[ Python 文章收集 ] Function Composition in Python

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Preface 
While I don’t consider myself a functional programming guru, all those hours spent in Haskell, Lisp and Scheme definitively changed my way of programming. So, after seeing a lot of unnecessarily complex implementations of function composition in Python on the Web, I decided to write this article to present a simple yet powerful solution that covers all use cases. If you are familiar with function composition, you may want to go to the solution. 

Composing two functions 
Function composition is a way of combining functions such that the result of each function is passed as the argument of the next function. For example, the composition of two functions f and g is denoted f(g(x)). x is the argument of g, the result of g is passed as the argument of f and the result of the composition is the result of f. 

Let’s define compose2, a function that takes two functions as arguments (f and g) and returns a function representing their composition: 

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1. def compose2(f, g):  
2.     return lambda x: f(g(x))  

Example: 

>>> def double(x):
... return x * 2
...
>>> def inc(x):
... return x + 1
...
>>> inc_and_double = compose2(double, inc)
>>> inc_and_double(10)
22

Composing n functions 
Now that we know how to compose two functions, it would be interesting to generalize it to accept n functions. Since the solution is based on compose2, let’s first look at the composition of three functions using compose2. 

>>> def dec(x):
... return x - 1
...
>>> inc_double_and_dec = compose2(compose2(dec, double), inc) # inc > double > dec
>>> inc_double_and_dec(10)
21

Do you see the pattern? First, we compose the first two functions, then we compose the newly created function with the next one and so on. Let’s write this in Python. 

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1. import functools  
2.   
3. def compose(*functions):  
4.     def compose2(f, g):  
5.         return lambda x: f(g(x))  
6.     return functools.reduce(compose2, functions, lambda x: x)  

Or in a more compact way: 

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1. def compose(*functions):  
2.     return functools.reduce(lambda f, g: lambda x: f(g(x)), functions, lambda x: x)  

Example: 

>>> inc_double_and_dec = compose(dec, double, inc)
>>> inc_double_and_dec(10)
21

Note that functools.reduce is also called fold. 

Multiple-argument functions 
The reason why implementations get complex is because they support multiple-argument functions. But there is no need to do so, because any function can be transformed to a one-argument function using higher-order functions such as functools.partial, decorators or our own functions. 

>>> def second(*args):
... return args[1]
...
>>> def second_wrapper(lst):
... return second(*lst)
...
>>> pipeline = compose(second_wrapper, list, range)
>>> pipeline(5)
1
>>> def sub(a, b):
... return a - b
...
>>> pipeline = compose(functools.partial(sub, b=4), operator.neg)
>>> pipeline(-6)
2

If you want to learn about functional programming in Python, I recommend this document.