Spring Semester 2005

Equivalence of Programs

frilled.cs.indiana.edu%cat One.java
class One {
    public static void main(String[] args) {

        int x = 1; 
	if (x > 0) {
	    if (x < 5) {
		System.out.println(" 0 < " + x + " < 5"); 
	    } 
        } else { 
	    System.out.println(x + " <= 0"); 
        } 

    } 
}
frilled.cs.indiana.edu%javac One.java
frilled.cs.indiana.edu%java One
 0 < 1 < 5
frilled.cs.indiana.edu%

The program above is extremely clear, since it uses curly braces.

(It would be good if you could draw a flow chart for it, too).

In any event, am equivalent program would be:

class One {
    public static void main(String[] args) {

        int x = 1; 

	if (x > 0 && x < 5) System.out.println(" 0 < " + x + " < 5"); 

        if (x <= 0) 	    System.out.println(x + " <= 0"); 

    } 
}

There are other ways of writing a program that's equivalent to the one we started from.

(Do you understand how the two programs discussed above behave in the exact same way?)

The Dangling else Problem

class One {
    public static void main(String[] args) {

        int x = 1; 
	if (x > 0) {
	    if (x < 5) {
		System.out.println(" 0 < " + x + " < 5"); 
	    } 
        } else { 
	    System.out.println(x + " <= 0"); 
        } 

    } 
}

class One {
    public static void main(String[] args) {

        int x = 1; 
	if (x > 0) {
	    if (x < 5) {
		System.out.println(" 0 < " + x + " < 5"); 
	    } 
        } else  
	    System.out.println(x + " <= 0"); 


    } 
}

Now if in the resulting program

class One {
    public static void main(String[] args) {

        int x = 1; 
	if (x > 0) {
	    if (x < 5) {
		System.out.println(" 0 < " + x + " < 5"); 
	    }  
        } else  
	    System.out.println(x + " <= 0"); 


    } 
}

Therefore the curly braces that surround it are not grouping more than one statement.

Therefore they are not needed (the block they define has only one statement).

And from this reason we can just drop them.

We obtain:

class One {
    public static void main(String[] args) {

        int x = 1; 
	if (x > 0) 
	    if (x < 5) {
		System.out.println(" 0 < " + x + " < 5"); 
	    }      
          else  
	    System.out.println(x + " <= 0"); 


    } 
}

So we carefully re-indent it to obtain:

class One {
    public static void main(String[] args) {

        int x = 1; 
	if (x > 0) 
	    if (x < 5) {
		System.out.println(" 0 < " + x + " < 5"); 
	    } else  
	      System.out.println(x + " <= 0"); 
    } 
}

The program above (try it for x = 10) does not run correctly.

(It reports that 10 is less than 0).

Here's what this program is equivalent to now:

class One {
    public static void main(String[] args) {

        int x = 1; 

        if (x > 0 && x < 5) System.out.println(" 0 < " + x + " < 5"); 

        if (x > 0 && ! (x < 5) ) System.out.println(x + " <= 0"); 

    } 
}

See, there were three pairs of curly braces in the original code.

The first one we removed: was redundant.

The second one we removed: we removed it for the wrong reason.

Its purpose was not to create a block of one statement.

Its purpose was to keep the inner if without an else.

By removing it, the else start sliding, gravitating towards the inner if, and binding to it.

(The third pair of curly braces also can be removed, like the first).

The Use of booleans

class One {
    public static void main(String[] args) {

        int x = 1; 

        boolean a = x > 0; 

        boolean b = x < 5; 

        if (a && b) System.out.println(" 0 < " + x + " < 5"); 

        if (a && ! b ) System.out.println(x + " <= 0"); 

    } 
}