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Correctness of concurrent objects is defined in terms of safety propertiessuch as linearizability, sequential consistency, and quiescent consistency, andprogress properties such as wait-, lock-, and obstruction-freedom. Theseproperties, however, only refer to the behaviours of the object in isolation,which does not tell us what guarantees these correctness conditions onconcurrent objects provide to their client programs. This paper investigatesthe links between safety and progress properties of concurrent objects and aform of trace refinement for client programs, called contextual tracerefinement. In particular, we show that linearizability together with a minimalnotion of progress are sufficient properties of concurrent objects to ensurecontextual trace refinement, but sequential consistency and quiescentconsistency are both too weak. Our reasoning is carried out in the actionsystems framework with procedure calls, which we extend to cope with non-atomicoperations.

Contextual trace refinement for concurrent objects: Safety and progress