A generalization of Dijkstra's calculus

Dijsktra's calculus of guarded commands can be generalized and simplified by dropping the law of the excluded miracle. This paper gives a self-contained account of the generalized calculus from first principles through the semantics of recursion. The treatment of recursion uses the fixpoint method from denotational semantics. The paper relies only on the algebraic properties of predicates; individual states are not mentioned (except for motivation). To achieve this, we apply the correspondence between programs and predicates that underlies predicative programming. The paper is written from the axiomatic semantic point of view, but its contents can be described from the denotational semantic point of view roughly as follows: The Plotkin-Apt correspondence between wp semantics and the Smyth powerdomain is extended to a correspondence between the full wp/wlp semantics and the Plotkin powerdomain extended with the empty set.