Reconciling Retrenchments and Refinements

The more obvious and well known drawbacks of using refinement as the sole means of progressing from an abstract model to a concrete implementation are reviewed. Retrenchment is presented in a simple partial correctness framework as a more flexible development concept for formally capturing the early otherwise preformal stages of development, and briefly justified. 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. A construction is given that solves the problem in a universal manner, giving the most abstract reconciliation of the two. The universality amounts to the fact that any similar reconciliation of the original retrenchment and refinement is refinable from the universal one, factoring through it.