Combining computational effects: Commutativity and sum

Abstract

We seek a unified account of modularity for computational effects, using the notion of enriched Lawvere theory, together with its relationship with strong monads, to reformulate Moggi's paradigm for modelling computational effects. Effects qua theories are then combined by appropriate bifunctors (on the category of theories). We give a theory of the commutative combination of effects, which in particular yields Moggi's side-effects monad transformer. And we give a theory for the sum of computational effects, which in particular yields Moggi's exceptions monad transformer.