A Reflection on Continuation-Composing Style

摘要

We present a study of the continuation-composing style (CCS) that describes the image of the CPS translation of Danvy and Filinskia??s shift and reset delimited-control operators. In CCS continuations are composable rather than abortive as in the traditional CPS, and, therefore, the structure of terms is considerably more complex. We show that the CPS translation from Moggia??s computational lambda calculus extended with shift and reset has a right inverse and that the two translations form a reflection i.e., a Galois connection in which the target is isomorphic to a subset of the source (the orders are given by the reduction relations). Furthermore, we use this result to show that Plotkina??s call-by-value lambda calculus extended with shift and reset is isomorphic to the image of the CPS translation. This result, in particular, provides a first direct-style transformation for delimited continuations that is an inverse of the CPS transformation up to syntactic identity.