Tit-Coq (1948) de Gratien Gélinas

Développement modulaire de théories et gestion de l'espace de nom pour l'assistant de preuve Coq. (Modular development of theories and name-space management for the Coq proof assistant)

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Coq in Coq

We formalize the deenition and the metatheory of the Calculus of Constructions (CC) using the proof assistant Coq. In particular, we prove strong nor-malization and decidability of type inference. From the latter proof, we extract a certiied Objective Caml program which performs type inference in CC and use this code to build a small-scale certiied proof-checker.

Algèbres de Kleene, réécriture modulo AC et circuits en coq. (Kleene algebra, Rewriting modulo AC and Circuits in Coq)

ing from the implementation. The semantics of a circuit defines precisely its behaviour, but may be too precise, e.g., it may leak some internal implementation details (recall that it is defined by induction over the structure of the circuit). The standard technique [112] to prove that circuits meet some high-level specifications is to prove the following kind of entailment, where the high-leve...

Programmation fonctionnelle certifiée : L'extraction de programmes dans l'assistant Coq. (Certified functional programming : Program extraction within Coq proof assistant)

This work concerns the generation of programs which are certified to be correct byconstruction. These programs are obtained by extracting relevant information from construc-tive proofs made with the Coq proof assistant.Such a translation, named “extraction”, of constructive proofs into functional programsis not new, and corresponds to an isomorphism known as Curry-Howard’s. ...

De nouveaux outils pour calculer avec des inductifs en Coq. (New tool to compute with inductive in Coq)