12.3 Composite design

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

The idea is that we can define a new function, f ∘g(x), that combines two other functions, f(y) and g(x).

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 f ∘ g(x). The @f_deco decorator must define and return the composite function by merging an internal definition of f(y) with the provided base function, g(x).

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, g(x), will include a wrapper function, w(y), that has two parts. One portion of the wrapper, w_α(y), applies to the arguments of...