Polymorphism is in short the ability to call different functions by just using one type of function call. It is a lot useful since it can group classes and their functions together. It is the most important part of Object-Oriented Programming. Polymorphism is the core of object-oriented programming .C++ supports polymorphism by allowing member functions defined in classes to be overridden with member functions having the same names, but different implementations, in derived classes. In selecting the appropriate member function to call in response to a function invocation, C++ distinguishes between the static type of a reference and the dynamic type of the object it refers to at a given point. The dynamic type must be a descendant of the static type The invocation is type-checked based on the static type of the reference. If the function called is a virtual member function, the member function associated with the actual object pointed to is called dynamically at run time. If the function is non-virtual, the call will have been statically bound to the member function of the reference's class at compile time. Polymorphism allows an entity (for example, variable, function or object) to take a variety of representations. Therefore we have to distinguish different types of polymorphism which will be outlined here. The first type is similar to the concept of dynamic binding. Here, the type of a variable depends on its content. Thus, its type depends on the content at a specific time: Code: v := 123 /* v is integer */ ... /* use v as integer */ v := 'abc' /* v "switches" to string */ ... /* use v as string */ Another type of polymorphism can be defined for functions. For example, suppose you want to define a function isNull() which returns TRUE if its argument is 0 (zero) and FALSE otherwise. For integer numbers this is easy: Code: boolean isNull(int a) { if (a == 0) then return TRUE else return FALSE endif } However, if we want to check this for real numbers, we should use another comparison due to the precision problem: Code: boolean isNull(real x) { if (x < 0.01 and x > -0.99) then return TRUE else return FALSE endif } In both cases we want the function to have the name isNull. In programming languages without polymorphism for functions we cannot declare these two functions because the name isNull would be doubly defined. Without polymorphism for functions, doubly defined names would be ambiguous. However, if the language would take the parameters of the function into account it would work. Thus, functions (or methods) are uniquely identified by: • the name and • the types of its parameter list. Since the parameter list of both isNull functions differ, the compiler is able to figure out the correct function call by using the actual types of the arguments: Code: var a : integer var x : real a = 0 x = 0.0 ... if (isNull(a)) then ... /* Use isNull(int) */ ... if (isNull(x)) then ... /* Use isNull(real) */ If a function (or method) is defined by the combination of • its name and • the list of types of its parameters we can say polymorphism. This type of polymorphism allows us to reuse the same name for functions (or methods) as long as the parameter list differs. Sometimes this type of polymorphism is called overloading. The last type of polymorphism allows an object to choose correct methods. Consider the function move() again, which takes an object of class Point as its argument. We have used this function with any object of derived classes, because the is-a relation holds. Now consider a function display() which should be used to display drawable objects. The declaration of this function might look like this: Code: display(DrawableObject o) { ... o.print() ... } We would like to use this function with objects of classes derived from DrawableObject: Circle acircle Point apoint Rectangle arectangle display(apoint) /* Should invoke apoint.print() */ display(acircle) /* Should invoke acircle.print() */ display(arectangle) /* Should invoke arectangle.print() */ The actual method should be defined by the content of the object o of function display(). Since this is somewhat complicated, here is a more abstract example: Code: class Base { attributes: methods: virtual f () funy() } class Derived inherits from Base { attributes: methods: virtual funx () funy() } demo(Base o) { o.funx () o.funy() } Base abase Derived aderived demo(abase) demo(aderived) In this example we define two classes Base and Derived. Each class defines two methods funx() and funy(). The first method is defined as virtual. This means that if this method is invoked its definition should be evaluated by the content of the object. We then define a function demo() which takes a Base object as its argument. Consequently, we can use this function with objects of class Derived as the is-a relation holds. We call this function with a Base object and a Derived object, respectively. Suppose, that funx() and funy() are defined to just print out their name and the class in which they are defined. Then the output is as follows: funx() of Base called. funy() of Base called. funx() of Derived called. funy() of Base called. The first call to demo() uses a Base object. Thus, the function's argument is ``filled'' with an object of class Base. When it is time to invoke method funx() it's actual functionality is chosen based on the current content of the corresponding object o. This time, it is a Base object. Consequently, funx() as defined in class Base is called. The call to funy() is not subject to this content resolution. It is not marked as virtual. Consequently, funy() is called in the scope of class Base. The second call to demo() takes a Derived object as its argument. Thus, the argument o is filled with a Derived object. However, o itself just represents the Base part of the provided object aderived. Now, the call to funx() is evaluated by examining the content of o, hence, it is called within the scope of Derived. On the other hand, funy() is still evaluated within the scope of Base.