Function composition and piping (or chaining) using reduce

compose.py

from functools import partial
from functools import reduce

def _chain(order, *functions):
    ordered_functions = list(order(functions))
    first_fn = ordered_functions[0]
    rest_fn = ordered_functions[1:]
    def _apply(x, f):
        return f(x)
    def composite(*args, **kwargs):
        return reduce(_apply, rest_fn, first_fn(*args, **kwargs))
    return composite

o_ = partial(_chain, reversed)
o_.__doc__ = "Function composition: o_(f1, ..., fn)(x1, ..., xm) = f1(...(fn(x1, ..., xm)))"
p_ = partial(_chain, lambda _:_)
o_.__doc__ = "Pipe the functions: p_(f1, ..., fn)(x1, ..., xm) = fn(...(f1(x1, ..., xm)))"


# Test
import unittest

class TestKnowCases(unittest.TestCase):

    def setUp(self):
        self.add = lambda a, b: a + b
        self.inc = lambda x: x + 1

    def test_know_composition(self):
        add_and_increment = o_(self.inc, self.add)
        self.assertTrue(add_and_increment(1,2), 4)

    def test_know_piping(self):
        add_and_increment = p_(self.add, self.inc)
        self.assertTrue(add_and_increment(1,2), 4)

    def test_composition_equals_piping(self):
        add_and_increment_o = o_(self.inc, self.add)
        add_and_increment_p = p_(self.add, self.inc)
        self.assertEqual(
            add_and_increment_o(1,2),
            add_and_increment_p(1,2))

    def test_idempotence_of_composition(self):
        add_and_increment_o = o_(self.inc, self.add)
        self.assertEqual(
            add_and_increment_o(1, 2),
            add_and_increment_o(1, 2))