package coq-hoare-tut

Hoare logics are "program logics" suitable for reasoning about imperative programs. This work is both an introduction to Hoare logic and a demo illustrating Coq nice features. It formalizes the generation of PO (proof obligations) in a Hoare logic for a very basic imperative programming language. It proves the soundness and the completeness of the PO generation both in partial and total correctness. At last, it examplifies on a very simple example (a GCD computation) how the PO generation can simplify concrete proofs. Coq is indeed able to compute PO on concrete programs: we say here that the generation of proof obligations is reflected in Coq. Technically, the PO generation is here performed through Dijkstra's weakest-precondition calculus.