Instances for Codensity (Semigroup, Monoid, numeric classes)

[Icelandjack]

There are some trivial instances for Managed that could be implemented for Codensity, the Monoid instance is put to good use by Gabriel Gonzales in his Applied category theory and abstract algebra talk

instance Semigroup a => Semigroup (Codensity m a) where
  (<>) = liftA2 (<>)

instance Monoid a => Monoid (Codensity m a) where
  mempty = pure mempty

#if !(MIN_VERSION_base(5,0,0))
  mappend = liftA2 (<>)
#endif

Same with Num, Fractional, Floating.

[Atry]

Why not use Ap (Codensity m) a instead?
https://hackage.haskell.org/package/base-4.12.0.0/docs/Data-Monoid.html#t:Ap