What happens if we call factorial and give it 1.5 as an argument?
>>> factorial(1.5)RuntimeError: Maximum recursion depth exceeded
It looks like an inﬁnite recursion. But how can that be? There is a base case—when n == 0. But if n is not an integer, we can miss the base case and recurse forever.
In the ﬁrst recursive call, the value of n is 0.5. In the next, it is -0.5. From there, it gets smaller (more negative), but it will never be 0.
We have two choices. We can try to generalize the factorial function to work with ﬂoating-point numbers, or we can make factorial check the type of its argument. The ﬁrst option is called the gamma function and it’s a little beyond the scope of this book. So we’ll go for the second.
We can use the built-in function isinstance to verify the type of the argument. While we’re at it, we can also make sure the argument is positive:
def factorial (n): if not isinstance(n, int): print 'Factorial is only defined for integers.' return None elif n < 0: print 'Factorial is not defined for negative integers.' return None elif n == 0: return 1 else: return n * factorial(n-1)
The ﬁrst base case handles nonintegers; the second catches negative integers. In both cases, the program prints an error message and returns None to indicate that something went wrong:
>>> factorial('fred')Factorial is only defined for integers.None>>> factorial(-2)Factorial is not defined for negative integers.None
If we get past both checks, then we know that n is positive or zero, so we can prove that the recursion terminates.
This program demonstrates a pattern sometimes called a guardian. The ﬁrst two condi tionals act as guardians, protecting the code that follows from values that might cause an error. The guardians make it possible to prove the correctness of the code.
In Reverse lookup we will see a more ﬂexible alternative to printing an error message: raising an exception.