# No import needed


# No import required...
from functools import reduce # ... but it can be loaded from the functools module


from functools import reduce # mandatory

reduce reduces an iterable by applying a function repeatedly on the next element of an iterable and the cumulative result so far.

def add(s1, s2):
    return s1 + s2

asequence = [1, 2, 3]

reduce(add, asequence)  # equivalent to: add(add(1,2),3)
# Out: 6

In this example, we defined our own add function. However, Python comes with a standard equivalent function in the operator module:

import operator
reduce(operator.add, asequence)
# Out: 6

reduce can also be passed a starting value:

reduce(add, asequence, 10)
# Out: 16

def multiply(s1, s2):
    print('{arg1} * {arg2} = {res}'.format(arg1=s1, 
                                           arg2=s2, 
                                           res=s1*s2))
    return s1 * s2

asequence = [1, 2, 3]

Given an initializer the function is started by applying it to the initializer and the first iterable element:

cumprod = reduce(multiply, asequence, 5)
# Out: 5 * 1 = 5
#      5 * 2 = 10
#      10 * 3 = 30
print(cumprod)
# Out: 30

Without initializer parameter the reduce starts by applying the function to the first two list elements:

cumprod = reduce(multiply, asequence)
# Out: 1 * 2 = 2
#      2 * 3 = 6
print(cumprod)
# Out: 6

import operator
reduce(operator.mul, [10, 5, -3])
# Out: -150

reduce will not terminate the iteration before the iterable has been completly iterated over so it can be used to create a non short-circuit any() or all() function:

import operator
# non short-circuit "all"
reduce(operator.and_, [False, True, True, True]) # = False

# non short-circuit "any"
reduce(operator.or_, [True, False, False, False]) # = True

# First falsy element or last element if all are truthy:
reduce(lambda i, j: i and j, [100, [], 20, 10])    # = []
reduce(lambda i, j: i and j, [100, 50, 20, 10])    # = 10

# First truthy element or last element if all falsy:
reduce(lambda i, j: i or j, [100, [], 20, 0])     # = 100
reduce(lambda i, j: i or j, ['', {}, [], None])   # = None

Instead of creating a lambda-function it is generally recommended to create a named function:

def do_or(i, j):
    return i or j

def do_and(i, j):
    return i and j

reduce(do_or, [100, [], 20, 0])                   # = 100
reduce(do_and, [100, [], 20, 0])                  # = []