How to Remove a Dynamic Prompt: Static and Dynamic Delimited Continuation Operators Are Equally Expressible

Abstract

We show how to remove a dynamic prompt (aka reset) and thus to turn so-called static delimited continuation operators (shift/reset) into dynamic ones: control, control0, shift0. Our technique extends the continuation captured by shift by composing it with the previous fragments of the `stack'. Composition of context fragments can be done via regular functional composition. We thus demonstrate that all the above delimited continuation operators are macro-expressible in terms of each other --- without capturing undelimited continuations and without using mutable state. Furthermore, the operators shift, control, control0, shift0 are the members of a single parameterized family, and the standard CPS is sufficient to express their denotational semantics. We give the simplest Scheme implementation of the dynamic control operators. We give a formal simulation proof that control realized through shift indeed has its standard reduction semantics.