The Theory of Classification, Part 13: Template Classes and Genericity.

The Theory of Classification, Part 16: Rules of Extension and the Typing of Inheritance.

“…One observation emerging from this is that the ability to replace fields with subtype fields is not a frequent requirement in object-oriented languages. The subclassing model of inheritance only requires type-equality, because all the field types are unified prior to combination, whether by parameter unification [3], or instantiation [5]. Simons and Bruce were the first to note the poor match between simple subtyping and natural…”

“…In fact, it is always the case, in the subclassing model, that self-type parameters are unified before record combination. Likewise, generic type parameters may be unified before combination [5] (see also 5.4 below). So, the simpler union ∪ of type-records appears to be all that we need in the subclassing model.…”

“…We showed how short-hand inheritance expressions can be simplified to yield a canonical subclass definition that is type compatible with the base superclass from which it was derived. Further aspects of inheritance have included method combination [7], mixin inheritance [8] and inheritance among generic classes [5].…”

“…Earlier articles have built up λ-calculus models of objects [1], classes [2], inheritance [3,4] and generic template types [5]. Classification describes the way in which typed objects fit into a hierarchy of classes, which nest inside each other [3].…”

The Theory of Classification Part 15: Mixins and the Superclass Interface.

“…Earlier articles have built up λ-calculus models of objects [1], classes [2], inheritance [3,4] and generic template types [5]. These features are common to a number of popular object-oriented languages, such as C++, Eiffel and Java (which now has templates in the latest version).…”