Using a Continuation Twice and Its Implications for the Expressive Power of Call/CC

We study the implications for the expressive power of call/cc of upward continuations , speciically the idiom of using a continuation twice. Although such control eeects were known to Landin and Reynolds when they invented J and escape, the forebears of call/cc, they still act as a conceptual pitfall for some attempts to reason about continuations. We use this idiom to refute some recent conjectures about equivalences in a language with continuations, but no other eeects. This shows that rst-class continuations as given by call/cc have greater expressive power than one would expect from goto or exits.