A theoretical basis for stepwise refinement and the programming calculus

AbstractA uniform treatment of specifications, programs, and programming is presented. The treatment is based on adding a specification statement to a given procedural language and defining its semantics. The extended language is thus a specification language and programs are viewed as a subclass of specifications. A partial ordering on specifications/programs corresponding to ‘more defined’ is defined. In this partial ordering the program/specification hybrids that arise in the construction of a program by stepwise refinement form a monotonic sequence. We show how Dijkstra's calculus for the derivation of programs corresponds to constructing this monotonic sequence. Formalizing the calculus thus gives some insight into the intellectual activity it demands and allows us to hint at further developments