The theory of classification part 7: a class is a type family

The notion of class which defines class as family of types which share minimum common structure is described using the Cook's F-bounded quantification. The languages such as Java and C++ adopt this simple view which is found to challenge the frequent use of type downcasting needed to overcome inadequacies of first-order type systems based on types and subtyping. The systematic modeling of polymorphism is also described which uses type parameters. The relationship between universal quantification which supports definition of generic types and F-bounded quantification which supports definition of classes are also described.