Abstraction

The problem has not changed in that it still deals with the same geometric shape, a rectangle, described in terms of the same dimensions, its width and height. What vary are simply the values of the width and the height. The formula to compute the area of a rectangle given its width and height does not change:

width * height

We just want to think of the width and height of a given rectangle as elements of the set of real numbers. In computing, we group values with common characteristics into a set and called it a type. In Java, the type double is the set of real numbers that are implemented inside the computer in some specific way. The details of this internal representation is immaterial for our purpose and thus can be ignored. In addition to the type double, Java provides many more pre-built types such as int to represent the set of integers and char to represent the set of characters. We will examine and use them as their need arises in future examples. As to our problem, we only need to restrict ourselves to the type double.

We can define the width and the height of a rectangle as double in Java as follows.

  double width;  double height;  

The above two statements are called variable definitions where width and height are said to be variable names. In Java, a variable represents a memory location inside the computer. We define a variable by first declare its type, then follow the type by the name of the variable, and terminate the definition with a semi-colon. This a Java syntax rule. Violating a syntax rule constitutes an error. When we define a variable in this manner, its associated memory content is initialized to a default value specified by the Java language. For variables of type double, the default value is 0.

Once we have defined the width and height variables, we can solve our problem by writing the expression that computes the area of the associated rectangle in terms of width and height as follows.

width * height

Observe that the two variable definitions together with the expression to compute the area presented in the above directly translate the description of the problem -two real numbers representing the width and the height of a rectangle- and the high-level thinking of what the solution of the problem should be -area is the width times the height. We have just expressed the invariants of the problem and its solution. Now, how do we vary width and height in Java? We use what is called the assignment operation. To assign the value 4.5 to the variable width and the value 7.2 to the variable height, we write the following Java assignment statements.

  width = 4.5;  height = 7.2;

The syntax rule for the assignment statement in Java is: first write the name of the variable, then follow it by the equal sign, then follow the equal sign by a Java expression, and terminate it with a semi-colon. The semantic (i.e. meaning) of such an assignment is: evaluate the expression on the right hand side of the equal sign and assign the resulting value into the memory location represented by the variable name on the left hand side of the equal side. It is an error if the type of the expression on the right hand side is not a subset of the type of the variable on the left hand side.

Now if we evaluate width * height again (using the Interactions Window of DrJava), we should get the desired answer. Life is good so far, though there is a little bit of inconvenience here: we have to type the expression width * height each time we are asked to compute the area of a rectangle with a given width and a given height. This may be OK for such a simple formula, but what if the formula is something much more complex, like computing the length of the diagonal of a rectangle? Re-typing the formula each time is quite an error-prone process. Is there a way to have the computer memorize the formula and perform the computation behind the scene so that we do not have to memorize it and rewrite it ourselves? The answer is yes, and it takes a little bit more work to achieve this goal in Java.

What we would like to do is to build the equivalent of a black box that takes in as inputs two real numbers (recall type double) with a button. When we put in two numbers and depress the button, "magically" the black box will compute the product of the two input numbers and spit out the result, which we will interpret as the area of a rectangle whose width and height are given by the two input numbers. This black box is in essence a specialized calculator that can only compute one thing: the area of a rectangle given a width and a height. To build this box in Java, we use a construct called a class, which looks like the following.

class AreaCalc {
	double rectangle(double width, double height) {
		return width * height;      
	}
}  

Here is an example of how we use AreaCalc to compute area of a rectanglee of width 4.5 and height 7.2. In the Interactions pane of DrJava, enter the following lines of code.

AreaCalc calc = new AreaCalc();  
calc.rectangle(4.5, 7.2)   

calc.rectangle(5.6, 8.4);

There are at least two different designs for such a calculator.

For the first few years of his life, Peter did not have a clue what birthdays were, let alone his own birth date. He was incapable of responding to your inquiry on his birthday. It was his parents who planned for his elaborate birthday parties months in advance. We can think of Peter then as a rather "dumb" person with very little intelligence and capability. Now Peter is a college student. There is a piece of memory in his brain that stores his birth date: it's September 12, 1985! Peter is now a rather smart person. He can figure out how many more months till his next birthday and e-mail his wish list two months before his birth day. How do we model a "smart" person like Peter? Modeling such a person entails modeling

public class Person {
	/**
     * All data fields are private in order to prevent code outside of this 
     * class to access them.
     */
    private int _bDay;   // birth day
    private int _bMonth; // birth month; for example, 3 means March.
    private int _bYear;  // birth year
    
    /**
     * Constructor: a special code used to initialize the fields of the class.
     * The only way to instantiate a Person object is to call new on the constructor.
     * For example: new Person(28, 2, 1945) will create a Person object with 
     * birth date February 28, 1945.
     */
    public Person(int day, int month, int year) {
       _bDay = day;
       _bMonth = month;
       _bYear = year;
    }
    
    /**
     * Uses "modulo" arithmetic to compute the number of months till the next 
     * birth day given the current month.
     * @param currentMonth an int representing the current month.
     */
    public int nMonthTillBD(int currentMonth) {
        return (_bMonth - currentMonth + 12) % 12;
    }
 }