A Declarative Semantics for Logic Program Refinement

The refinement calculus provides a framework for the stepwise development of imperative programs from specifications. This paper presents a semantics for a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic programming language, including executable constructs such as sequential conjunction, disjunction, and existential quantification, as well as specifications constructs (general predicates and assumptions) and universal quantification. A semantics is defined for this wide-spectrum language based on {\em executions}, which are partial functions from states to states, where a state is represented as a set of bindings. This execution semantics is used to define the meaning of programs and specifications, including parameters and recursion. To complete the calculus, a notion of correctness-preserving refinement over programs in the wide-spectrum language is defined and a refinement law for introducing recursive procedures is presented