Typed Exeptions and Continuations Cannot Macro-Express Each Other

The most powerful control constructs in modern programming languages are continuations and exceptions. Although they can be used interchangeably in some cases, they are fundamentally different semantically. We consider two simply-typed functional languages with exceptions and continuations, respectively. We give theorems, one that holds in the language with exceptions and one that holds in the language with continuations. A fortiori, these theorems imply that exception constructs cannot be used to macro-express continuation constructs, and that continuation constructs cannot be used to macro-express exception constructs.