Sure there is: take an undelimited continuation API, and restrict the resulting continuations to be called only once. Most use cases still work just fine, and I

Sure there is: take an undelimited continuation API, and restrict the resulting continuations to be called only once. Most use cases still work just fine, and I think it would be strange to call that anything other than "undelimited one-shot continuations". Maybe what you have in mind, though, is the traditional argument, that there's no such thing as undelimited continuations. All continuations are naturally "delimited" by the boundary of the language runtime, operating system, etc, even with undelimited, multi-shot continuations. One-shot continuations make this argument more natural, because they have an obvious stack-based implementation for both delimited and undelimited continuations, and stacks are clearly delimited.