Refactoring, Refinement, and Reasoning - A Logical Characterization for Hybrid Systems

Refactoring of code is a common device in software engineering. As cyber-physical systems CPS become ever more complex, similar engineering practices become more common in CPS development. Proper safe developments of CPS designs are accompanied by a proof of correctness. Since the inherent complexities of CPS practically mandate iterative development, frequent changes of models are standard practice, but require reverification of the resulting models after every change. To overcome this issue, we develop proof-aware refactorings for CPS. That is, we study model transformations on CPS and show how they correspond to relations on correctness proofs. As the main technical device, we show how the impact of model transformations on correctness can be characterized by different notions of refinement in differential dynamic logic. Furthermore, we demonstrate the application of refinements on a series of safety-preserving and liveness-preserving refactorings. For some of these we can give strong results by proving on a meta-level that they are correct. Where this is impossible, we construct proof obligations for showing that the refactoring respects the refinement relation.