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Termination Modulo Combinations of Equational Theories

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Frontiers of Combining Systems (FroCoS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5749))

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Abstract

Rewriting with rules R modulo axioms E is a widely used technique in both rule-based programming languages and in automated deduction. Termination methods for rewriting systems modulo specific axioms E (e.g., associativity-commutativity) are known. However, much less seems to be known about termination methods that can be modular in the set E of axioms. In fact, current termination tools and proof methods cannot be applied to commonly occurring combinations of axioms that fall outside their scope. This work proposes a modular termination proof method based on semantics- and termination-preserving transformations that can reduce the proof of termination of rules R modulo E to an equivalent proof of termination of the transformed rules modulo a typically much simpler set B of axioms. Our method is based on the notion of variants of a term recently proposed by Comon and Delaune. We illustrate its practical usefulness by considering the very common case in which E is an arbitrary combination of associativity, commutativity, left- and right-identity axioms for various function symbols.

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Author information

Authors and Affiliations

  1. LCC, Universidad de Málaga, Spain

    Francisco Durán

  2. DSIC, Universidad Politécnica de Valencia, Spain

    Salvador Lucas

  3. CS Dept., University of Illinois at Urbana-Champaign, IL, USA

    José Meseguer

Authors
  1. Francisco Durán
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  2. Salvador Lucas
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  3. José Meseguer
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Università degli Studi di Milano, Via Comelico 39, 20135, Milano, Italy

    Silvio Ghilardi

  2. Dipartemento di Ingegneria e Scienza dell’Informazione, Università di Trento, Facoltà di Scienze, Via Sommarive 14, 38050, Povo, Trento, Italy

    Roberto Sebastiani

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Durán, F., Lucas, S., Meseguer, J. (2009). Termination Modulo Combinations of Equational Theories. In: Ghilardi, S., Sebastiani, R. (eds) Frontiers of Combining Systems. FroCoS 2009. Lecture Notes in Computer Science(), vol 5749. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04222-5_15

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  • DOI: https://doi.org/10.1007/978-3-642-04222-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04221-8

  • Online ISBN: 978-3-642-04222-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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