Monoids extend semigroups, objects with an associative binary operator, by adding the notion of an identity element.

Given the mcat operator as ⋅, monoids must satisfy:

∀ a. identity ⋅ a = a ⋅ identity = a ∀ a b c. a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c

Built-in instances

Built in instances are defined for List, Map, and Stream. For example:

iex> Monoid.mplus([1, 2], [3, 4]) [1, 2, 3, 4]

iex> Monoid.identity([1, 2, 3]) []

iex> Monoid.identity(%{foo: :bar}) %{}