In Python, the fundamental abstraction of a computation is as a procedure (other  books call them "functions" instead; we will end  up  using  both  values).   A function that  takes  a number as an argument and returns the argument value  plus 1 is de?ned as:

def f(x):

return x + 1

The indentation is important here, too. All of the instructions of the procedure have to be indented one level below  the def.  It is important  to remind the return statement at the end,  if you want your  method to give a value.  So, if you described f as above,  then  operated with  it in the shell,4 you may  get something like that:

>>> f

>>> f(4)

5

>>> f(f(f(4)))

7

If we just evaluate f, Python tells us it is a method. Then we can give it to 4 and get 5, or give it multiple times, as given.

What if we de?ne

def g(x):

x + 1

Now,  when  we play with it, we might  get something like this:

>>> g(4)

>>> g(g(4))

Traceback (most recent call last):

File "", line 1, in ? File "", line 2, in g

TypeError: unsupported operand type(s) for +: 'NoneType' and 'int'

What happened!! First, when  we calculated g(4), we take nothing at all, because  our definition of g did not give anything. Well...strictly speaking, it given a special number known as None, which the file does  not bother printing out.  The number  None has a special  type,  known  NoneType.   So, then,  when  we tried  to give g to the  answer  of g(4),  it ended up  trying  to calculate g(None), which  made  it try to evaluate None + 1, which  made  it complain that  it did  not know  how  to add  something of type NoneType and something of type int.