A Concurrent Semantics for Concurrent Constraint Programs via Contextual Nets

We propose a concurrent semantics for concurrent constraint (cc) programs. A contextual net, that is a net with context conditions, besides pre-and post-conditions, is associated to each cc program. Context conditions are items which have to be present in order for an event to take place, but which are not aaected by the event. They are very useful for describing situations where diierent events share a common resource and want to read it simultaneously. The reason we use contextual nets for cc programs is that 1) nets allow a direct representation of concurrent information and 2) cc programs are naturally context-dependent (since the ask operation is a generalized read). While the causal dependency relation of the net induces a partial order among events in the same computation, its mutual exclusion relation provides a way of expressing nondeterministic information (and thus diierent computations). The information contained in the net, possibly abstracted to have a nite semantics even for recursive programs, can be of great help to a scheduler in order to obtain an eecient execution of the program, or also to a compile-time optimizer.