Unit 14: Polymorphism

Learning Objectives

After reading this unit, students should

• understand polymorphism
• be aware of dynamic binding
• be aware of the equals method and the need to override it to customize the equality test
• understand when narrowing type conversion and type casting are allowed

Taking on Many Forms

Method overriding enables polymorphism, the fourth and the last pillar of OOP, and arguably the most powerful one. It allows us to change how existing code behaves, without changing a single line of the existing code (or even having access to the code).

Consider the function say(Object) below:

void say(Object obj) {
  System.out.println("Hi, I am " + obj.toString());
}

Note that this method receives an Object instance. Since both Point <: Object and Circle <: Object, we can do the following:

Point p = new Point(0, 0);
say(p);
Circle c = new Circle(p, 4);
say(c);

When executed, say will first print Hi, I am (0.0, 0.0), followed by Hi, I am { center: (0.0, 0.0), radius: 4.0 }. We are invoking the overriding Point::toString() in the first call, and Circle::toString() in the second call. The same method invocation obj.toString() causes two different methods to be called in two separate invocations!

In biology, polymorphism means that an organism can have many different forms. Here, the variable obj can have many forms as well. Which method is invoked is decided during run-time, depending on the run-time type of the obj. This is called dynamic binding or late binding or dynamic dispatch.

Before we get into this in more detail, let's consider overriding Object::equals(Object).

The equals method

Object::equals(Object) compares if two object references refer to the same object. Suppose we have:

Circle c0 = new Circle(new Point(0, 0), 10);
Circle c1 = new Circle(new Point(0, 0), 10);
Circle c2 = c1;

c2.equals(c1) returns true, but c0.equals(c1) returns false. Even though c0 and c1 are semantically the same, they refer to two different objects.

To compare if two circles are semantically the same, we need to override this method¹. After all, Java does not know what it means for two circles to be equal, so we have to define it.

import java.lang.Math;

/**
 * A Circle object encapsulates a circle on a 2D plane.
 */
class Circle {
  private Point c;   // the center
  private double r;  // the length of the radius

  /**
   * Create a circle centered on Point c with given radius r
   */
  public Circle(Point c, double r) {
    this.c = c;
    this.r = r;
  }

  /**
   * Return the area of the circle.
   */
  public double getArea() {
    return Math.PI * this.r * this.r;
  }

  /**
   * Return true if the given point p is within the circle.
   */
  public boolean contains(Point p) {
    return false;
    // TODO: Left as an exercise
  }

  /**
   * Return the string representation of this circle.
   */
  @Override
  public String toString() {
    return "{ center: " + this.c + ", radius: " + this.r + " }";
  }

  /**
   * Return true the object is the same circle (i.e., same center, same radius).
   */
  @Override
  public boolean equals(Object obj) {
    if (obj instanceof Circle) {
      Circle circle = (Circle) obj;
      return (circle.c.equals(this.c) && circle.r == this.r);
    }
    return false;
  }
}

This is more complicated than toString. There are a few new concepts involved here:

• equals takes in a parameter of compile-time type Object. It only makes sense if we compare (during run-time) a circle with another circle. So, we first check if the run-time type of obj is a subtype of Circle. This is done using the instanceof operator. The operator returns true if obj has a run-time type that is a subtype of Circle.
• To compare this circle with the given circle, we have to access the center c and radius r. But if we access obj.c or obj.r, the compiler will complain. As far as the compiler is concerned, obj has the compile-time type Object, and there is no such fields c and r in the class Object! This is why, after assuring that the run-time type of obj is a subtype of Circle, we assign obj to another variable circle that has the compile-time type Circle. We finally check if the two centers are equal (again, Point::equals is left as an exercise) and if the two radii are equal².
• The statement that assigns obj to circle involves type casting. We mentioned before that Java is strongly typed, so it is very strict about type conversion. Here, Java allows type casting from type \(T\) to \(S\) if \(S <: T\). ³: This is called narrowing type conversion. Unlike widening type conversion, which is always allowed and always correct, a narrowing type conversion requires explicit typecasting and validation during run-time. If we do not ensure that obj has the correct run-time type, casting can lead to a run-time error (which if you recall, is bad).

All these complications would go away, however, if we define Circle::equals to take in a Circle as a parameter, like this:

class Circle {
    :
  /**
   * Return true the object is the same circle (i.e., same center, same radius).
   */
  @Override
  public boolean equals(Circle circle) {
    return (circle.c.equals(this.c) && circle.r == this.r);
  }
}

This version of equals, however, does not override Object::equals(Object). Since we hinted to the compiler that we meant this to be an overriding method, using @Override, the compiler will give us an error. This method is not treated as method overriding, since the method signature for Circle::equals(Circle) is different from Object::equals(Object).

Why then is overriding important? Why not just leave out the line @Override and live with the non-overriding, one-line, equals method above?

The Power of Polymorphism

Let's consider the following example. Suppose we have a general contains method that takes in an array of objects. The array can store any type of object: Circle, Square, Rectangle, Point, String, etc. The method contains also takes in a target obj to search for, and returns true if there is an object in array that equals to obj.

boolean contains(Object[] array, Object obj) {
  for (Object curr : array) {
    if (curr.equals(obj)) {
      return true;
    }
  }
  return false;
}

With overriding and polymorphism, the magic happens in Line 3 — depending on the run-time type of curr, the corresponding, customized version of equals is called to compare against obj. So if the run-time type of curr is Circle, then we will invoke Circle::equals(Object) and if the run-time type of curr is Point, then we will invoke Point::equals(Object). This, of course, assumes that Object::equals(Object) is overridden in both classes.

However, if Circle::equals(Object) takes in a Circle as the parameter, the call to equals inside the method contains would not invoke Circle::equals(Circle). It would invoke Object::equals(Object) instead due to the matching method signature, and we cannot search for Circle based on semantic equality.

Why is this the case? Look closely at how the method is invoked: curr.equals(obj). Here, we can see that the parameter we are passing is obj. The compile-time type of obj is Object as seen from the parameter declaration at Line 2. So at compile-time, we only know that its type is Object.

To have a generic contains method without polymorphism and overriding, we will have to do something like this:

boolean contains(Object[] array, Object obj) {
  for (Object curr : array) {
    if (obj instanceof Circle) {
      if (curr.equals((Circle)obj)) {
        return true;
      }
    } else if (obj instanceof Square) {
      if (curr.equals((Square)obj)) {
        return true;
      }
    } else if (obj instanceof Point) {
      if (curr.equals((Point)obj)) {
        return true;
      }
    }
     :
  }
  return false;
}

which is not scalable since every time we add a new class, we have to come back to this method and add a new branch to the if-else statement!

As this example has shown, polymorphism allows us to write succinct code that is future-proof. By dynamically deciding which method implementation to execute during run-time, the implementer can write short yet very general code that works for existing classes as well as new classes that might be added in the future by the client, without even the need to re-compile.

---

1. If we override equals(), we should generally override hashCode() as well, but let's leave that for another lesson on another day. ↩

2. The right way to compare two floating-point numbers is to take their absolute difference and check if the difference is small enough. We are sloppy here to keep the already complicated code a bit simpler. You shouldn't do this in your code. ↩

3. This is not the only condition where type casting is allowed. We will look at other conditions in later units. ↩