Monoid to Semigroup

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

Make it actually do anything one day

Starting to look familiar, but still useless

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

data C f a = a :< f (C f a)
  deriving Foldable

instance Foldable f => Foldable1 (C f) where
  foldMap1 :: forall a m. Semigroup m => (a -> m) -> (C f a -> m)
  foldMap1 f (a :< as) = do
    let 
      -- u = foldMap f :: _ -> FMG _

    undefined

ekmett/free#157