This module extends the standard-library's functools, in much the same way that more-itertools extends itertools.
Most of the functions should be familiar from Haskell, Lisp, or other functional languages.
Collin Winter's functional module appears to be defunct; it doesn't quite work with 2.7, or at all with 3.x, without passing it through 2to3. However, it's still referenced in the Python howto documentation as of 2.7. The documentation for the module can be accessed via the Wayback Machine.
The partial function is now in the standard library as functools.partial. The map and filter functions are unnecessary—the odd quirks with subclasses of standard sequence types are long gone; if you need to get a list you can always compose(list, map); if you don't like the behavior with None just don't pass it. The id function has been renamed to identity, to avoid collision with the built-in.
But everything else has been reimplemented here. So, you can follow that howto and just change the name of the module you get the functions from.
Python now has almost everything from the Haskell Prelude that makes sense for Python, but not quite everything.
Some of the missing functions are more iterator-related than HOF-related, so they can be found in more-itertools.
There are a few functions that are handy to have, even if they don't have an impressive pedigree, so they're here.
compose(*funcs, unpack=False)
compose(outer, middle, inner) is equivalent to
outer(middle(inner(*args, **kw))).
compose(outer, middle, inner, unpack=True) is equivalent to outer(*inner(*middle(*args, **kw))).
compose(f) is just f, and compose() is identity.
const(x, *args, **kw)
Returns x, ignoring all other arguments.
constantly(x)
Returns the function const(x).
flip(func)
Returns a function that's the equivalent of func(*reversed(args), **kw).
foldl(func, start, iterable)
foldl(f, 0, [1, 2, 3]) is equivalent to f(f(f(0, 1), 2), 3). This is equivalent to
reduce(func, iterable, start), and is only provided for symmetry with foldr.
foldl1(func, iterable)
foldl1(f, iterable) is equivalent to foldl(f, next(iterable), iterable). This is
equivalent to reduce(func, iterable), and is only provided for symmetry with foldr1.
foldl(f, [0, 1, 2, 3]) is equivalent to f(f(f(0, 1), 2), 3).
foldr(func, start, iterable)
foldr(f, 0, [1, 2, 3]) is equivalent to f(1, f(2, f(3, 0))).
foldr1(func, iterable)
foldr1(f, [1, 2, 3, 0]) is equivalent to f(1, f(2, f(3, 0))).
identity(x)
Returns x.
nullable(func)
nullable(f) is equivalent to None if any(arg is None for arg in args) else f(*args, **kw).
For example, nullable(int)(None) returns None instead of raising a TypeError.
scanl(func, start, iterable)
scanl(f, 0, [1, 2]) yields 0, f(0, 1), f(f(0, 1), 2).
scanl1(func, iterable)
scanl1(f, [0, 1, 2]) yields 0, f(0, 1), f(f(0, 1), 2). This is
identical to itertools.accumulate(iterable, func).
scanr(func, start, iterable)
scanr(f, 0, [1, 2]) yields f(1, f(2, 0)), f(2, 0), 0.
scanr1(func, iterable)
scanr1(f, [1, 2, 0]) yields f(1, f(2, 0)), f(2, 0), 0.