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Generalising Diverging Sequences of Rewrite Rules by Synthesising New Sorts

  • Conference paper
Functional Programming, Glasgow 1990

Part of the book series: Workshops in Computing ((WORKSHOPS COMP.))

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Abstract

Confluence, termination and typing are crucial issues in term rewriting. When a set of rules is terminating and confluent, then each term has a unique normal form. The Knuth-Bendix completion algorithm [KB70], given a termination ordering, tests for the confluence property by generating a confluent set of rules from a given set of equations. The algorithm is not guaranteed to terminate, even when the word problem defined by the given system of equations is decidable. When the completion (semi) algorithm diverges and results in an infinite sequence of confluent rewrite rules, then we only have a semi-decision procedure for the word problem.

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References

  1. J. Hoperoft, D. Ullman, Introduction to automata theory, languages, and computation, Addison-Wesley, 1979.

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  2. St. Lange, Towards a Set of Inference Rules for Solving Divergence in Knuth-Bendix Completion, Proc. Analogical and Inductive Inference ‘89, GDR, Lecture Notes in Computer Science 367, Springer-Verlag, 1989.

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  4. M. Thomas, K.P. Jantke, Inductive Inference for Solving Divergence in Knuth-Bendix Completion, Proc. Analogical and Inductive Inference ‘89, GDR, Lecture Notes in Computer Science 367, Springer-Verlag,1989.

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Author information

Authors and Affiliations

  1. Dept. of Computing Science, University of Glasgow, UK

    Muffy Thomas & Phil Watson

Authors
  1. Muffy Thomas
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  2. Phil Watson
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Editor information

Simon L. Peyton Jones Graham Hutton Carsten Kehler Holst

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© 1991 Springer-Verlag Berlin Heidelberg

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Thomas, M., Watson, P. (1991). Generalising Diverging Sequences of Rewrite Rules by Synthesising New Sorts. In: Jones, S.L.P., Hutton, G., Holst, C.K. (eds) Functional Programming, Glasgow 1990. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3810-5_23

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  • DOI: https://doi.org/10.1007/978-1-4471-3810-5_23

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19667-9

  • Online ISBN: 978-1-4471-3810-5

  • eBook Packages: Springer Book Archive

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