Asynchronous Progress

We propose weakening the definition of progress to a branching-time operator, making it more amenable to compositional proof and simplifying the predicates needed to reason about highly asynchronous programs. The new progress operator (“achieves”) coincides with the “leads-to” operator on all “observable” progress properties (those where the target predicate is stable) and satisfies the same composition properties as leads-to, including the PSP theorem. The advantage of achievement lies in its compositionality: a program inherits all achievement properties of its “decoupled components”. (For example, a dataflow network inherits achievement properties from each of its processes.) The compositionality of achievement captures, in a UNITY-like logic, the well-known operational trick of reasoning about an asynchronous program by considering only certain well-behaved executions.