January 2013

While I don't consider myself a functional programming expert, 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 online, 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.

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:

```
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
```

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)
```

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!

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 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 reading https://docs.python.org/3/howto/functional.html.