Completion for Rewriting Modulo a Congruence

We present completion methods for rewriting modulo a congruence, generalizing previous methods by Peterson and Stickel (1981) and Jouannaud and Kirchner (1986). We formalize our methods as equational inference systems and describe techniques for reasoning about such systems.

[1]  Nachum Dershowitz,et al.  Critical-pair criteria for the Knuth-Bendix completion procedure , 1986, SYMSAC '86.

[2]  Jieh Hsiang,et al.  Refutational Theorem Proving Using Term-Rewriting Systems , 1985, Artif. Intell..

[3]  Hélène Kirchner,et al.  Completion of a Set of Rules Modulo a Set of Equations , 1986, SIAM J. Comput..

[4]  Franz Winkler.  The Church-Rosser property in computer algebra and special theorem proving: an investigation of critical-pair/completion algorithms (Ph.D. thesis) , 1984, SIGS.

[5]  Mark E. Stickel,et al.  A Unification Algorithm for Associative-Commutative Functions , 1981, JACM.

[6]  Wayne Snyder,et al.  A General Complete E-Unification Procedure , 1987, RTA.

[7]  Gerard Huet,et al.  Conflunt reductions: Abstract properties and applications to term rewriting systems , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[8]  Gérard P. Huet,et al.  Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems , 1980, J. ACM.

[9]  LEO BACHMAIR,et al.  Termination Orderings for Associative-Commutative Rewriting Systems , 1985, J. Symb. Comput..

[10]  D. Knuth,et al.  Simple Word Problems in Universal Algebras , 1983 .

[11]  Mark E. Stickel.  A Complete Unification Algorithm for Associative-Commutative Functions , 1975, IJCAI.

[12]  Pierre Lescanne,et al.  Termination of Rewriting Systems by Polynomial Interpretations and Its Implementation , 1987, Sci. Comput. Program..

[13]  Jean-Pierre Jouannaud,et al.  Confluent and Coherent Equational Term Rewriting Systems: Application to Proofs in Abstract Data Types , 1983, CAAP.

[14]  J. Hullot.  A Catalogue of Canonical Term Rewriting Systems. , 1980 .

[15]  Nachum Dershowitz,et al.  Orderings for Equational Proofs , 1986, LICS.

[16]  François Fages,et al.  Complete Sets of Unifiers and Matchers in Equational Theories , 1983, CAAP.

[17]  James R. Slagle,et al.  Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity , 1974, JACM.

[18]  Paliath Narendran,et al.  Only Prime Superpositions Need be Considered in the Knuth-Bendix Completion Procedure , 1988, J. Symb. Comput..

[19]  Nachum Dershowitz,et al.  Critical Pair Criteria for Completion , 1988, J. Symb. Comput..

[20]  Leo Bachmair.  Proof methods for equational theories , 1987 .

[21]  Claude Kirchner.  Computing Unification Algorithms , 1986, LICS.

[22]  Mark E. Stickel,et al.  Complete Sets of Reductions for Some Equational Theories , 1981, JACM.

[23]  Zohar Manna,et al.  Proving termination with multiset orderings , 1979, CACM.

[24]  Jörg H. Siekmann,et al.  Universal Unification , 1982, GWAI.