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Tactics for Reasoning Modulo AC in Coq

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Certified Programs and Proofs (CPP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7086))

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Abstract

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element.

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Author information

Authors and Affiliations

  1. LIG, UMR 5217, CNRS, INRIA, Grenoble, France

    Thomas Braibant & Damien Pous

Authors
  1. Thomas Braibant
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  2. Damien Pous
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Editor information

Editors and Affiliations

  1. Tsinghua University, FIT 3-603, 100084, Beijing, China

    Jean-Pierre Jouannaud

  2. Department of Computer Science, Yale University, 51 Prospect Street, 06520-8285, New Haven, CT, USA

    Zhong Shao

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Braibant, T., Pous, D. (2011). Tactics for Reasoning Modulo AC in Coq. In: Jouannaud, JP., Shao, Z. (eds) Certified Programs and Proofs. CPP 2011. Lecture Notes in Computer Science, vol 7086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25379-9_14

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  • DOI: https://doi.org/10.1007/978-3-642-25379-9_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25378-2

  • Online ISBN: 978-3-642-25379-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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