Fair Operational Semantics

Fairness properties, which state that a sequence of bad events cannot happen infinitely before a good event takes place, are often crucial in program verification. However, general methods for expressing and reasoning about various kinds of fairness properties are relatively underdeveloped compared to those for safety properties. This paper proposes FOS (Fair Operational Semantics), a theory capable of expressing arbitrary notions of fairness as an operational semantics and reasoning about these notions of fairness. In addition, FOS enables thread-local reasoning about fairness by providing thread-local simulation relations equipped with separation- logic-style resource algebras. We verify a ticket lock implementation and a client of the ticket lock under weak memory concurrency as an example, which requires reasoning about different notions of fairness including fairness of a scheduler, fairness of the ticket lock implementation, and even fairness of weak memory. The theory of FOS, as well as the examples in the paper, are fully formalized in Coq.