Specification synthesis with constrained Horn clauses

The problem of synthesizing specifications of undefined procedures has a broad range of applications, but the usefulness of the generated specifications depends on their quality. In this paper, we propose a technique for finding maximal and non-vacuous specifications. Maximality allows for more choices for implementations of undefined procedures, and non-vacuity ensures that safety assertions are reachable. To handle programs with complex control flow, our technique discovers not only specifications but also inductive invariants. Our iterative algorithm lazily generalizes non-vacuous specifications in a counterexample-guided loop. The key component of our technique is an effective non-vacuous specification synthesis algorithm. We have implemented the approach in a tool called HornSpec, taking as input systems of constrained Horn clauses. We have experimentally demonstrated the tool's effectiveness, efficiency, and the quality of generated specifications on a range of benchmarks.