How to multiply functions in python?
Question:
def sub3(n):
return n - 3
def square(n):
return n * n
It’s 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, to use the composition as a key it’s awkward, you have to use them in another function which calls both functions in turn:
>>> 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 ComposableFunction(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 different in ways I don’t fully understand, and it’s arguably even uglier than just using the "lameda". Is it possible to get composition working directly with functions somehow?
Answers:
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.
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.
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))
You can compose functions using SSPipe library:
from sspipe import p, px
sub3 = px - 3
square = px * px
composed = sub3 | square
print(5 | composed)
def sub3(n):
return n - 3
def square(n):
return n * n
It’s 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, to use the composition as a key it’s awkward, you have to use them in another function which calls both functions in turn:
>>> 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 ComposableFunction(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 different in ways I don’t fully understand, and it’s arguably even uglier than just using the "lameda". Is it possible to get composition working directly with functions somehow?
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.
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.
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))
You can compose functions using SSPipe library:
from sspipe import p, px
sub3 = px - 3
square = px * px
composed = sub3 | square
print(5 | composed)