Disclaimer: I don't really know all about category theory, so some definitions might not be absolutely correct.

Monoid is the category of all types that have a empty value and an append operation.

The best example is a list.

instance Monoid [a] where
mempty = []
mappend = (++)


Why do I need it? Well, you can think of a function where you need to incrementally store data.

Storing them to a Monoid, you can start with a list and then change to a Set, without changing the function itself, because it would be defined based on the Monoid operations.

instance Ord a => Monoid (Set a) where
mempty = empty
mappend = union
mconcat = unions

Hope I have helped!

Regards,

Rafael






--
Rafael Gustavo da Cunha Pereira Pinto

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