Tracking Captured Variables in Types

by Aleksander Boruch-Gruszecki, Jonathan Immanuel Brachthäuser, Edward Lee, Ondrej Lhoták, and Martin Odersky

In CoRR abs/2105.11896, 2021.

This publication is related to the Type- and Effect Systems research project.


Type systems usually characterize the shape of values but not their free variables. However, there are many desirable safety properties one could guarantee if one could track how references can escape. For example, one may implement algebraic effect handlers using capabilities – a value which permits one to perform the effect – safely if one can guarantee that the capability itself does not escape the scope bound by the effect handler. To this end, we study the CF<: calculus, a conservative and lightweight extension of System F<:, to track how values and their references can be captured and escape. We show that existing terms in System F<: embed naturally in our calculus, and that many natural problems can be expressed in a system that tracks variable references like we do in CF<:. We also give mechanized proofs of the soundness properties of CF<: in Coq. The type system presented in CF<: is powerful enough to reason about safety in the context of many natural extensions of CF<: such as region-based memory-management, non-local returns, and effect handlers.