How to multiply functions in python?

Question

def sub3(n):
    return n - 3

def square(n):
    return n * n

It's dead easy to compose functions in python:

>>> my_list
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> [square(sub3(n)) for n in my_list]
[9, 4, 1, 0, 1, 4, 9, 16, 25, 36]

Unfortunately, when wanting to use the composition as a key, it's kind of lame:

>>> sorted(my_list, key=lambda n: square(sub3(n)))
[3, 2, 4, 1, 5, 0, 6, 7, 8, 9]

This should really just be sorted(my_list, key=square*sub3), because heck, function __mul__ isn't used for anything else anyway:

>>> square * sub3
TypeError: unsupported operand type(s) for *: 'function' and 'function'

Well let's just define it then!

>>> type(sub3).__mul__ = 'something'
TypeError: can't set attributes of built-in/extension type 'function'

D'oh!

>>> class CoolerFunction(types.FunctionType):
...     pass
...
TypeError: Error when calling the metaclass bases
    type 'function' is not an acceptable base type

D'oh!

class Hack(object):
    def __init__(self, function):
        self.function = function
    def __call__(self, *args, **kwargs):
        return self.function(*args, **kwargs)
    def __mul__(self, other):
        def hack(*args, **kwargs):
            return self.function(other(*args, **kwargs))
        return Hack(hack)

Hey, now we're getting somewhere..

>>> square = Hack(square)
>>> sub3 = Hack(sub3)
>>> [square(sub3(n)) for n in my_list]
[9, 4, 1, 0, 1, 4, 9, 16, 25, 36]
>>> [(square*sub3)(n) for n in my_list]
[9, 4, 1, 0, 1, 4, 9, 16, 25, 36]
>>> sorted(my_list, key=square*sub3)
[3, 2, 4, 1, 5, 0, 6, 7, 8, 9]

But I don't want a Hack callable class! The scoping rules are totally different in ways I don't fully understand, and this is even uglier than the "lameda" arguably. I want to monkeypatch the functions. How can I do that?

Answer 1

You can use your hack class as a decorator pretty much as it's written, though you'd likely want to choose a more appropriate name for the class.

Like this:

class Composable(object):
    def __init__(self, function):
        self.function = function
    def __call__(self, *args, **kwargs):
        return self.function(*args, **kwargs)
    def __mul__(self, other):
        @Composable
        def composed(*args, **kwargs):
            return self.function(other(*args, **kwargs))
        return composed
    def __rmul__(self, other):
        @Composable
        def composed(*args, **kwargs):
            return other(self.function(*args, **kwargs))
        return composed

You can then decorate your functions like so:

@Composable
def sub3(n):
    return n - 3

@Composable
def square(n):
    return n * n

And compose them like so:

(square * sub3)(n)

Basically it's the same thing you've accomplished using your hack class, but using it as a decorator.

Answer 2

Python does not (and likely will never) have support for function composition either at the syntactic level or as a standard library function. There are various 3rd party modules (such as functional) that provide a higher-order function that implements function composition.

Answer 3

Maybe something like this:

class Composition(object):
    def __init__(self, *args):
        self.functions = args

    def __call__(self, arg):
        result = arg
        for f in reversed(self.functions):
            result = f(result)

        return result

And then:

sorted(my_list, key=Composition(square, sub3))

Answer 4

You can compose functions using SSPipe library:

from sspipe import p, px

sub3 = px - 3
square = px * px
composed = sub3 | square
print(5 | composed)