Implementing this protocol allows Interval to infer the implementation to use for a value, which allows you to pass the values to Interval.new/1 without specifying a module option:

iex> Interval.new(left: 1, right: 2)

Instead of

iex> Interval.new(module: Interval.Integer, left: 1, right: 2)
# or equivalent
iex> Interval.Integer.new(left: 1, right: 2)

This functionality is purely for ergonomic reasons, and is not required to be able to define custom intervals, or to use the builtin ones.

Explicitly calling Interval.Integer.new/1 could be preferred in certain situations because you know exactly what implementation you are getting.