In normal typed λ-calculi, variables may be used multiple times, in multiple contexts, for multiple reasons, as long as the types agree. The disciplines of linear types and coeffects refine this by tracking how variables are used. For instance, we might track how many times a variable is used, or whether it is used covariantly, contravariantly, or invariantly. Such a discipline yields a general framework of “context constrained computing”, where constraints on variables in the context tell us something interesting about the computation being performed.

We will present work in progress on capturing the “intensional” properties of programs via a family of Kripke indexed relational semantics that refines a simple set-theoretic semantics of programs. The value of our approach lies in its generality and the range of examples covered.