ESOP 1986: ESOP 86 pp 351-374 | Cite as

Rewriting with a nondeterministic choice operator : From algebra to proofs

  • Stéphane Kaplan
Term Rewriting
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 213)

Abstract

The privileged field of classical algebra and term rewriting systems is that of strictly deterministic systems: the confluence property is generaly assumed to hold, which ensures determinism about the result of the computations, even if there exist several different computation paths. In this paper, we develop a new formalism introducing a bounded nondeterministic choice operator ‘↑’ into algebraic specifications and related term rewriting systems; nondeterminism about the result becomes allowed in this framework. We define the algebraic and the operational aspects of such systems, and investigate their relationship. Methods à la Knuth-Bendix are developed for automatic theorem proving in such theories. Several examples are considered, including a toy concurrent language, for which non-trivial properties may be automatically proved.

Keywords

Normal Form Transitive Closure Critical Pair Classical Term Automatic Theorem Prove 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Stéphane Kaplan
    • 1
    • 2
  1. 1.Department of Applied MathematicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.LRI. Bat. 490Université des SciencesOrsayFrance

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