arXiv subjects

David Delahaye

Publications and source records attributed to David Delahaye.

5 recordsLinked to original sources

arXiv2026

A Strategy Language for Controlled Proof Search

This paper introduces the strategy language of Pgeon, a meta-prover with a clear separation between inference rules and proof search. We give the semantics of strategies as functions over proof states, and of the operators that are used to combine them, allowing for sequential composition, choice, repetition and interleaving of strategies. This language is designed to handle the challenge of fair proof search in semi-decidable logics, where simple depth-first exploration of the proof space is not guaranteed to achieve completeness. We showcase the expressiveness and effectiveness of the approach through case studies in first-order and modal logics.

cs.LO↗

arXiv2023

Dedukti: a Logical Framework based on the $λ$$Π$-Calculus Modulo Theory

Dedukti is a Logical Framework based on the $λ$$Π$-Calculus Modulo Theory. We show that many theories can be expressed in Dedukti: constructive and classical predicate logic, Simple type theory, programming languages, Pure type systems, the Calculus of inductive constructions with universes, etc. and that permits to used it to check large libraries of proofs developed in other proof systems: Zenon, iProver, FoCaLiZe, HOL Light, and Matita.

cs.LO↗

arXiv2015

Recovering Intuition from Automated Formal Proofs using Tableaux with Superdeduction

We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and uses the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. We present two implementations of this method, which consist of extensions of the Zenon automated theorem prover. The first implementation is a version dedicated to the set theory of the B formal method, while the second implementation is a generic version able to deal with any first order theory. We also provide several examples of problems, which can be handled by these tools and which come from different theories, such as the B set theory or theories of the TPTP library.

cs.LO↗

arXiv2015

Tableaux Modulo Theories Using Superdeduction

We propose a method that allows us to develop tableaux modulo theories using the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. This method is presented in the framework of the Zenon automated theorem prover, and is applied to the set theory of the B method. This allows us to provide another prover to Atelier B, which can be used to verify B proof rules in particular. We also propose some benchmarks, in which this prover is able to automatically verify a part of the rules coming from the database maintained by Siemens IC-MOL. Finally, we describe another extension of Zenon with superdeduction, which is able to deal with any first order theory, and provide a benchmark coming from the TPTP library, which contains a large set of first order problems.

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arXiv2005

Diophantus' 20th Problem and Fermat's Last Theorem for n=4: Formalization of Fermat's Proofs in the Coq Proof Assistant

We present the proof of Diophantus' 20th problem (book VI of Diophantus' Arithmetica), which consists in wondering if there exist right triangles whose sides may be measured as integers and whose surface may be a square. This problem was negatively solved by Fermat in the 17th century, who used the "wonderful" method (ipse dixit Fermat) of infinite descent. This method, which is, historically, the first use of induction, consists in producing smaller and smaller non-negative integer solutions assuming that one exists; this naturally leads to a reductio ad absurdum reasoning because we are bounded by zero. We describe the formalization of this proof which has been carried out in the Coq proof assistant. Moreover, as a direct and no less historical application, we also provide the proof (by Fermat) of Fermat's last theorem for n=4, as well as the corresponding formalization made in Coq.

cs.LO↗