Refinement Calculus, Part I: Sequential Nondeterministic Programs

A lattice theoretic framework for the calculus of program reenement is presented. Speciications and program statements are combined into a single (innnitary) language of commands which permits miraculous, angelic and demonic statements to be used in the description of program behavior. The weakest precondition calculus is extended to cover this larger class of statements and a game-theoretic interpretation is given for these constructs. The language is complete, in the sense that every monotonic predicate transformer can be expressed in it. The usual program constructs can be deened as derived notions in this language. The notion of inverse statements is deened and its use in formalizing the notion of data reenement is shown.