Tracking Captured Variables in Types
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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.
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