Rewrite methods for clausal and non-clausal theorem proving

Jieh Hsiang, Nachum Dershowitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Effective theorem provers are essential for automatic verification and generation of programs. The conventional resolution strategies, albeit complete, are inefficient. On the other hand, special purpose methods, such as term rewriting systems for solving word problems, are relatively efficient but applicable to only limited classes of problems. In this paper, a simple canonical set of rewrite rules for Boolean algebra is presented. Based on this set of rules, the notion of term rewriting systems is generalized to provide complete proof strategies for first order predicate calculus. The methods are conceptually simple and can frequently utilize lemmas in proofs. Moreover, when the variables of the predicates involve some domain that has a canonical system, that system can be incorporated as rewrite rules, with the algebraic simplifications being done simultaneously with the merging of clauses. This feature is particularly useful in program verification, data type specification, and programming language design, where axioms can be expressed as equations (rewrite rules). Preliminary results from our implementation indicate that the methods are space-efficient with respect to the number of rules generated (as compared to the number of resolvents in resolution provers).

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 10th Colloquium
EditorsJosep Diaz
PublisherSpringer Verlag
Pages331-346
Number of pages16
ISBN (Print)9783540123170
DOIs
StatePublished - 1983
Externally publishedYes
Event10th International Colloquium on Automata, Languages and Programming, ICALP 1983 - Barcelona, Spain
Duration: 18 Jul 198322 Jul 1983

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume154 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th International Colloquium on Automata, Languages and Programming, ICALP 1983
Country/TerritorySpain
CityBarcelona
Period18/07/8322/07/83

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