Partial Continuations as the Diierence of Continuations a Duumvirate of Control Operators ?

We deene a partial continuation as the diierence of two continuations. We exhibit, in a single framework, several design choices and their impact on semantics. The ability of partial continuations to manipulate stack frames blurs the nature of dynamic extent; therefore, we introduce a new concept of preexal extent that characterises the time during which a partial continuation can be reiied. We propose two equivalent formal semantics for partial continuations: a context-rewriting system and a cps translation. Two new and realistic examples illustrate both the interest of partial continuations and the expressiveness of our choices.