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 the form is as follows:

@f
def g(x):
    something

This is vaguely equivalent to . The equivalence isn't very precise because the @f decorator isn't the same as the mathematical abstraction of composing and . For the purposes of discussing function composition, we'll ignore the implementation disconnect between the abstraction of and the @f decorator.

Because decorators wrap another function, Python offers a slightly more generalized composition. We can think of Python design as follows:

A decorator applied to some application function, , will include a wrapper function. One portion of the wrapper, , applies before the wrapped function and the other portion, , applies after the wrapped function.

The Wrapper() function often looks as follows:

@wraps(argument_function)
def something_wrapper...