sum and product

Given a container of numbers, of a type in the Num type class, we can compute their sum or product:

sum     :: Num a => t a -> a
product :: Num a => t a -> a

These are just the generalizations of sum and product for lists to arbitrary foldable containers:

GHCi

>>> sum Nothing
0
>>> sum (Just 1)
1
>>> product Nothing
1
>>> product (Just 5)
5
>>> sum tree
11
>>> product tree
30

For the empty container, sum and product return the unit elements of addition and multiplication, which are 0 and 1.

As we discussed before, sum and product can be implemented via foldl or, in the interest of efficiency, its strict cousin foldl':

sum     = foldl' (+) 0
product = foldl' (*) 1

The actual default implementations provided in the standard library use the Sum and Product monoids, the strict version of foldMap and a low-level version of function composition:

sum     = getSum     #. foldMap' Sum
product = getProduct #. foldMap' Product

In spirit, these are the same as our implementations using foldl'.