Continuations, Processes, and Sharing

Continuation-passing style (CPS) transforms have long been important tools in the study of programming. They have been shown to correspond to abstract machines and, when combined with a naming transform that expresses shared values, they enjoy a direct correspondence with encodings into process calculi such as the π-calculus. We present our notion of correctness and discuss the sufficient conditions that guarantee the correctness of transforms. We then consider the call-by-value, call-by-name and call-by-need evaluation strategies for the λ-calculus and present their CPS transforms, abstract machines, π-encodings, and proofs of correctness. Our analysis covers a uniform CPS transform, which differentiates the three evaluation strategies only by the treatment of function calls. This leads to a new CPS transform for call-by-need requiring a less expressive form of side effect, which we call constructive update.