Improved semigroups

Improve.hs

import Data.Semigroup

data Improve a = Improve (a -> a) a

instance Semigroup (Improve a) where
    ~(Improve a' a) <> ~(Improve b' b) = Improve (a' . b') (a' b)

improve :: Semigroup a => a -> Improve a
improve a = Improve (a <>) a

disprove :: Improve a -> a
disprove ~(Improve _ a) = a

--

infixr 6 :<>
data M a = M a | M a :<> M a
    deriving Show

instance Semigroup (M a) where
    (<>) = (:<>)

m :: a -> Improve (M a)
m = improve . M

-- >>> disprove $ ((m 1 <> m 2) <> m 3)
-- M 1 :<> (M 2 :<> M 3)
--
-- >>> disprove $ fix ((m 1 <> m 2) <>)
-- M 1 :<> (M 2 :<> (M 1 :<> (M 2 :<> (...