Logical Relations for Fine-Grained Concurrency
Fine-grained concurrent data structures (or FCDs) reduce the granularity of critical sections in both time and space, thus making it possible for clients to access different parts of a mutable data structure in parallel. However, the tradeoff is that the implementations of FCDs are very subtle and tricky to reason about directly. Consequently, they are carefully designed to be contextual refinements of their coarse-grained counterparts, meaning that their clients can reason about them as if all access to them were sequentialized. In this paper, we propose a new semantic model, based on Kripke logical relations, that supports direct proofs of contextual refinement in the setting of a type-safe high-level language. The key idea behind our model is to provide a simple way of expressing the "local life stories" of individual pieces of an FCD's hidden state by means of protocols that the threads concurrently accessing that state must follow. By endowing these protocols with a simple yet powerful transition structure, as well as the ability to assert invariants on both heap states and specification code, we are able to support clean and intuitive refinement proofs for the most sophisticated types of FCDs, such as conditional compare-and-set (CCAS).
logical relations fine-grained concurrency refinement linearizability separation logic data abstraction local state