Abstraction  (Page 2/9)

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; }} What this Java code means is something like: AreaCalc is a blue print of a specialized computing machine that is capable of accepting two input doubles , one labeled width and the other labeled height, computing their product and returning the result. This computation is given a name: rectangle . In Java parlance, it is called a method for the class AreaCalc .