Slothrop: Knuth-Bendix completion with a modern termination checker

  • Authors:

  • Ian Wehrman;Aaron Stump;Edwin Westbrook

  • Affiliations:

  • Dept. of Computer Science and Engineering, Washington University in St. Louis, St. Louis, MO;Dept. of Computer Science and Engineering, Washington University in St. Louis, St. Louis, MO;Dept. of Computer Science and Engineering, Washington University in St. Louis, St. Louis, MO

  • Venue:
  • RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
  • Year:
  • 2006

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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.