Science of Computer Programming 23(1):19{53, 1994. Static Typing for Object-Oriented Programming Jens Palsberg Michael I. Schwartzbach
[email protected] [email protected] Computer Science Department Aarhus University Ny Munkegade DK-8000 Arh˚ us C, Denmark Abstract We develop a theory of statically typed object-oriented languages. It rep- resents classes as labeled, regular trees, types as finite sets of classes, and subclassing as a partial order on trees. We show that our subclassing or- der 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 [25] in which a large number of reusable classes have been written. Smalltalk, however, is untyped. Though this is ideal for prototyping and exploratory development, a static type system is required to ensure that programs are readable, reliable, and efficient. This paper studies an idealized subset of Smalltalk, equipped with a novel static type system. Our analysis results in the definition of a new genericity mechanism, called class substitution, which we prove to be the order-theoretic complement of inheritance.