Higher-Ranked Annotation Polymorphic Dependency Analysis

The precision of a static analysis can be improved by increasing the context-sensitivity of the analysis. In a type-based formulation of static analysis for functional languages this can be achieved by, e.g., introducing let-polyvariance or subtyping. In this paper we go one step further by defining a higher-ranked polyvariant type system so that even properties of lambda-bound identifiers can be generalized over. We do this for dependency analysis, a generic analysis that can be instantiated to a range of different analyses that in this way all can profit. We prove that our analysis is sound with respect to a call-by-name semantics and that it satisfies a so-called noninterference property. We provide a type reconstruction algorithm that we have proven to be terminating, and sound and complete with respect to its declarative specification. Our principled description can serve as a blueprint for making other analyses higher-ranked.