Implementations of concurrent objects should guarantee linearizability and a progress property such as wait-freedom, lock-freedom, starvation-freedom, or deadlock-freedom. These progress properties describe conditions under which a method call is guaranteed to complete. However, they fail to describe how clients are affected, making it difficult to utilize them in layered and modular program verification. Also, we lack verification techniques for starvation-free or deadlock-free objects. They are challenging to verify because the fairness assumption introduces complicated interdependencies among progress of threads. Even worse, none of the existing results applies to concurrent objects with partial methods, i.e., methods that are supposed NOT to return under certain circumstances.

In this talk we examine the progress properties of concurrent objects. We formulate each progress property (together with linearizability as a basic correctness requirement) in terms of contextual refinement. This essentially gives us progress-aware abstraction for concurrent objects. Thus, when verifying clients of the objects, we can soundly replace the concrete object implementations with their abstractions, achieving modular verification. For concurrent objects with partial methods, we formulate two new progress properties, partial starvation-freedom (PSF) and partial deadlock-freedom (PDF). Finally, we introduce a rely-guarantee style program logic LiLi for verifying linearizability and progress together for concurrent objects. It unifies thread-modular reasoning about all the six progress properties (wait-freedom, lock-freedom, starvation-freedom, deadlock-freedom, PSF and PDF) in one framework. We have successfully applied LiLi to verify starvation-freedom or deadlock-freedom of representative algorithms such as lock-coupling lists, optimistic lists and lazy lists, and PSF or PDF of lock algorithms.