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Communication Dans Un Congrès Année : 2008

From formal proofs to mathematical proofs: a safe, incremental way for building in first-order decision procedures

Résumé

We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order decision procedures: deduction is still in charge of the CIC kernel, while computation is outsourced to dedicated first-order decision procedures that can be taken from the shelves provided they deliver a proof certificate. The soundness of the whole system becomes an incremental property following from the soundness of the certificate checkers and that of the kernel. A detailed example shows that the resulting style of proofs becomes closer to that of the working mathematician.
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Dates et versions

inria-00275382 , version 1 (23-04-2008)

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Citer

Frédéric Blanqui, Jean-Pierre Jouannaud, Pierre-Yves Strub. From formal proofs to mathematical proofs: a safe, incremental way for building in first-order decision procedures. 5th IFIP International Conference on Theoretical Computer Science - TCS 2008, Sep 2008, Milan, Italy. ⟨10.1007/978-0-387-09680-3_24⟩. ⟨inria-00275382⟩
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