Capsules and Closures

Capsules are a clean representation of the state of a computation in higher-order programming languages with effects. Their intent is to simplify and replace the notion of closure. They naturally provide support for functional and imperative features, including recursion and mutable bindings, and ensure lexical scoping without the use of closures, heaps, stacks or combinators. We present a comparison of the use of closures and capsules in the semantics of higher-order programming languages with effects. In proving soundness of one to the other, we give a precise account of how capsule environments and closure environments relate to each other.