This project is the one requested for the MPRI course "Foundation of proof systems" (MPRI 2.7.1).
--
It contains two independant Coq proofs:
-
arith.v contains a formalization of Peano and Heyting arithmetic, a proof that Heyting arithmetic is consistent in Coq (with reflection of Heyting arithmetic), and the proof through Friedman-translation that Peano arithmetic is Pi_0^2-conservative over Heyting arithmetic. See the task description (in French) (mirror).
-
while.v contains verified computation of the weakest preconditions for the language While. See the task description (in French) (mirror).