Data refinement for true concurrency

The majority of modern systems exhibit sophisticated concurrent behaviour, where several system components modify and observe the system state with fine-grained atomicity. Many systems (e.g., multi-core processors, real-time controllers) also exhibit truly concurrent behaviour, where multiple events can occur simultaneously. This paper presents data refinement defined in terms of an interval-based framework, which includes high-level operators that capture non-deterministic expression evaluation. By modifying the type of an interval, our theory may be specialised to cover data refinement of both discrete and continuous systems. We present an interval-based encoding of forward simulation, then prove that our forward simulation rule is sound with respect to our data refinement definition. A number of rules for decomposing forward simulation proofs over both sequential and parallel composition are developed.