Multi-Context Rewriting Induction with Termination Checkers

Haruhiko SATO  Masahito KURIHARA  

IEICE TRANSACTIONS on Information and Systems   Vol.E93-D   No.5   pp.942-952
Publication Date: 2010/05/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E93.D.942
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Formal Approach)
Category: Term Rewriting Systems
equational theorem proving,  term rewriting systems,  mathematical induction,  rewriting induction,  multi-completion,  

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Inductive theorem proving plays an important role in the field of formal verification of systems. The rewriting induction (RI) is a method for inductive theorem proving proposed by Reddy. In order to obtain successful proofs, it is very important to choose appropriate contexts (such as in which direction each equation should be oriented) when applying RI inference rules. If the choice is not appropriate, the procedure may diverge or the users have to come up with several lemmas to prove together with the main theorem. Therefore we have a good reason to consider parallel execution of several instances of the rewriting induction procedure, each in charge of a distinguished single context in search of a successful proof. In this paper, we propose a new procedure, called multi-context rewriting induction, which efficiently simulates parallel execution of rewriting induction procedures in a single process, based on the idea of the multi-completion procedure. By the experiments with a well-known problem set, we discuss the effectiveness of the proposed procedure when searching along various contexts for a successful inductive proof.