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\documentclass{article}
\usepackage{open-axiom}
\title{\$SPAD/src/algebra coerce.spad}
\author{Richard Jenks, Manuel Bronstein, Gabriel Dos Reis}
\begin{document}
\maketitle
\begin{abstract}
\end{abstract}
\tableofcontents
\eject
\section{category TYPE Type}
<<category TYPE Type>>=
)abbrev category TYPE Type
++ Author: Richard Jenks
++ Date Created: 14 May 1992
++ Date Last Updated: February 12, 2012
++ Description: The fundamental Type;
Type(): Category == Join()
@
\section{Category UnionType}
<<category UTYPE UnionType>>=
)abbrev category UTYPE UnionType
++ Author: Gabriel Dos Reis
++ Date Created: December 17, 2007
++ Date Last Modified: December 17, 2007
++ Description: The category of domains that act like unions.
++ UnionType, like Type or Category, acts mostly as a take that
++ communicates `union-like' intended semantics to the compiler.
++ A domain D that satifies UnionType should provide definitions
++ for `case' operators, with corresponding `autoCoerce' operators.
UnionType(): Category == with nil
@
\section{category KOERCE CoercibleTo}
<<category KOERCE CoercibleTo>>=
)abbrev category KOERCE CoercibleTo
++ Category for coerce
++ Author: Manuel Bronstein
++ Date Created: ???
++ Date Last Updated: 14 May 1991
++ Description:
++ A is coercible to B means any element of A can automatically be
++ converted into an element of B by the interpreter.
CoercibleTo(S:Type): Category == with
coerce: % -> S
++ coerce(a) transforms a into an element of S.
@
\section{category KRCFROM CoercibleFrom}
<<category KRCFROM CoercibleFrom>>=
)abbrev category KRCFROM CoercibleFrom
++ Author: Gabriel Dos Reis
++ Date Create: November 19, 2008
++ Date Last Modified: November 19, 2008
++ See Also: CoercibleTo
++ Description:
++ A is coercible from B iff any element of domain B can be
++ automically converted into an element of domain A.
CoercibleFrom(S: Type): Category == with
coerce: S -> %
++ coerce(s) transforms `s' into an element of `%'.
@
\section{category HOMOTOP HomotopicTo}
<<category HOMOTOP HomotopicTo>>=
)abbrev category HOMOTOP HomotopicTo
++ Author: Gabriel Dos Reis
++ Date Create: November 19, 2008
++ Date Last Modified: November 19, 2008
++ See Also: CoercibleTo, CoercibleFrom
++ Description:
++ A is homotopic to B iff any element of domain B can be
++ automically converted into an element of domain B, and nay
++ element of domain B can be automatically converted into an A.
HomotopicTo(S: Type): Category == Join(CoercibleTo S, CoercibleFrom S)
@
\section{category KONVERT ConvertibleTo}
<<category KONVERT ConvertibleTo>>=
)abbrev category KONVERT ConvertibleTo
++ Category for convert
++ Author: Manuel Bronstein
++ Date Created: ???
++ Date Last Updated: 14 May 1991
++ Description:
++ A is convertible to B means any element of A
++ can be converted into an element of B,
++ but not automatically by the interpreter.
ConvertibleTo(S:Type): Category == with
convert: % -> S
++ convert(a) transforms a into an element of S.
@
\section{category KVTFROM ConvertibleFrom}
<<category KVTFROM ConvertibleFrom>>=
)abbrev category KVTFROM ConvertibleFrom
++ Author: Gabriel Dos Reis
++ Date Create: November 19, 2008
++ Date Last Modified: November 19, 2008
++ See Also: ConvertibleTo
++ Description:
++ A is convertible from B iff any element of domain B can be
++ explicitly converted into an element of domain A.
ConvertibleFrom(S: Type): Category == with
convert: S -> %
++ convert(s) transforms `s' into an element of `%'.
@
\section{category RETRACT RetractableTo}
<<category RETRACT RetractableTo>>=
)abbrev category RETRACT RetractableTo
++ Category for retract
++ Author: ???
++ Date Created: ???
++ Date Last Updated: November 19, 2008
++ Related Constructor: CoercibleFrom
++ Description:
++ A is retractable to B means that some elementsif A can be converted
++ into elements of B and any element of B can be converted into an
++ element of A.
RetractableTo(S: Type): Category == CoercibleFrom S with
retractIfCan: % -> Union(S,"failed")
++ retractIfCan(a) transforms a into an element of S if possible.
++ Returns "failed" if a cannot be made into an element of S.
retract: % -> S
++ retract(a) transforms a into an element of S if possible.
++ Error: if a cannot be made into an element of S.
add
retract(s) ==
(u:=retractIfCan s) case "failed" => error "not retractable"
u
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--Copyright (C) 2007-2008, 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>>
<<category TYPE Type>>
<<category UTYPE UnionType>>
<<category KOERCE CoercibleTo>>
<<category KRCFROM CoercibleFrom>>
<<category HOMOTOP HomotopicTo>>
<<category KONVERT ConvertibleTo>>
<<category KVTFROM ConvertibleFrom>>
<<category RETRACT RetractableTo>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
