A Mechanical Formalization of Several Fairness Notions

Fairness abstractions are useful for reasoning about computations of non-deterministic programs. This paper presents proof rules for reasoning about three fairness notions and one safety assumption with an automated theorem prover. These proof rules have been integrated into a mechanization of the Unity logic [13, 14] and are suitable for the mechanical verification of concurrent programs. Mechanical verification provides greater trust in the correctness of a proof. The three fairness notions presented here are unconditional, weak, and strong fairness [11]. The safety assumption is deadlock freedom which guarantees that no deadlock occurs during the computation. These abstractions are demonstrated by the mechanically verified proof of a dining philosopher’s program, also discussed here.