Categorical Semantics of Parallel Program Design

Ð We formalise, using Category Theory, modularisation techniques for parallel and distributed systems based on the notion of superposition, showing that parallel program design obeys the "universal laws" formulated by J.Goguen for General Systems Theory, as well as other algebraic properties of modularity formulated for Specification Theory. The resulting categorical formalisation unifies the different notions of superposition that have been proposed in the literature and clarifies their algebraic properties with respect to modularisation. It also suggests ways of extending or revising existing languages in order to provide higher levels of reusability, modularity and incrementality in system design.