A Probabilistic Model for Parametric Fairness in Isabelle/HOL

In paper [1], a liveness proof method suitable for inductive protocol verification is proposed. The utility of this method has been confirmed by several machine checked formal verifications[2–4]. One remaining question about [1] is the meaning of Parametric Fairness, a new fairness notion adapted from Pnueli’s Extreme Fairness[5] to suit the setting of higher-order logic. This paper tries to answer this question. As a standard practice in establishing a fairness notion, this paper constructs a probabilistic model for parametric fairness in Isabelle/HOL. Using this model, it is shown that most infinite executions of a concurrent system are parametrically fair. Therefore the definition of parametric fairness in paper [1] is reasonable. This work gives a firmer basis for existing and forthcoming formal verifications based on the method of paper [1].