A Hyperdoctrinal View of Concurrent Constraint Programming

We study a relationship between logic and computation via concurrent constraint programming. In previous papers it has been shown how a simple language for specifying asynchronous concurrent processes can be interpreted in terms of constraints. In the present paper we show that the programming interpretation via closure operators is intimately related to the logic of the constraints. More precisely we show how the usual hyperdoctrinal description of rst order logic can be functorially related to another hyperdoctrine built out of closure operators. The logical connectives map onto constructions on closure operators that turn out to model programming constructs, speci cally conjunction becomes parallel composition and existential quanti cation becomes hiding of local variables.