Adding Fair Choice to Dijkstra's Calculus

The paper studies the incorporation of a fair nondeterministic choice operator into a generalization of Dijkstra's calculus of guarded commands. The generalization drops the law of the excluded miracle to allow commands that correspond to partial relations. Because of fairness, the new operator is not monotonic for the orderings that are generally used for proving the existence of least fixed points for recursive definitions. To prove the existence of fixed points it is necessary to consider several orderings at once, and to restrict the class of recursive definitions.