Polymorphism

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:

  v := 123        /* v is integer */
  ...             /* use v as integer */
  v := 'abc'      /* v "switches" to string */
  ...             /* use v as string */

Definition (Polymorphism (1)) The concept of dynamic binding allows a variable to take different types dependent on the content at a particular time. This ability of a variable is called polymorphism.

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:

  boolean isNull(int i) {
    if (i == 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:

  boolean isNull(real r) {
    if (r < 0.01 and r > -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 of the function (or method) 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:

  var i : integer
  var r : real

  i = 0
  r = 0.0

  ...

  if (isNull(i)) then ...   /* Use isNull(int) */
  ...
  if (isNull(r)) then ...   /* Use isNull(real) */

Definition (Polymorphism (2)) If a function (or method) is defined by the combination of

• its name and
• the list of types of its parameters

we speak of 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:

  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:

  class Base {
  attributes:

  methods:
    virtual foo()
    bar()
  }

  class Derived inherits from Base {
  attributes:

  methods:
    virtual foo()
    bar()
  }

  demo(Base o) {
    o.foo()
    o.bar()
  }

  Base abase
  Derived aderived

  demo(abase)
  demo(aderived)

In this example we define two classes Base and Derived. Each class defines two methods foo() and bar(). 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 foo() and bar() are defined to just print out their name and the class in which they are defined. Then the output is as follows:

  foo() of Base called.
  bar() of Base called.
  foo() of Derived called.
  bar() of Base called.

Why is this so? Let's see what happens. 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 foo() it's actual functionality is chosen based on the current content of the corresponding object o. This time, it is a Base object. Consequently, foo() as defined in class Base is called.

The call to bar() is not subject to this content resolution. It is not marked as virtual. Consequently, bar() 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 foo() is evaluated by examining the content of o, hence, it is called within the scope of Derived. On the other hand, bar() is still evaluated within the scope of Base.

Definition (Polymorphism (3)) Objects of superclasses can be filled with objects of their subclasses. Operators and methods of subclasses can be defined to be evaluated in two contexts:

1.    Based on object type, leading to an evaluation within the scope
      of the superclass.
2.    Based on object content, leading to an evaluation within the
      scope of the contained subclass.

The second type is called polymorphism.

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