CCR 2.0: High-level Reasoning for Conditional Refinements

Abstract: 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 separation logic. These two approaches are very different in nature and offer complementary benefits in terms of compositionality. Recently, to fuse these benefits in a unified mechanism, a new approach called Conditional Contextual Refinement (CCR 1.0 for short) was proposed. In this paper, we advance the model of CCR 1.0 and provide novel and intuitive reasoning principles, resulting in: CCR 2.0. Specifically, CCR 2.0 (i) comes with a better compositionality theorem, having the practical benefit of facilitating more proof reuse, and (ii) provides a proof technique that hides model-level (i.e., resources of the separation logic) details from the user. Achieving this goal was challenging due to non-trivial counterexamples which necessitated us to devise novel notions. Our results are formalized in Coq.