We present Hindley-Milner-Cousots (HMC), an algorithm that allows any
interprocedural analysis for first-order imperative programs to be used to
verify safety properties of typed higher-order functional programs. HMC works
as follows. First, it uses the type structure of the functional program to
generate a set of logical refinement constraints whose satisfaction implies the
safety of the source program. Next, it transforms the logical refinement
constraints into a simple first-order imperative program that is safe iff the
constraints are satisfiable. Thus, in one swoop, HMC makes tools for invariant
generation, e.g., based on abstract domains, predicate abstraction,
counterexample-guided refinement, and Craig interpolation be directly
applicable to verify safety properties of modern functional languages in a
fully automatic manner. We have implemented HMC and describe preliminary
experimental results using two imperative checkers -- ARMC and InterProc -- to
verify OCaml programs. Thus, by composing type-based reasoning grounded in
program syntax and state-based reasoning grounded in abstract interpretation,
HMC opens the door to automatic verification of programs written in modern
programming languages.Comment: 12 page
