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Reducibility of operation symbols in term rewriting systems and its application to behavioral specifications
en
Algebraic specification
Behavioral coherence
Behavioral specification
Observational transition system
Term rewriting system
Nakamura Masaki
Ogata Kazuhiro
Futatsugi Kokichi
金沢大学理工研究域電子情報学系
Journal of Symbolic Computation
45
5
551-573
2010-01-01
0747-7171
AA10460294
10.1016/j.jsc.2010.01.008
Elsevier
In this paper, we propose the notion of reducibility of symbols in term rewriting systems (TRSs). For a given algebraic specification, operation symbols can be classified on the basis of their denotations: the operation symbols for functions and those for constructors. In a model, each term constructed by using only constructors should denote an element, and functions are defined on sets formed by these elements. A term rewriting system provides operational semantics to an algebraic specification. Given a TRS, a term is called reducible if some rewrite rule can be applied to it. An irreducible term can be regarded as an answer in a sense. In this paper, we define the reducibility of operation symbols as follows: an operation symbol is reducible if any term containing the operation symbol is reducible. Non-trivial properties of context-sensitive rewriting, which is a simple restriction of rewriting, can be obtained by restricting the terms on the basis of variable occurrences, its sort, etc. We confirm the usefulness of the reducibility of operation symbols by applying them to behavioral specifications for proving the behavioral coherence property. © 2010 Elsevier Ltd. All rights reserved.