Static Typing for Object-Oriented Programming

We develop a theory of statically typed object-oriented languages. It represents classes as labeled, regular trees, types as finite sets of classes, and subclassing as a partial order on trees. We show that our subclassing order strictly generalizes inheritance, and that a novel genericity mechanism arises as an order-theoretic complement. This mechanism, called class substitution, is pragmatically useful and can be implemented efficiently. 1 Introduction Object-oriented programming is becoming widespread. Numerous programming languages supporting object-oriented concepts are in use, and theories about object-oriented design and implementation are being developed and applied [21, 3, 14]. An important issue in object-oriented programming is to obtain reusable software components [30]. This is achieved through the notions of object, class, inheritance, late binding, and the imperative constructs of variables and assignments. Such features are found for example in the Smalltalk language ..