Total-Correctness Refinement for Sequential Reactive Systems

We introduce a coinductively-defined refinement relation on sequential non-deterministic reactive systems that guarantees total correctness. It allows the more refined system to both have less non-determinism in its outputs and to accept more inputs than the less refined system. Data reification in VDM is a special case of this refinement. Systems are considered at what we have called fine and medium levels of granularity. At the fine-grain level, a system’s internal computational steps are described. The fine-grain level abstracts to a medium-grain level where only input/output and termination behaviour is described. The refinement relation applies to medium grain systems. We consider fine grain systems as contexts for medium grain systems, and prove the refinement relation to be a precongruence with respect to these contexts. The development has been mechanized in PVS to support its use in case studies.