A Weakest Precondition Semantics for Refinement of Object-Oriented Programs
IEEE Transactions on Software Engineering
Specifying Java Frameworks Using Abstract Programs
TOOLS '99 Proceedings of the Technology of Object-Oriented Languages and Systems
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Constructing new classes from existing ones by inheritance or subclassing is a characteristic feature of object-oriented development. Imposing semantic constraints on subclassing allows us to ensure that subclass instances may be substituted for the corresponding superclass instances without invalidating the clients. We define the class refinement relation which captures these semantic constraints. Clients of class instances are modeled as programs making an iterative choice over invocation of class methods, and we prove that when a subclass refines its superclass, substituting subclass instances for superclass instances is refinement for the clients.