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Proving inductive theorems based on term rewriting systems

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Algebraic and Logic Programming (ALP 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 343))

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Abstract

Sufficient criteria for an equation to be in the inductive theory of a term rewriting system are given. Inspecting only special critical pairs, we need not require the underlying system to be confluent, not even on ground terms. We are able to deal with equations which — if viewed as rules — are possibly not terminating if added to the given rewrite system; we have to restrict, however, their use in the induction process. Modular use of lemmata, already known inductive theorems, is incorporated into the results. As examples we treat natural number arithmetic, sorting lists of natural numbers, and sorting lists over arbitrary data structures.

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Author information

Authors and Affiliations

  1. Technische Universität Berlin, Fachbereich 20 (Informatik), FR 6-2, Franklinstr. 28/29, D - 1000, Berlin 10

    Ralf-Detlef Kutsche

Authors
  1. Dieter Hofbauer
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  2. Ralf-Detlef Kutsche
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Editor information

J. Grabowski P. Lescanne W. Wechler

Additional information

Dedicated to the 50th anniversary of Prof. Dirk Siefkes.

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© 1988 Akademie-Verlag Berlin

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Hofbauer, D., Kutsche, RD. (1988). Proving inductive theorems based on term rewriting systems. In: Grabowski, J., Lescanne, P., Wechler, W. (eds) Algebraic and Logic Programming. ALP 1988. Lecture Notes in Computer Science, vol 343. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50667-5_70

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  • DOI: https://doi.org/10.1007/3-540-50667-5_70

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50667-6

  • Online ISBN: 978-3-540-46063-3

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