The Theory of Classification, Part 18: Polymorphism through the Looking Glass

In this, the eighteenth article in a regular series on object-oriented type theory, we look at how object-oriented languages might evolve in the future, given that the formal notion of class is now better understood than at the outset. Object-oriented languages were the first family to suppose that there might be systematic sets of relationships between all the program data types and use this as the basis for a kind of type compatibility. However, the early formal models chosen were based on simple types and subtyping [1] and struggled in practice to support all the obvious, systematic relationships that programmers intuitively recognised [2]. For a while, objects were thought to have class and type independently, where class was demoted to a mere implementation construct. Later, it was realised that the notion of class is also a typeful construct that requires at least a bounded second-order λ-calculus model to explain it [3]. We have developed this model in the Theory of Classification, showing how it deals properly with typed inheritance [4, 5] and generic types [6] in a consistent framework.