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Nominal Unification from a Higher-Order Perspective

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Rewriting Techniques and Applications (RTA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5117))

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Abstract

Nominal Logic is an extension of first-order logic with equality, name-binding, name-swapping, and freshness of names. Contrarily to higher-order logic, bound variables are treated as atoms, and only free variables are proper unknowns in nominal unification. This allows “variable capture”, breaking a fundamental principle of lambda-calculus. Despite this difference, nominal unification can be seen from a higher-order perspective. From this view, we show that nominal unification can be reduced to a particular fragment of higher-order unification problems: higher-order patterns unification. This reduction proves that nominal unification can be decided in quadratic deterministic time.

This research has been partially founded by the CICYT research project TIN2007-68005-C04-01/02/03.

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Authors and Affiliations

  1. Artificial Intelligence Research Institute (IIIA), Spanish Council for Scientific Research (CSIC), Barcelona, Spain

    Jordi Levy

  2. Departament d’Informàtica i Matemàtica Aplicada (IMA), Universitat de Girona (UdG), Girona, Spain

    Mateu Villaret

Authors
  1. Jordi Levy
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  2. Mateu Villaret
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Andrei Voronkov

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Levy, J., Villaret, M. (2008). Nominal Unification from a Higher-Order Perspective. In: Voronkov, A. (eds) Rewriting Techniques and Applications. RTA 2008. Lecture Notes in Computer Science, vol 5117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70590-1_17

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  • DOI: https://doi.org/10.1007/978-3-540-70590-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70588-8

  • Online ISBN: 978-3-540-70590-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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