monoid (haskell)

First look at the semigroup type class (see Typeclasses in Haskell for more information)

class Semigroup a where
   (<>) :: a -> a -> a

The prefix version of (<>) is called mappend.

Then, the monoid type class is:

class Semigroup a => Monoid a where
mempty :: a

A monoid is a semigroup with an identity element.

import Data.Monoid
getSum $ Sum 1 <> Sum 2

foldable and traversable (haskell)

• In algebra, a monoid is a set with an identity element and an associative operation that is closed. (see group (algebra))

• semigroup
• monoid