A Re ection on Call - by - ValueAMR

One way to model a sound and complete translation from a source calculus into a target calculus is with an adjoint or a Galois connection. In the special case of a reeection, one also has that the target calculus is isomorphic to a subset of the source. We show that three widely studied translations form reeections. We use as our source language Moggi's computational lambda calculus, which is an extension of Plotkin's call-by-value calculus. We show that Plotkin's CPS translation , Moggi's monad translation, and Girard's translation to linear logic can all be regarded as reeections from this source language, and we put forward the computational lambda calculus as a model of call-by-value computation that improves on the traditional call-by-value calculus. Our work strengthens Plotkin's and Moggi's original results and improves on recent work based on equational correspondence, which uses equations rather than reductions.