To illustrate, I'll use the tree example. We'd like to build, say trees of integers, and tree of floating point numbers. These are two types, but as they share something in common: their "treeness". We'd like them to inherit the characteristics common to all trees from a common base type.

The key to making this work is to use bounded genericity.

This abstract class captures the "treeness" of its subclasses. Any object of type Tree<T> has children of type T where T is a type that extends Tree<T>.

Now we can both specialize and concretize to create a type that represents trees of integers

Now we can both specialize and concretize to create a type that represents trees of integers

Each object of type IntTree is a tree that has IntTree objects as children and a field of type int.

Equally we could have a tree of floating point variables.

Equally we could have a tree of floating point variables.

That we can do this is only really interesting if we can write generic code to deal with data (trees in this case) at the generic level of abstraction. And we can. For example here is a class of depth-first tree traversers.

Then we can specialize and concretize this class to create a visitor that finds the sum of the integers in an IntTree.

Finally I'll just briefly describe the systems where these issues came up.

- For the hierarchical graph types of the JHigraph system we defined: first, a mutually recursive set of generic interfaces; next, a mutually recursive set of abstract classes; and, finally, a mutually recursive set of abstract classes that use a tag system similar to XML and ensure validity. These three sets of types define the model at various levels of abstraction. Based on the interfaces, we then defined a set of generic view classes and layout managers for visualizing the nodes and edges of the graph. An application can be built by specializing and concretizing either set of generic, abstract node and edge classes to hold the appropriate kind of data and by specializing and concretizing the view classes.
- The second application is a language processor in which the parser produces an abstract syntax tree and then the type checker produces a typed abstract syntax tree. The plain and the typed abstract syntax tree types share a common generic superclass.