A denotational semantics of Simulink with higher-order UTP

Matlab/Simulink is a de-facto industrial standard for modelling embedded systems. Reflecting the complexity of cyber-physical system (CPS) design, the semantics of Simulink is complex, mixing discrete and continuous time and events. In this paper, we define a compositional semantics of hierarchical Simulink diagrams using Higher-order Unifying Theories of Programming (HUTP) for CPS design. The HUTP theory satisfies the suitable algebraic properties to serve as a mathematical foundation for expressing the semantics of CPSs, in particular Simulink diagrams. We characterise a class of well-formed Simulink diagrams and prove the determinacy of their HUTP semantics. Moreover, we construct a framework for proving the consistency between Simulink diagrams and their translation to HCSP (Hybrid Communicating Sequential Processes). Finally, we provide a case study to illustrate and justify this translation.