4.4 Using len() and sum() on collections

The len() and sum() functions provide two simple reductions—a count of the elements and the sum of the elements in a sequence. These two functions are mathematically similar, but their Python implementation is quite different.

Mathematically, we can observe this cool parallelism:

• The len() function returns the sum of ones for each value in a collection, X: ∑ _x∈X1 = ∑ _x∈Xx⁰.

• The sum() function returns the sum of each value in a collection, X: ∑ _x∈Xx = ∑ _x∈Xx¹.

The sum() function works for any iterable. The len() function doesn’t apply to iterables; it only applies to sequences. This little asymmetry in the implementation of these functions is a little awkward around the edges of statistical algorithms.

As noted above, for empty sequences, both of these functions return a proper additive identity value of zero:

>>> sum(()) 
0 
>>> len(()) ...