Composite design

The common mathematical notation for a composite function looks as follows:

 

The idea is that we can define a new function, 

, that combines two other functions,

 and

.

Python's multiple-line definition of a composition function can be done through the following code:

@f_deco
def g(x):
    something  

The resulting function can be essentially equivalent to

 . The f_deco() decorator must define and return the composite function by merging an internal definition of f() with the provided g(). 

The implementation details show that Python actually provides a slightly more complex kind of composition. The structure of a wrapper makes it helpful to think of Python decorator composition as follows:

A decorator applied to some application function, 

, will include a wrapper function,

, that has two parts. One portion of the wrapper, 

, applies to the arguments of the wrapped function,

, and the other portion, 

 , applies to the result of the wrapped function.

Here's a more concrete idea, shown...