I was surprised not to find any documentation regarding interactions of Ord and Bounded. Are there any instances where

minBound <= x == True

and

maxBound >= x == True

don't hold for every x?

Possibly relatedly, I was looking for Bounded instances for Maybe and Either. To me the following instances seem sensible:

instance Bounded a => Bounded (Maybe a) where

   minBound = Nothing

   maxBound = Just maxBound

instance (Bounded a, Bounded b) => Bounded (Either a b) where

  minBound = Left minBound

  maxBound = Right maxBound

Are these instances omitted for a reason? Interestingly, both types do have corresponding Ord instances.

Lastly, I noticed that Natural has a lower bound (0) but not an upper one, and therefore cannot have a Bounded instance. Is anyone aware of some prior art regarding a LowerBounded class or similar?

Cheers,

Simon