Proving interesting and expressive safety properties of first-order programs typically involves generating verification conditions that can be solved by a first-order decision procedure. Higher-order functions make it complicated, however, to infer the necessary path constraints required to do the same for functional programs. In this talk, we consider a solution to this problem that encodes higher-order features into pure first-order logic formula, whose solution can be extracted using a lightweight counterexample guided refinement loop. Our approach extracts initial verification conditions from dependent typing rules derived by a syntactic scan of the program. Specification of higher-order functions are captured via subtyping chains generated from these types by treating such functions as uninterpreted first-order constructs.
Our technique enables inference and compositional verification of useful safety properties for ML programs, additionally provides counterexamples that serve as witnesses of unsound assertions, does not entail a complex translation or encoding of the original source program into a first-order representation, and is fully integrated within the MLton compiler toolchain.
This is joint work with He Zhu.