* algebra/term.spad.pamphlet: New. Implement Arity and

	OperatorCategory. 
	* algebra/Makefile.pamphlet (axiom_algebra_layer_15): Include ARITY.
	(axiom_algebra_layer_16): Include OPERCAT.
	* share/algebra: Update databases.

1 files changed, 132 insertions, 0 deletions

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+\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 04, 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'.
+      operator: S -> %
+        ++ operator(s) returns an operator object with external name `s',
+        ++ and of arbitrary arity.
+      operator: (S,NonNegativeInteger) -> %
+        ++ operator(s,n) returns an operator object with external 
+        ++ name `s', and of arity `n'.
+  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}