Abstract
Retrenchment is a flexible model evolution formalism that compensates for the limitations imposed by specific formulations of refinement. Its refinement-like proof obligations feature additional predicates for accommodating design data describing the model change. The best results are obtained when refinement and retrenchment cooperate, the paradigmatic scheme for this being the commuting square or tower, in which ‘horizontal retrenchment rungs’ commute with ‘vertical refinement columns’ to navigate through a much more extensive design space than permitted by refinement alone. In practice, the navigation is accomplished through ‘square completion’ constructions, and we present and prove a full suite of square completion theorems.
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