Proving Equalities in a Commutative Ring Done Right in Coq

Grégoire, Benjamin; Mahboubi, Assia

doi:10.1007/11541868_7

Cited by 70 publications

(80 citation statements)

References 8 publications

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“…The data structure used by the Coq validator is a a modified Hörner form provided by the ring tactic [GM05]. We tried another implementation based on lists of monomials, but the computation time was similar.…”

Section: Benchmarkmentioning

confidence: 99%

Formalization of Wu’s Simple Method in Coq

Génevaux

Narboux

Schreck

2011

Certified Programs and Proofs

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Section: Benchmarkmentioning

confidence: 99%

Formalization of Wu’s Simple Method in Coq

Génevaux

Narboux

Schreck

2011

Certified Programs and Proofs

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“…Potential applications include the design of reflective tactics, which encode decision procedures in Coq, and allow to achieve smaller and faster proofs, see e.g. [16] for a reflective tactic based on rewriting. The encoding is also of interest for confluent term rewriting systems, because it allows to defer the proof of confluence, or equivalently of functionality of its graph; this allows for example to rely on termination to prove confluence.…”

Section: Applications To Relationsmentioning

confidence: 99%

Defining and Reasoning About Recursive Functions: A Practical Tool for the Coq Proof Assistant

Barthe

Forest

Pichardie

et al. 2006

Functional and Logic Programming

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Abstract. We present a practical tool for defining and proving properties of recursive functions in the Coq proof assistant. The tool generates from pseudo-code the graph of the intended function as an inductive relation. Then it proves that the relation actually represents a function, which is by construction the function that we are trying to define. Then, we generate induction and inversion principles, and a fixpoint equation for proving other properties of the function. Our tool builds upon stateof-the-art techniques for defining recursive functions, and can also be used to generate executable functions from inductive descriptions of their graph. We illustrate the benefits of our tool on two case studies.

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“…First, we can rely on an external tool, written in an other programming language than Coq, that builds a Coq proof term for each formula it can prove. The main limit of this approach is the size of the exchanged proof term, especially when many rewriting steps are required [17]. Second, we can verify the prover by directly programming it in Coq and mechanically proving its soundness.…”

Section: Introductionmentioning

confidence: 99%