Concept:
List monoid
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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