Compositional reasoning and decidable checking for dependent contract types

Simple type systems perform compositional reasoning in that the type of a term depends only on the types of its subterms, and not on their semantics. Contracts offer more expressive abstractions, but static contract checking systems typically violate those abstractions and base their reasoning directly upon the semantics of terms. Pragmatically, this noncompositionality makes the decidability of static checking unpredictable. We first show how compositional reasoning may be restored using standard type-theoretic techniques, namely existential types and subtyping. Despite its compositional nature, our type system is exact, in that the type of a term can completely capture its semantics, hence demonstrating that precision and compositionality are compatible. We then address predictability of static checking for contract types by giving a type-checking algorithm for an important class of programs with contract predicates drawn from a decidable theory. Our algorithm relies crucially on the fact that the type of a term depends only the types of its subterms (which fall into the decidable theory) and not their semantics (which will not, in general).