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 connectionknown 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.