Icelandjack/MonoidToSemigroup.markdown

## MonoidToSemigroup.markdown

      
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              MonoidToSemigroup.markdown
            
          
    demoteMonoid :: (forall m. Monoid m => m) -> Semigroup m => Maybe m
demoteMonoid k = eval k where
  eval :: MONOID m -> Semigroup m => Maybe m
  eval = getOption . foldMap (Option . Just)

data MONOID a = NIL | SING a | MONOID a :<> MONOID a
  deriving Foldable

instance Monoid (MONOID a) where
  mempty  = NIL
  mappend = (:<>)
like http://comonad.com/reader/2015/free-monoids-in-haskell/

However, one might wonder what a free monoid would look like as something closer to a traditional data type. To construct that, first ignore the required equations, and consider only the generators; we get:
data FMG a = None | Single a | FMG a :<> FMG a