From formal proofs to mathematical proofs: a safe, incremental way for building in first-order decision procedures
Logic in Computer Science
2008-12-18 v1
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.
Cite
@article{arxiv.0804.3762,
title = {From formal proofs to mathematical proofs: a safe, incremental way for building in first-order decision procedures},
author = {Frédéric Blanqui and Jean-Pierre Jouannaud and Pierre-Yves Strub},
journal= {arXiv preprint arXiv:0804.3762},
year = {2008}
}