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International Conference on Rewriting Techniques and Applications

RTA 2007: Term Rewriting and Applications pp 78–92Cite as

Confluence of Pattern-Based Calculi

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4533))

Abstract

Different pattern calculi integrate the functional mechanisms from the λ-calculus and the matching capabilities from rewriting. Several approaches are used to obtain the confluence but in practice the proof methods share the same structure and each variation on the way pattern-abstractions are applied needs another proof of confluence.

We propose here a generic confluence proof where the way pattern-abstractions are applied is axiomatized. Intuitively, the conditions guarantee that the matching is stable by substitution and by reduction.

We show that our approach directly applies to different pattern calculi, namely the lambda calculus with patterns, the pure pattern calculus and the rewriting calculus. We also characterize a class of matching algorithms and consequently of pattern-calculi that are not confluent.

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Authors and Affiliations

  1. Université Nancy 2 & Université Henri Poincaré & LORIA, BP 239, F-54506 Vandoeuvre-lès-Nancy, France

    Horatiu Cirstea & Germain Faure

Authors
  1. Horatiu Cirstea
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  2. Germain Faure
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Franz Baader

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© 2007 Springer-Verlag Berlin Heidelberg

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Cirstea, H., Faure, G. (2007). Confluence of Pattern-Based Calculi. In: Baader, F. (eds) Term Rewriting and Applications. RTA 2007. Lecture Notes in Computer Science, vol 4533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73449-9_8

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  • DOI: https://doi.org/10.1007/978-3-540-73449-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73447-5

  • Online ISBN: 978-3-540-73449-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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