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diff --git a/src/algebra/term.spad.pamphlet b/src/algebra/term.spad.pamphlet new file mode 100644 index 00000000..532bd720 --- /dev/null +++ b/src/algebra/term.spad.pamphlet @@ -0,0 +1,132 @@ +\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} |