\documentclass{article}
\usepackage{open-axiom}

\title{src/algebra term.spad}

\begin{document}
\author{Gabriel Dos~Reis}
\maketitle

\begin{abstract}
\end{abstract}
  This file contains specifications and implementations for basic
  support of term algebras, in the sense of Universal Algebra.
\tableofcontents
\eject


\section{The \code{Arity} domain}

<<domain ARITY Arity>>=
)abbrev domain ARITY Arity
++ Author: Gabriel Dos Reis
++ Date Created: December 04, 2008
++ Date Last Updated: December 04, 2008
++ Description:
++   This domain implements the arity of a function or an operator,
++   e.g. the number of arguments that an operator can take.  An 
++   arity is either a definition nonnegative integer, and the special
++   value `arbitrary', signifying that an operation can take any
++   number of arguments.
Arity(): Public == Private where
  Public == Join(SetCategory, RetractableTo NonNegativeInteger) with
    arbitrary: %
      ++ aribitrary is the arity of a function that accepts any
      ++ number of arguments.
  Private == add
    Rep == SingleInteger
    arbitrary == per(-1)
    hash x == hash rep x
    x = y == rep x = rep y
    coerce(x: %): OutputForm == 
      x = arbitrary => 'arbitrary::OutputForm
      rep(x)::OutputForm
    coerce(n: NonNegativeInteger): % == 
      max()$SingleInteger < n => 
        error "arity is too large for OpenAxiom"
      per(n::SingleInteger)
    retractIfCan x ==
      (n := rep x) < 0 => "failed"
      n::Integer::NonNegativeInteger
   
@


\section{Operator Interface: \code{OperatorCategory}}

<<category OPERCAT OperatorCategory>>=
)abbrev category OPERCAT OperatorCategory
++ Author: Gabriel Dos Reis
++ Date Created: December 04, 2008
++ Date Last Updated: December 17, 2008
++ Description:
++   This category specifies the interface for operators used to build
++   terms, in the sense of Universal Algebra.  The domain parameter S
++   provides representation for the `external name' of an operator.
OperatorCategory(S: SetCategory): Category ==
    SetCategory with
      name: % -> S
        ++ name(op) returns the externam name of `op'.
      arity: % -> Arity
        ++ arity(op) returns the arity of the operator `op'.
  add
    coerce(op: %): OutputForm == name(op)::OutputForm

@


\section{License}

<<license>>=
--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.

@


\section{Putting It Altogether}

<<*>>=
<<license>>
<<domain ARITY Arity>>
<<category OPERCAT OperatorCategory>>

@



\end{document}