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arXiv · 0804.3762

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

Frédéric Blanqui·Jean-Pierre Jouannaud·Pierre-Yves Strub
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Abstract

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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Frédéric Blanqui, Jean-Pierre Jouannaud, Pierre-Yves Strub. 2008-04-23. From formal proofs to mathematical proofs: a safe, incremental way for building in first-order decision procedures. https://arxiv.org/abs/0804.3762

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