A reflection on call-by-value

A number of compilers exploit the following strategy: translate a term to continuation-passing style (CPS) and optimize the resulting term using a sequence of reductions. Recent work suggests that an alternative strategy is superior: optimize directly in an extended source calculus. We suggest that the appropriate relation between the source and target calculi may be captured by a special case of a Galois connection known as a reflection . Previous work has focused on the weaker notion of an equational correspondence , which is based on equality rather than reduction. We show that Moggi's monad translation and Plotkin's CPS translation can both be regarded as reflections, and thereby strengthen a number of results in the literature.