Rewriting with a nondeterministic choice operator : From algebra to proofs

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


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.


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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