Separating Separation Logic – Modular Verification of Red-Black Trees

Interactive theorem provers typically use abstract algebraic data structures to focus on algorithmic correctness. Verification of programs in real programming languages also has deal with pointer structures, aliasing and, the case C, memory management. While progress been made by using Separation Logic, direct verification code still both aspects at once. In this paper, we show a refinement-based approach that separates two issues suitable modular structure. We exemplify correctness proof for red-black trees, demonstrating our can generate efficient C uses parent pointers and avoids recursion. The is split into large part almost identical high-level proofs separate small Logic verify primitive operations structures.