Proof rules and transformations dealing with fairness

AbstractWe provide proof rules enabling the treatment of two fairness assumptions in the context of Dijkstra's do-od-programs. These proof rules are derived by considering a transformed version of the original program which uses random assignments z≔? and admits only fair computations. Various, increasingly complicated, examples are discussed. In all cases reasonably simple proofs can be given. The proof rules use well-founded structures corresponding to infinite ordinals and deal with the original programs and not their translated versions