Systèmes de preuve interopérables.

Abstract : Developments of formal specifications and proofs have spectacularly blossomed over the last decades, hosted by a diversity of frameworks, systems and communities. And yet, the heterogeneity of these environments has hindered some fundamental steps in the scientific process: the sharing and reuse of results. This dissertation proposes a way of distributing the same formal development between various proof systems, thus augmenting their interoperability. Chapters 1 and 2 present the logical framework that is used to centralize the formal specifications and proofs. In particular, it is based on a variation of the λµ˜ µ-calculus designed to support interactive proof developments. Chapters 3 and 4 develop the rewriting and categorical structures required to give strict semantics to proof languages. Based upon these first results, chapters 5 and 6 respectively use a type system for proof languages to secure a type safety proposition, and expose a series of translations of the centralized developments into other major formal frameworks. Among other things, the latter contributes to a simplification of Frege Hilbert deduction systems. Finally, chapters 7 and 8 deal with the problems arising from the implementation of our centralized proof development system. Of special notice is the presentation of a theory of classes, that allows for the finite first-order expression of axiom schemes.
Mots-clés : Preuve interopérable
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Florent Kirchner. Systèmes de preuve interopérables.. Informatique [cs]. Ecole Polytechnique X, 2007. Français. ⟨pastel-00003192⟩

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