Modularity in Denotational Semantics

AbstractWe consider a modular approach to denotational semantics. We reformulate and extend the idea of monads as notions of computation to algebraic structure together with a construction of an extended semantic category. We show that upon making that reformulation, one can obtain some account of modularity, in particular accounting for the interaction between side-effects and various forms of nondeterminism. That involves extending the notion of distributivity of a monad over another monad to distributivity of a monad over any algebraic structure. We give a general theorem which asserts when algebraic structure extends along a Kleisli category, thus allowing modularity