Headline

A monoid for appending lists

Illustration

We illustrate the list monoid in Language:Haskell on the grounds of the type class Monoid with the first two members needed for a minimal complete definition:

-- The type class Monoid
class Monoid a
  where
    mempty :: a -- neutral element
    mappend :: a -> a -> a -- associative operation
    mconcat :: [a] -> a -- fold
    mconcat = foldr mappend mempty

Lists form a monoid in the following way:

-- The Monoid instance for lists
instance Monoid [a]
  where
    mempty = []
    mappend = (++)
    mconcat = concat

Now it is interesting to observe how concat is (or could be) defined:

-- Appending many lists
concat :: [[a]] -> [a]
concat = foldr (++) []

Please observe the above default definition of mconcat within the type class Monoid; it generalizes this sort of fold and thus, the definition of mconcat would not be needed in the case of the list instance of Monoid.

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