Procedures and Recursion in the Refinement Calculus

Morgan's approach to program development is a refinement calculus: using this method, programs are developed from specifications through the successive application of refinement laws. This programming technique has been widely accepted, but it has been shown that Morgan's approach to procedures and parameters has an inconsistency. Back presents an alternative formalisation of procedures and parameters which is consistent, but does not propose any refinement law. In this paper, we present refinement laws that allow the development of (possibly parametrised and recursive) procedures in the style of Morgan, and derive these laws based on Back's formalism. Some of the refinement laws we present have a counterpart in Morgan's calculus, but some are new laws that support his approach to the development of recursive procedures.

Keywords: formal methods, program development, refinement laws.