
)abbrev domain ITUPLE InfiniteTuple
++ Infinite tuples for the interpreter
++ Author: Clifton J. Williamson
++ Date Created: 16 February 1990
++ Date Last Updated: May 13, 2013.
++ Keywords:
++ Examples:
++ References:
++ Description:
++ This package implements 'infinite tuples' for the interpreter.
++ The representation is a stream.
InfiniteTuple(S:Type): Exports == Implementation where
Exports == Join(Functorial S,CoercibleTo OutputForm) with
filterWhile: (S -> Boolean, %) -> %
++ filterWhile(p,t) returns \spad{[x for x in t while p(x)]}.
filterUntil: (S -> Boolean, %) -> %
++ filterUntil(p,t) returns \spad{[x for x in t while not p(x)]}.
select: (S -> Boolean, %) -> %
++ select(p,t) returns \spad{[x for x in t | p(x)]}.
generate: (S -> S,S) -> %
++ generate(f,s) returns \spad{[s,f(s),f(f(s)),...]}.
construct: % -> Stream S
++ construct(t) converts an infinite tuple to a stream.
Implementation == add
Rep == Stream S
generate(f,x) == per generate(f,x)$Stream(S)
filterWhile(f, x) == per filterWhile(f,rep x)$Stream(S)
filterUntil(f, x) == per filterUntil(f,rep x)$Stream(S)
select(f, x) == per select(f,rep x)$Stream(S)
construct x == rep x
map(f,x) == per map(f, rep x)$Stream(S)
coerce(x: %): OutputForm == rep(x)::OutputForm
@
\section{package ITFUN2 InfiniteTupleFunctions2}
<<package ITFUN2 InfiniteTupleFunctions2>>=
import Type
import InfiniteTuple
import Stream
)abbrev package ITFUN2 InfiniteTupleFunctions2
++ Description:
++ Functions defined on streams with entries in two sets.
InfiniteTupleFunctions2(A:Type,B:Type): Exports == Implementation where
macro IT == InfiniteTuple
Exports == Type with
map: ((A -> B),IT A) -> IT B
++ \spad{map(f,[x0,x1,x2,...])} returns \spad{[f(x0),f(x1),f(x2),..]}.
Implementation == add
map(f,x) ==
map(f,x pretend Stream(A))$StreamFunctions2(A,B) pretend IT(B)
@
\section{package ITFUN3 InfiniteTupleFunctions3}
<<package ITFUN3 InfiniteTupleFunctions3>>=
import Type
import InfiniteTuple
import Stream
)abbrev package ITFUN3 InfiniteTupleFunctions3
InfiniteTupleFunctions3(A:Type, B:Type,C:Type): Exports
== Implementation where
++ Functions defined on streams with entries in two sets.
IT ==> InfiniteTuple
ST ==> Stream
SF3 ==> StreamFunctions3(A,B,C)
FUN ==> ((A,B)->C)
Exports ==> with
map: (((A,B)->C), IT A, IT B) -> IT C
++ map(f,a,b) \undocumented
map: (((A,B)->C), ST A, IT B) -> ST C
++ map(f,a,b) \undocumented
map: (((A,B)->C), IT A, ST B) -> ST C
++ map(f,a,b) \undocumented
Implementation ==> add
map(f:FUN, s1:IT A, s2:IT B):IT C ==
map(f, s1 pretend Stream(A), s2 pretend Stream(B))$SF3 pretend IT(C)
map(f:FUN, s1:ST A, s2:IT B):ST C ==
map(f, s1, s2 pretend Stream(B))$SF3
map(f:FUN, s1:IT A, s2:ST B):ST C ==
map(f, s1 pretend Stream(A), s2)$SF3
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--Copyright (C) 2007-2013, Gabriel Dos Reis.
--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>>
<<domain ITUPLE InfiniteTuple>>
<<package ITFUN2 InfiniteTupleFunctions2>>
<<package ITFUN3 InfiniteTupleFunctions3>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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