"Delimited" in continuations doesn't refer to a non-first-class hack. Delimited continuations are first-class, built-into-the-language objects (unless kludged otherwise, which is true of any continuations). They are just semantically nuanced relative to undelimited continuations in that they allow the program to clamp the future computation to within a specified dynamic contour. When the restarted continuation bubbles out to that boundary, it terminates and returns a value to whomever dispatched the continuation. And of course, it can be called again and again to do the same thing. That's why delimited continuations behave like functions and are composable.