A Proof Slicing Framework for Program Verification

Abstract. In the context of program verification, we propose a formal frame-work for proof slicing that can aggressively reduce the size of proof obligations as a means of performance improvement. In particular, each large proof obliga-tion may be broken down into smaller proofs, for which the overall processing cost can be greatly reduced, and be even more effective under proof caching. Our proposal is built on top of existing automatic provers, including the state-of-the-art prover Z3, and can also be viewed as a re-engineering effort in proof decomposition that attempts to avoid large-sized proofs for which these provers may be particularly inefficient. In our approach, we first develop a calculus that formalizes a complete proof slicing procedure, which is followed by the devel-opment of an aggressive proof slicing method. Retaining completeness is impor-tant, and thus in our experiments the complete method serves as a backup for the cases when the aggressive procedure fails. The foundations of the aggressive slicing procedure are based on a novel lightweight annotation scheme that cap-tures weak links between sub-formulas of a proof obligation; the annotations can be inferred automatically in practice, and thus both methods are fully automated. We support our theoretical developments with experimental results, which show significant improvements in the verification of complex programs, where richer specifications are often captured via loosely connected static properties.