A UTP semantics for communicating processes with shared variables

CSP# (Communicating Sequential Programs) is a modelling language designed for specifying concurrent systems by integrating CSP-like compositional operators with sequential programs updating shared variables. In this paper, we define an observation-oriented denotational semantics in an open environment for the CSP# language based on the UTP framework. To deal with shared variables, we lift traditional event-based traces into hybrid traces which consist of event-state pairs for recording process behaviours. We also define refinement to check process equivalence and present a set of algebraic laws which are established based on our denotational semantics. Our approach thus provides a rigorous means for reasoning about the correctness of CSP# process behaviours. We further derive a closed semantics by focusing on special types of hybrid traces; this closed semantics can be linked with existing CSP# operational semantics.