Formally Verified Bug-free Implementations of (Logical) Algorithms

Notwithstanding the advancements of formal methods, which already permit their adoption in a industrial context (consider, for instance, the notorious examples of Airbus, Amazon Web-Services, Facebook, or Intel), there is still no widespread endorsement. Namely, in the Portuguese case, it is seldom the case companies use them consistently, systematically, or both. One possible reason is the still low emphasis placed by academic institutions on formal methods (broadly consider as developments methodologies, verification, and tests), making their use a challenge for the current practitioners. Formal methods build on logics, “the calculus of Computer Science”. Computational Logic is thus an essential field of Computer Science. Courses on this subject are usually either too informal (only providing pseudo-code specifications) or too formal (only presenting rigorous mathematical definitions) when describing algorithms. In either case, there is an emphasis on paper-and-pencil definitions and proofs rather than on computational approaches. It is scarcely the case where these courses provide executable code, even if the pedagogical advantages of using tools is well know. In this dissertation, we present an approach to develop formally verified implementations of classical Computational Logic algorithms. We choose the Why3 platform as it allows one to implement functions with very similar characteristics to the mathematical definitions, as well as it concedes a high degree of automation in the verification process. As proofs of concept, we implement and show correct the conversion algorithms from propositional formulae to conjunctive normal form and from this form to Horn clauses