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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra equation1.spad}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\tableofcontents
\eject
\section{category IEVALAB InnerEvalable}
<<category IEVALAB InnerEvalable>>=
import SetCategory
import Type
import List
)abbrev category IEVALAB InnerEvalable
-- FOR THE BENEFIT OF LIBAX0 GENERATION
++ Author:
++ Date Created:
++ Date Last Updated: June 3, 1991
++ Basic Operations:
++ Related Domains:
++ Also See: Evalable
++ AMS Classifications:
++ Keywords: equation
++ Examples:
++ References:
++ Description:
++ This category provides \spadfun{eval} operations.
++ A domain may belong to this category if it is possible to make
++ ``evaluation'' substitutions. The difference between this
++ and \spadtype{Evalable} is that the operations in this category
++ specify the substitution as a pair of arguments rather than as
++ an equation.
InnerEvalable(A:SetCategory, B:Type): Category == with
eval: ($, A, B) -> $
++ eval(f, x, v) replaces x by v in f.
eval: ($, List A, List B) -> $
++ eval(f, [x1,...,xn], [v1,...,vn]) replaces xi by vi in f.
add
eval(f:$, x:A, v:B) == eval(f, [x], [v])
@
\section{category EVALAB Evalable}
<<category EVALAB Evalable>>=
import SetCategory
import InnerEvalable
import Equation
import List
)abbrev category EVALAB Evalable
++ Author:
++ Date Created:
++ Date Last Updated: June 3, 1991
++ Basic Operations:
++ Related Domains:
++ Also See: FullyEvalable
++ AMS Classifications:
++ Keywords: equation
++ Examples:
++ References:
++ Description:
++ This category provides \spadfun{eval} operations.
++ A domain may belong to this category if it is possible to make
++ ``evaluation'' substitutions.
Evalable(R:SetCategory): Category == InnerEvalable(R,R) with
eval: ($, Equation R) -> $
++ eval(f,x = v) replaces x by v in f.
eval: ($, List Equation R) -> $
++ eval(f, [x1 = v1,...,xn = vn]) replaces xi by vi in f.
add
eval(f:$, eq:Equation R) == eval(f, [eq])
eval(f:$, xs:List R,vs:List R) == eval(f,[x=v for x in xs for v in vs])
@
\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>>
<<category IEVALAB InnerEvalable>>
<<category EVALAB Evalable>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
