Static program analysis is a core technology for both verifying and finding errors in programs but most static analyzers are complex pieces of software that are not without error. A Static analysis formalised as an abstract interpreter can be proved sound, however such proofs are significantly harder to do on the actual implementation of an analyser. To alleviate this problem we propose to generate Verification Conditions (VCs, formulae valid only if the results of the analyser are correct) and to discharge them using an Automated Theorem Prover (ATP). We generate formulae in Many-Sorted First-Order Logic (MSFOL), a logic that has been successfully used in deductive program verification. MSFOL is expressive enough to describe the results of complex analyses and to formalise the operational semantics of object-oriented languages. Using the same logic for both tasks allows us to prove the soundness of the VC generator using deductive verification tools. To ensure that VCs can be automatically discharged for complex analyses of the heap, we introduce a VC calculus that produces formulae belonging to a decidable fragment of MSFOL. Furthermore, to be able to certify different analyses with the same calculus, we describe a family of analyses with a parametric concretisation function and instrumentation of the semantics. To improve the reliability of ATPs, we also studied the result certification of Satisfiability Modulo Theory solvers, a family of ATPs dedicated to MSFOL. We propose a modular proof-system and a modular proof-verifier programmed and proved correct in Coq, that rely on exchangeable verifiers for each of the underlying theories.
