The monoid identity property allows us to handle empty collections in a general way. So, instead of having the following:
def reduceLeft(op: (A, A) => A): A
We'll have a definition that takes an identity element as another parameter. By convention, this approach is called fold:
def foldLeft(identity: A)(op: (A, A) => A): A
The reason for the name foldLeft is that the identity element is used as an initial argument for reducing the collection, which leads to the following sequence of calls:
op(op(op(op(identity, a1), a2), a3), a4), ...
Optionally, it is represented in postfix-notation:
(((identity op a1) op a2) op a3) ...
Which is, well, kind of folding the collection, starting with the identity and the first element of it.
The ...
