A monoid is an interface with two operations: one that produces an element out of thin air, and one that combines two elements. It also comes with a contract,

A monoid is an interface with two operations: one that produces an element out of thin air, and one that combines two elements. It also comes with a contract, like the contracts of "equals", "hashCode" or Comparable in Java. The contract says that the operation must be associative, and that the element you produce out of thin air must be neutral: when you combine it with another element it leaves the other element unchanged. One benefit of having such general interfaces is that you can reuse code across a wide range of domains. For example: the Comparator interface in Java can be seen as a monoid, with the "thenComparing" function as the combination operation: https://docs.oracle.com/javase/8/docs/api/java/util/Comparator.html#thenComparing-java.util.Comparator- https://docs.oracle.com/javase/8/docs/api/java/util/Comparat... You could build a list of comparators and concatenate it, map a function that produces a comparator over a list and concatenate it, and so on. Another benefit is that you can be quite general when specifying requirements for your functions. In Haskell, the Writer monad only requires the type of the accumulator to be an instance of Monoid. So you can user regular lists, difference lists, or the integers under addition. Also in Haskell some composite types automatically satisfy an interface if their components do, saving you work. For example, a tuple of monoids is automatically a monoid. Any function that returns a monoid is itself a monoid as well. (Functions that begin and end in the same type can be monoids in a different way: the neutral element is the identity function and the combination operation is composition.)