Leap of Faith

Following the flow of execution is one way to read programs, but as you saw in the previous section, it can quickly become labarynthine. An alternative is what I call the "leap of faith." When you come to a method invocation, instead of following the flow of execution, you assume that the method works correctly and returns the appropriate value.

In fact, you are already practicing this leap of faith when you use built-in methods. When you invoke Math.cos or drawOval, you don't examine the implementations of those methods. You just assume that they work, because the people who wrote the built-in classes were good programmers.

Well, the same is true when you invoke one of your own methods. For example, in Section 5.7 we wrote a method called isSingleDigit that determines whether a number is between 0 and 9. Once we have convinced ourselves that this method is correct---by testing and examination of the code---we can use the method without ever looking at the code again.

The same is true of recursive programs. When you get to the recursive invocation, instead of following the flow of execution, you should assume that the recursive invocation works (yields the correct result), and then ask yourself, "Assuming that I can find the factorial of n-1, can I compute the factorial of n?" In this case, it is clear that you can, by multiplying by n.

Of course, it is a bit strange to assume that the method works correctly when you have not even finished writing it, but that's why it's called a leap of faith!