AC Dependency Pairs Revisited
نویسندگان
چکیده
Rewriting modulo AC, i.e., associativity and/or commutativity of certain symbols, is among the most frequently used extensions of term rewriting by equational theories. In this paper we present a generalization of the dependency pair framework for termination analysis to rewriting modulo AC. It subsumes existing variants of AC dependency pairs, admits standard dependency graph analyses, and in particular enjoys the minimality property in the standard sense. As a direct benefit, important termination techniques are easily extended; we describe usable rules and the subterm criterion for AC termination, which properly generalize the non-AC versions. We also perform these extensions within IsaFoR – the Isabelle formalization of rewriting – and thereby provide the first formalization of AC dependency pairs. Consequently, our certifier CeTA now supports checking proofs of AC termination. 1998 ACM Subject Classification F.3.1 Specifying and Verifying and Reasoning about Programs, F.4.1 Mathematical Logic, F.4.2 Grammars and Other Rewriting Systems
منابع مشابه
Termination , AC - Termination and Dependency Pairs of Term Rewriting Systems
Recently, Arts and Giesl introduced the notion of dependency pairs, which gives effective methods for proving termination of term rewriting systems (TRSs). In this thesis, we extend the notion of dependency pairs to AC-TRSs, and introduce new methods for effectively proving AC-termination. Since it is impossible to directly apply the notion of dependency pairs to AC-TRSs, we introduce the head ...
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