Simple type systems are lacking in flexibility

  Languages like Object Pascal, Modula-3, and C++ arose as object-oriented extensions of imperative programming languages. The static type systems of these languages have relatively simple and straightforward type systems whose features are similar to those of the procedural languages from which they were derived. In these simple type systems, the programmer has little flexibility in redefining methods in subclasses, as they require that a redefined method have exactly the same type as the original method in the superclass. However, when a method is inherited or redefined in the subclass, one is often able to deduce more refined types for methods than the language allows to be written. We present examples illustrating this below.

First a note on the terminology used in our examples. We use the convention in this paper of writing ${\it {CType}}$ for the type of objects generated by class ${\it {C}}$. Thus in Figure 7, ${\it {NodeType}}$ is the type of objects generated by class ${\it {Node}}$. As mentioned in the previous subsection, we will find it helpful to keep the notions of class and type separate. The type represents only the public interface of the object (in our case the types of all of the methods, but none of the instance variables), while the class includes initial values for instance variables and code for methods.