Unifying Program Construction and Modification

We propose a method which integrates program modification to the refinement calculus style of program development. Given a program developed through stepwise refinement of a specification, we propose an approach to specify modifications and to derive a new program from the existing refinement steps. This approach is based on the refinement lattice operator meet. A modification to a specification is represented by taking the meet of the old specification and the new feature to add. A solution to the new specification is constructed by coercing the new feature to match the structure of the existing refinement steps. The method fosters reuse of refinement steps and their proofs. We also show that program construction is streamlined by using coercion