Faithful Translations between Polyvariant Flows and Polymorphic Types

Recent work has shown equivalences between various type systems and flow logics. Ideally, the translations upon which such equivalences are based should be faithful in the sense that information is not lost in round-trip translations from flows to types and back or from types to flows and back. Building on the work of Nielson & Nielson and of Palsberg & Pavlopoulou, we present the first faithful translations between a class of finitary polyvariant flow analyses and a type system supporting polymorphism in the form of intersection and union types. Additionally, our flow/type correspondence solves several open problems posed by Palsberg & Pavlopoulou: (1) it expresses call-string based polyvariance (such as k-CFA) as well as argument based polyvariance; (2) it enjoys a subject reduction property for flows as well as for types; and (3) it supports a flow-oriented perspective rather than a type-oriented one.