\documentclass{article}
\usepackage{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
++ The new fundamental Type (keeping Object for 1.5 as well)
++ Author: Richard Jenks
++ Date Created: 14 May 1992
++ Date Last Updated: 14 May 1992
++ Description: The fundamental Type;
Type(): Category == with nil

@


\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}