Static Typing for Object-Oriented Programming

Abstract

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.