Learning to Specify

We present a type-based program analysis capable of inferring expressive invariants over array programs. Our system combines dependent types with two additional key elements. First, we associate dependent types with effects and precisely track effectful array updates, yielding a sound flow-sensitive dependent type system that can capture invariants associated with side-effecting array programs. Second, without imposing an annotation burden for quantified invariants on array indices, we automatically infer useful array invariants by initially guessing very coarse invariant templates, using test suites to exercise the functionality of the program to faithfully instantiate these templates with more precise (likely) invariants. These inferred invariants are subsequently encoded as dependent types for validation. Experimental results demonstrate the utility of our approach, with respect to both expressivity of the invariants inferred, and the time necessary to converge to a result.