Compositional and Lightweight Dependent Type Inference for ML

Abstract

We consider the problem of inferring expressive safety properties of higher-order functional programs using first-order decision procedures. Our approach encodes higher-order features into first-order logic formula whose solution can be derived using a lightweight counterexample guided refinement loop. To do so, we extract initial verification conditions from dependent typing rules derived by a syntactic scan of the program. Subsequent type-checking and type-refinement phases infer and propagate specifications of higher order functions, which are treated as uninterpreted first-order constructs, via subtyping chains. Our technique provides several benefits not found in existing systems: (1) it enables compositional verification and inference of useful safety properties for functional programs; (2) additionally provides counterexamples that serve as witnesses of unsound assertions: (3) does not entail a complex translation or encoding of the original source program into a first-order representation; and, (4) most importantly, profitably employs the large body of existing work on verification of first-order imperative programs to enable efficient analysis of higher-order ones. We have implemented the technique as part of the MLton SML compiler toolchain, where it has shown to be effective in discovering useful invariants with low annotation burden.