From Polyvariant Flow Information to Intersection and Union Types

Abstract

Many polyvariant program analyses have been studied in the 199Os, including k-CFA, poly-k-CFA, and the Cartesian product algorithm. The idea of polyvariance is to analyze functions more than once and thereby obtain better precision for each call site. In this paper we present the first formal relationship between polyvariant analysis and standard notions of type. In the spirit of Nielson and Nielson, we study a parameterized flow analysis which can be instantiated to the analyses of Agesen, Schmidt, and as a simple case also 0-CFA. Extended with safety checks, the flow analysis accepts and rejects programs, much like a type checker. We prove that if a program can be safety-checked by a finitary instantiation of the flow analysis, then it can also be typed in a type system with intersection types, union types, subtyping, and recursive types, but no universal or existential quantifiers. This provides a framework for designing and understanding combinations of flow analyses and type systems.