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Tactics for Reasoning modulo AC in Coq

Thomas Braibant 1 Damien Pous 2
2 PLUME - Preuves et Langages
LIP - Laboratoire de l'Informatique du Parallélisme
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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https://hal.archives-ouvertes.fr/hal-00484871
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Submitted on : Thursday, September 22, 2011 - 10:34:00 AM
Last modification on : Tuesday, October 19, 2021 - 11:16:41 PM
Long-term archiving on: : Sunday, December 4, 2016 - 8:15:02 PM

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Thomas Braibant, Damien Pous. Tactics for Reasoning modulo AC in Coq. Certified Proofs and Programs, 2011, Taiwan. pp167-182, ⟨10.1007/978-3-642-25379-9_14⟩. ⟨hal-00484871v4⟩

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