Towards a Reflection for Effect Handlers

A reflection is a relationship between compiling and decompiling functions. This concept has been studied as a means to ensure correctness of compilers, in particular, those for languages featuring control effects. We aim to develop a reflection for algebraic effects and handlers. As a first step towards this goal, we investigate what we obtain by following the existing recipe for control operators. We show that, if we use the simplest CPS translation as the compiling function, we can prove most but not all theorems required of a reflection. From this result, we identify two conditions of the CPS translation that would lead to a reflection for effect handlers.