Abstract
A Knuth-Bendix completion procedure is parametrized by a reduction ordering used to ensure termination of intermediate and resulting rewriting systems. While in principle any reduction ordering can be used, modern completion tools typically implement only Knuth-Bendix and path orderings. Consequently, the theories for which completion can possibly yield a decision procedure are limited to those that can be oriented with a single path order.
In this paper, we present a variant on the Knuth-Bendix completion procedure in which no ordering is assumed. Instead we rely on a modern termination checker to verify termination of rewriting systems. The new method is correct if it terminates; the resulting rewrite system is convergent and equivalent to the input theory. Completions are also not just ground-convergent, but fully convergent. We present an implementation of the new procedure, Slothrop, which automatically obtains such completions for theories that do not admit path orderings.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Bachmair, L.: Canonical Equational Proofs. In: Progress in Theoretical Computer Science. Birkhäuser (1991)
Bachmair, L., Dershowitz, N., Plaisted, D.A.: Completion Without Failure. In: Resolution of Equations in Algebraic Structures, Rewriting Techniques, vol. 2, pp. 1–30. Academic Press, London (1989)
Contejean, E., Marché, C., Urbain, X.: CiME3 (2004), available at: http://cime.lri.fr/
Filliâtre, J.-C.: Ocaml data structures, available at: http://www.lri.fr/~filliatr/software.en.html
Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Automated Termination Proofs with AProVE. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 210–220. Springer, Heidelberg (2004)
Huet, G.: A Complete Proof of Correctness of the Knuth-Bendix Completion Algorithm. Journal of Computer and System Science 23(1), 11–21 (1981)
Knuth, D., Bendix, P.: Simple Word Problems in Universal Algebras. In: Leech, J. (ed.) Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, Oxford (1970)
Löchner, B., Hillenbrand, T.: The Next Waldmeister Loop. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 486–500. Springer, Heidelberg (2002)
Sattler-Klein, A.: About Changing the Ordering During Knuth-Bendix Completion. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds.) STACS 1994. LNCS, vol. 775, pp. 176–186. Springer, Heidelberg (1994)
Stump, A., Löchner, B.: Knuth-Bendix Completion of Theories of Commuting Group Endomorphisms. In: Information Processing Letters (to appear, 2006)
Wehrman, I., Stump, A.: Mining Propositional Simplification Proofs for Small Validating Clauses. In: Armando, A., Cimatti, A. (eds.) 3rd International Workshop on Pragmatics of Decision Procedures in Automated Reasoning (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wehrman, I., Stump, A., Westbrook, E. (2006). Slothrop: Knuth-Bendix Completion with a Modern Termination Checker. In: Pfenning, F. (eds) Term Rewriting and Applications. RTA 2006. Lecture Notes in Computer Science, vol 4098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11805618_22
Download citation
DOI: https://doi.org/10.1007/11805618_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36834-2
Online ISBN: 978-3-540-36835-9
eBook Packages: Computer ScienceComputer Science (R0)