Should a Function Continue?

Abstract

We show that two l-calculus terms can be observationally congruent (i.e., agree in all contexts) but their continuation-passing transforms may not be. We also show that two terms may be congruent in all untyped contexts but fail to be congruent in a language with call/ cc operators, and that two terms may have the same meaning in a direct semantics but in a continuation semantics.