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Theses

Integrating Automated Theorem Provers in Proof Assistants

Abstract : Lambdapi is a proof assistant that allows users to construct a proof of a given theorem in a universal language based on the lambda-pi-calculus. The goal of this thesis is to add more automation to Lambdapi to gain more time and effort for the users. This thesis presents three contributions associated with the integration of automated provers in proof assistants. The first contribution consists of the implementation of a tactic that calls automated provers from Lambdapi by using an external platform called Why3. Usually, automated provers do not generate a complete certificate of a given formula, thus, the second contribution presented in this thesis is the reconstruction in Lambdapi of proofs generated by first-order automated provers implemented in a tool called Ekstrakto. Finally, automated provers often perform some transformations on the formula that they are trying to solve. Among these transformations, we can find Skolemization steps. The last contribution is devoted to the certification of Skolemization steps performed by the automated provers in order to have a complete reconstruction. This has been implemented in a tool called Skonverto.
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https://tel.archives-ouvertes.fr/tel-03387912
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Submitted on : Friday, October 22, 2021 - 9:43:12 AM
Last modification on : Wednesday, March 16, 2022 - 3:43:45 AM

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  • HAL Id : tel-03387912, version 2

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Yacine El Haddad. Integrating Automated Theorem Provers in Proof Assistants. Logic in Computer Science [cs.LO]. Université Paris-Saclay, 2021. English. ⟨NNT : 2021UPASG052⟩. ⟨tel-03387912v2⟩

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