Polymorphism

From a theoretical perspective, object orientation may be characterized as combining abstract data types and polymorphism. These notions may be considered as the theoretical counterparts of the more operational notions of encapsulation and inheritance.

Polymorphism

abstract inheritance
subtypes
type abstraction
self-reference

Additional keywords and phrases: exceptions, type calculi, parametric types, coercion, ad hoc polymorphism, universal types, existential types, unfolding, intersection types

slide: Polymorphism

In this chapter we will study the notion of polymorphism. We start our exploration by looking at the role of inheritance in knowledge representation. Then we will formally characterize the (signature) subtype relation and explain the contravariance rule for function subtypes. To better understand polymorphism and its relation to inheritance, we will develop a type calculus, allowing us to define abstract types using universally and existentially quantified type expressions. In a similar way, we will look at polymorphism due to overloading and generic type definitions. Finally, we will look at the role of self-reference in typing object descriptions derived by inheritance. Together with developing the calculi, examples will be given that illustrate the properties of the C++ and Eiffel type systems.