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The Permutative λ-Calculus

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7180))

Abstract

We introduce the permutative λ-calculus, an extension of λ-calculus with three equations and one reduction rule for permuting constructors, generalising many calculi in the literature, in particular Regnier’s sigma-equivalence and Moggi’s assoc-equivalence. We prove confluence modulo the equations and preservation of beta-strong normalisation (PSN) by means of an auxiliary substitution calculus. The proof of confluence relies on M-developments, a new notion of development for λ-terms.

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Author information

Authors and Affiliations

  1. INRIA and LIX, École Polytechnique, France

    Beniamino Accattoli

  2. PPS, CNRS and Université Paris-Diderot, France

    Delia Kesner

Authors
  1. Beniamino Accattoli
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  2. Delia Kesner
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Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, 98052-6399, Redmond, WA, USA

    Nikolaj Bjørner

  2. School of computer Science, University of Manchester, Kilburn Building, Oxford Road, MP13 9PL, Manchester, UK

    Andrei Voronkov

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Accattoli, B., Kesner, D. (2012). The Permutative λ-Calculus. In: Bjørner, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2012. Lecture Notes in Computer Science, vol 7180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28717-6_5

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  • DOI: https://doi.org/10.1007/978-3-642-28717-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28716-9

  • Online ISBN: 978-3-642-28717-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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