| Combining computational e#ects: commutativity and sum Martin Hyland, (2007) | |||||||||||||||
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| Abstract. We begin to develop a unified account of modularity for computational e#ects. We use the notion of enriched Lawvere theory, together with its relationship with strong monads, to reformulate Moggi's paradigm for modelling computational e#ects; we emphasise the importance here of the operations that induce computational e#ects. E#ects qua theories are then combined by appropriate bifunctors (on the category of theories). We give a theory of the commutative combination of e#ects, which in particular yields Moggi's side-e#ects monad transformer (an application is the combination of side-e#ects with nondeterminism). And we give a theory for the sum of computational e#ects, which in particular yields Moggi's exceptions monad transformer (an application is the combination of exceptions with other e#ects). 1 | |||||||||||||||
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