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.Comment: Logic for Programming Artificial Intelligence and Reasoning (2013
