Reconciling Retrenchments and Refinements I

Some of the problems of using refinement alone in the construction of specifications from simple abstract models is used as the spur for the introduction of retrenchment, a method based on the main ideas of refinement, but one which is more liberal in character. The basics of the retrenchment mechanism are presented. The paper then examines one particular way in which a retrenchment and a refinement step can be combined by exploring the pushout-like problem of completing a square. Thus given both a retrenchment of an abstract model, and a refinement of the same model, the problem of finding a model that is both a refinement of the retrenchment and a retrenchment of the refinement is examined. The construction given solves the problem in a universal manner, in that it is the most abstract reconciliation of the initial retrenchment and refinement.