Enriching Subclass Speci cations

The standard approach to reasoning about polymorphic (also called recursive or self) methods is in terms of method reenement. That is, if the correctness of a (polymorphic) method f of class B depends on certain properties of another method g of B, then in any subclass of B in which g is redeened, the designer must make sure that g continues to exhibit these properties. While this allows the designer of the derived class to avoid re-veriication of f, it does not allow us to associate, in the derived class, richer behavior with the polymorphic function. We propose an approach that, by including somewhat more information in the speciication of f, enables us to arrive, in the derived class, at a richer speciication of the function while at the same time avoiding re-veriication. The approach is illustrated on a simple example.