Presheaf models and process calculi

Process calculi like CCS have been motivated and studied operationally, thus from the outset lacking the abstract mathematical treatment provided by a domain theory. Consequently, concurrency has become a rather separate study; in particular, higher-order and functional features as known from sequential programming are most often treated in an ad hoc fashion, if at all. The study of presheaf models of processes [3, 14] can be seen as an attempt to bring concurrency back within the realm of traditional denotational semantics by providing a domain theory for concurrent computation. Much of the work so far [4, 6, 7, 8, 9, 10, 27] has concentrated on developing the domain theory itself and on showing how to handle existing models and notions from process calculi within it. Meanwhile, a full operational understanding of presheaf models has still not been obtained. A sensible way to proceed would be to exploit the domain theory to define mathematically natural process calculi; and approach an operational understanding of presheaf models by investigating the operational semantics of these calculi.