Dependent Interoperability

In this paper we study the problem of interoperability – combining constructs from two separate programming languages within one program – in the case where one of the two languages is dependently typed and the other is simply typed. We present a core calculus called SD, which combines dependently- and simply-typed sub-languages and supports user-defined (dependent) datatypes, among other standard features. SD has “boundary terms" that mediate the interaction between the two sub-languages. The operational semantics of SD demonstrates how the necessary dynamic checks, which must be done when passing a value from the simply-typed world to the dependently typed world, can be extracted from the dependent type constructors themselves, modulo user-defined functions for marshaling values across the boundary. We establish type-safety and other meta-theoretic properties of SD, and contrast this approach to others in the literature.