A Float wrapper that implements Monoid, but not the monoid laws

monoids.hs

-- first monoid over Floats
data MaxNum = MaxNum Float deriving (Show)
instance Semigroup MaxNum where
  (MaxNum a) <> (MaxNum b) = MaxNum $ max a b
instance Monoid MaxNum where
  mempty = MaxNum 0 -- N.B. this does not fulfil the monoid laws fully. consider negative values!
aOne = MaxNum 4
aTwo = MaxNum 1
aThree = aOne <> aTwo
doMaxNum = print aThree  -- MaxNum 4.0

-- main :: IO ()
main = do
  doMaxNum

You can derive newtype MaxNum = MaxNum Float deriving Semigroup via Max Float but as you already noted the Monoid instance is invalid and you are prevented from deriving a Monoid

Nice! Did not know about deriving via before. :)