The Theory of Classification, Part 11: Adding Class Types to Object Implementations

This is the eleventh article in a regular series on object-oriented type theory, aimed specifically at non-theoreticians. In the Theory of Classification, we have so far considered the typeful aspect of classes [1, 2] and their implementation aspect [3, 4] separately. We have been concerned to point out how the notion of classification has a fully formal interpretation [2], in which, at the typeful level, a class is distinct from a type [1]. Likewise, we have explored the implementation level, in order to understand the operation of inheritance on objects [3] and give a precise meaning to the pseudo-variables self [3] and super [4] in different object-oriented languages.