Tracking Data-Flow with Open Closure Types

Type systems hide data that is captured by function closures in function types. In most cases this is a beneficial design that favors simplicity and compositionality. However, some applications require explicit information about the data that is captured in closures. This paper introduces open closure types, that is, function types that are decorated with type contexts. They are used to track data-flow from the environment into the function closure. A simply-typed lambda calculus is used to study the properties of the type theory of open closure types. A distinctive feature of this type theory is that an open closure type of a function can vary in different type contexts. To present an application of the type theory, it is shown that a type derivation establishes a simple non-interference property in the sense of information-flow theory. A publicly available prototype implementation of the system can be used to experiment with type derivations for example programs.