On the practical need for abstraction relations to verify abstract data type representations

The typical correspondence between a concrete representation and an abstract conceptual value of an abstract data type (ADT) variable (object) is a many-to-one function. For example, many different pointer aggregates give rise to exactly the same binary tree. The theoretical possibility that this correspondence generally should be relational has long been recognized. By using a nontrivial ADT for handling an optimization problem, we show why the need for generalizing from functions to relations arises naturally in practice. Making this generalization is among the steps essential for enhancing the practical applicability of formal reasoning methods to industrial-strength software systems.