Reflecting Proofs in First-Order Logic with Equality

Contejean, Evelyne; Corbineau, Pierre

doi:10.1007/11532231_2

Cited by 19 publications

(13 citation statements)

References 8 publications

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“…Unlike intuition, our tactic is unable to return a simplified goal when it cannot solve it completely, and in that sense it can be considered as less powerful. However, intuition's performance often becomes an issue in practice 6 , therefore we are convinced that the two tactics can prove really complementary in practice, with intuition being used as a simplifier and our tactic as a solver.…”

Section: Discussion and Limitationsmentioning

confidence: 92%

“…On the other hand, coarse-grained traces make proof reconstruction much harder since all implicit steps must be implemented in the proof assistant, for instance using reflection. Looking for an intermediate approach, Corbineau and Contejean [6] and Contejean et al [7] proposed integrations mixing traces and reflection.…”

Section: A Mixed Approach Based On Reflectionmentioning

confidence: 99%

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Improving Coq Propositional Reasoning Using a Lazy CNF Conversion Scheme

Lescuyer

Conchon

2009

Frontiers of Combining Systems

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Abstract. In an attempt to improve automation capabilities in the Coq proof assistant, we develop a tactic for the propositional fragment based on the DPLL procedure. Although formulas naturally arising in interactive proofs do not require a state-of-the-art SAT solver, the conversion to clausal form required by DPLL strongly damages the performance of the procedure. In this paper, we present a reflexive DPLL algorithm formalized in Coq which outperforms the existing tactics. It is tightly coupled with a lazy CNF conversion scheme which, unlike Tseitin-style approaches, does not disrupt the procedure. This conversion relies on a lazy mechanism which requires slight adaptations of the original DPLL. As far as we know, this is the first formal proof of this mechanism and its Coq implementation raises interesting challenges.

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Section: Discussion and Limitationsmentioning

confidence: 92%

Section: A Mixed Approach Based On Reflectionmentioning

confidence: 99%

Improving Coq Propositional Reasoning Using a Lazy CNF Conversion Scheme

Lescuyer

Conchon

2009

Frontiers of Combining Systems

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“…5 In our experiments we also interpret negated conjectures as goal equations. We set the following flags for KBCV and MKBTT:…”

Section: Methodsmentioning

confidence: 99%

Recording Completion for Certificates in Equational Reasoning

Sternagel

Winkler

Zankl

2015

Proceedings of the 2015 Conference on Certified Programs and Proofs

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We introduce recording completion, a variant of Knuth-Bendix completion which facilitates the construction of certificates for various equational logic proofs (completion proofs, entailment proofs and dis-proofs). The approach generalizes to more powerful variants of completion such as ordered completion and AC completion. We implemented recording completion in the tools KBCV and MKBTT. Both tools allow to choose among different formats of proof certificates, namely conversions, proof trees, and conversions with history. We report on experimental results in which all generated certificates have been verified by the trustable checker CeTA.

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“…Several approaches have been proposed to integrate new decision procedures in sceptical proof assistants for various theories. First-order provers have been integrated in Isabelle [25], HOL [18] or Coq [9]. These works rely generally on resolution proof trees.…”

Section: Related Workmentioning

confidence: 99%