@MISC{Goguen_scriticalpairs, author = {Joseph Goguen and Monica Marcus}, title = {Scritical Pairs and Sunification}, year = {} }

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Abstract

A general critical pair theory is given for rewriting many sorted terms with overloaded operations modulo equations. A main notion is sunification, which yields a set of scritical pairs, such that a set of rules is locally confluent iff they all converge. We prove a sufficient condition for overlaps to work instead of sunification, show that complete sunifier sets always exist, and are finite in important special cases. We also sketch a generalization based on category theory, for rewriting in free objects, e.g., algebras with additional structure, such as many sorts, ordered sorts, equationally defined subsorts, or continuity.