Alternative versions of common typeclasses, augmented with a phantom type
parameter x. The purpose of this is to deal with the case where a type has
more than one candidate instance for the original, unaugmented class.
The canonical example of this predicament is selecting the monoid instance for a
type which forms a ring (and thus has at least two strong candidates for
selection as the monoid), such as Integer. This therefore gives rise to the
Sum and Product newtype wrappers, corresponding to the additive and
multiplicative monoids respectively.
The traditional fold-based summation of a list of integers looks like this:
>>> import Data.Foldable (fold)
>>> import Data.Monoid (Sum (..))
>>> getSum (fold [Sum 2, Sum 3, Sum 5]) :: Integer
10By replacing fold with multi'fold, whose constraint is MultiMonoid rather
than Data.Monoid.Monoid, we can write the same thing without the newtype
wrapper:
>>> :set -XFlexibleContexts -XTypeApplications
>>> multi'fold @Addition [2, 3, 5] :: Integer
10