Computer Software
Print ISSN : 0289-6540
Lemma Generation Method in Rewriting Induction for Constrained Term Rewriting Systems
Naoki NAKABAYASHINaoki NISHIDAKeiichirou KUSAKARIToshiki SAKABEMasahiko SAKAI
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2011 Volume 28 Issue 1 Pages 1_173-1_189

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Abstract

Recently, the rewriting induction, which is one of induction principles for proving inductive theorems of an equational theory, has been extended to deal with constrained term rewriting systems. It has been applied to developing a method for proving equivalence of imperative programs. For proving inductive theorem, there are many cases where appropriate lemmas need to be added. To this end, several methods for lemma generation in term rewriting have been studied. However, these existing methods are not effective for cases in constrained term rewriting. In this paper, we propose a framework of lemma generation for constrained term rewriting systems, in which we formalize the correspondences of terms in divergent equations by means of given constrained rewrite rules. We also show an instance of the formalization, and show that due to the framework with the instance, there is no necessity to give lemmas in advance in the examples shown by the previous works.

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© Japan Society for Software Science and Technology 2011
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