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Matching Modulo Superdevelopments Application to Second-Order Matching

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4246))

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Abstract

To perform higher-order matching, we need to decide the βη-equivalence on λ-terms. The first way to do it is to use simply typed λ-calculus and this is the usual framework where higher-order matching is performed. Another approach consists in deciding a restricted equivalence based on finite superdevelopments. We consider higher-order matching modulo this equivalence over untyped λ-terms for which we propose a terminating, sound and complete matching algorithm.

This is in particular of interest since all second-order β-matches are matches modulo superdevelopments. We further propose a restriction to second-order matching that gives exactly all second-order matches.

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Author information

Authors and Affiliations

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

    Germain Faure

Authors
  1. Germain Faure
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Editors and Affiliations

  1. LIX (CNRS, UMR 7161), École Polytechnique, 91128, Palaiseau, France

    Miki Hermann

  2. University of Manchester, UK

    Andrei Voronkov

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Faure, G. (2006). Matching Modulo Superdevelopments Application to Second-Order Matching. In: Hermann, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2006. Lecture Notes in Computer Science(), vol 4246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11916277_5

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  • DOI: https://doi.org/10.1007/11916277_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-48281-9

  • Online ISBN: 978-3-540-48282-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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