Heuristics for completion in automatic proofs by structural induction

Authors:
Olav Lysne
Affiliations:
Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, N-0316 OSLO, Norway
Venue:
Nordic Journal of Computing
Year:
1994

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Abstract

A method for proof by structural induction is studied, and problems of automatizing the method is investigated. We specially consider the equational part of such proofs and we observe that the ability to cope with possibly infinite searches for non-existent equational proofs is crucial. Completion as a means to find an equational proof of equivalence of two given terms is studied. By heuristics we weaken the requirements of completeness on the resulting set, and thereby present modifications of both standard completion and ordered completion which guarantee termination.