Trustworthy Tools for Trustworthy Programs: Automatic Verification of Mutually Recursive Procedures

Verification Condition Generator (VCG) tools have been effective in simplifying the task of proving programs correct. However, in the past these VCG tools have in general not themselves been mechanically proven, so any proof using and depending on these VCGs might have contained errors. In our work, we define and rigorously prove correct a VCG tool within the HOL theorem proving system, for a standard imperative language, notably containing mutually recursive procedures and expressions with side effects. Starting from a structural operational semantics of this programming language, we prove as theorems the axioms and rules of inference of a Hoare-style axiomatic semantics, verifying their soundness. This axiomatic semantics is then used to define and prove correct a VCG tool for this language. Finally, this verified VCG is applied to example programs to verify their partial correctness.