CCR 2.0: High-level Reasoning for Conditional Refinements

In recent years, great progress has been made in the field of formal verification for low-level systems. Many of them are based on one of two popular approaches: refinement or unary separation logic. These two approaches are very different in nature and offer complementary benefits in compositionality. Recently, to fuse these benefits into a single unified mechanism, a new approach called Conditional Contextual Refinement (CCR 1.0 for short) was proposed. In this paper, we advance CCR 1.0 and provide novel and intuitive reasoning principles, resulting in CCR 2.0. Achieving this goal was challenging due to non-trivial counterexamples which necessitated elegant changes to the model of CCR 1.0. On top of CCR 2.0, we show how to fuse the benefits of refinement, unary separation logic, and also relational separation logic. Our results are formalized in Rocq.