A Presheaf Semantics of Value-Passing Processes
نویسنده
چکیده
This paper investigates presheaf models for process calculi with value passing. Denotational semantics in presheaf models are shown to correspond to operational semantics in that bisimulation obtained from open maps is proved to coincide with bisimulation as defined traditionally from the operational semantics. Both “early” and “late” semantics are considered, though the more interesting “late” semantics is emphasised. A presheaf model and denotational semantics is proposed for a language allowing process passing, though there remains the problem of relating the notion of bisimulation obtained from open maps to a more traditional definition from the operational semantics. A tentative beginning is made of a “domain theory” supporting presheaf models.
منابع مشابه
Presheaf Models for Concurrency
In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for ...
متن کاملAccessible functors and final coalgebras for named sets
In the field of programming language semantics and concurrency theory, wide attention is paid to the so called name-passing calculi, i.e. formalisms where name generation and passing play a fundamental role. A prototypical example is provided by the π-calculus. The peculiarities of name passing required to refine existing theoretical models and to invent new ones, such as coalgebras over preshe...
متن کاملPresheaf 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 mo...
متن کاملDomain theory for concurrency
Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey. A simple domain theory for concurrency is presented. Based on a categorical model of linear logic and associated comonads, it highlights the role of linearity in concurrent computation. Two choices of c...
متن کاملA Category of Explicit Fusions
Name passing calculi are nowadays an established field on its own. Besides their practical relevance, they offered an intriguing challenge, since the standard operational, denotational and logical methods often proved inadequate to reason about these formalisms. A domain which has been successfully employed for languages with asymmetric communication, like the π-calculus, are presheaf categorie...
متن کامل