A Foundation for Refining Concurrent Objects

We study the notion of class refinement in a concurrent object-oriented setting. Our model is based on a combination of action systems and classes. An action system describes the behavior of a concurrent, distributed, or interactive system in terms of the atomic actions that can take place during the execution of the system. Classes serve as templates for creating objects. To express concurrency with objects, we add actions to classes. We define class refinement based on trace refinement of action systems. Additionally, we give a simulation-based proof rule. We show that the easier to apply simulation rule implies the trace-based definition of class refinement. Class refinement embraces algorithmic refinement, data refinement, and atomicity refinement. Atomicity refinement allows us to split large atomic actions into several smaller ones. Thereby, it paves the way for more parallelism. We investigate the special case of atomicity refinement by early returns in methods.