今天在看functools中的 reduce时看到一篇很好的blog，这篇blog对这个函数的解释很好，尤其实在多个函数嵌套的使用中，但个人发现还是有些地方不是特别明了也有点小瑕疵，下面我做的补充和说明用红色字体表示出来，方便查看。原文虽然是英文的，但没有特别复杂的语句和单词，因此有点基础都能读懂，不足翻译了。

原文：https://mathieularose.com/function-composition-in-python/

Function Composition in Python

 January 2013 in ARTICLES

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 (fand g) and returns a function representing their composition:

def compose2(f, g): 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_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.

import functools def compose(*functions): def compose2(f, g): return lambda x: f(g(x)) return functools.reduce(compose2, functions, lambda x: x)

Or in a more compact way:

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

注：亲自测试过上述形式可以更加简洁，如下：

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

    ##lambda f, g: lambda x: f(g(x))这条语句的变量排列顺序非常重要，它会影响函数的最后复合形式，     ##例如functions=(f1,f2,f3,f4),那么上述函数最终产生的函数形式为：f1(f2(f3(f4(x))))     ##如果lambda f, g: lambda x: f(g(x))这条语句变为：     ##lambda f, g: lambda x: g(f(x))这条语句,     ##例如functions=(f1,f2,f3,f4),那么上述函数最终产生的函数形式为：f4(f3(f2(f1(x))))

下面我修改了f,g的顺序，做的实验如下：

def compose(*functions): return functools.reduce(lambda f, g: lambda x: g(f(x)), functions, lambda x: x) inc_double_and_dec = compose(dec, double, inc) a=inc_double_and_dec(10) print (a)##输出19

Example:

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

Note that functools.reduce is also called fold.

Edit: Handle the case when the list of functions is empty. Thanks to Matthew Singer for catching this!

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.

Examples:

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

If you want to learn about functional programming in Python, I recommend reading https://docs.python.org/3/howto/functional.html.