The Theory of Classification, Part 17: Multiple Inheritance and the Resolution of Inheritance Conflicts

This is the seventeenth article in a regular series on object-oriented theory for nonspecialists. Using a second-order λ-calculus model, we have previously modelled the notion of inheritance as a short-hand mechanism for defining subclasses by extending superclass definitions. Initially, we considered the inheritance of type [1] and implementation [2] separately, but later combined both of these in a model of typed inheritance [3]. By simplifying the short-hand inheritance expressions, we showed how these are equivalent to canonical class definitions. We also showed how classes derived by inheritance are type compatible with their superclass. Further aspects of inheritance have included method combination [4], mixin inheritance [5] and inheritance among generic classes [6].