Presheaf Models for CCS-like Languages

Abstract

The aim of this paper is to harness the mathematical machinery around
presheaves for the purposes of process calculi. Joyal, Nielsen and Winskel
proposed a general definition of bisimulation from open maps. Here we show
that open-map bisimulations within a range of presheaf models are congruences
for a general process language, in which CCS and related languages
are easily encoded. The results are then transferred to traditional models
for processes. By first establishing the congruence results for presheaf
models, abstract, general proofs of congruence properties can be provided
and the awkwardness caused through traditional models not always possessing
the cartesian liftings, used in the break-down of process operations,
are side-stepped. The abstract results are applied to show that hereditary
history-preserving bisimulation is a congruence for CCS-like languages to
which is added a refinement operator on event structures as proposed by
van Glabbeek and Goltz.