Haskell Book 15.15 Exercise 9

SemigroupExercises.hs

{-# LANGUAGE DeriveGeneric #-}

module SemigroupExercises where

import Data.Semigroup
import Test.QuickCheck
import GHC.Generics

-- ...

newtype Combine a b =
  Combine { unCombine :: (a -> b) }
  deriving (Generic)

instance Semigroup b
  => Semigroup (Combine a b) where
    Combine { unCombine = f } <> Combine { unCombine = g } = 
      Combine { unCombine = (\x -> (f x) <> (g x)) }

-- arbitrary :: Arbitrary a => Gen a
-- coarbitrary :: Coarbitrary a => a -> Gen b -> Gen b

instance (CoArbitrary a, Arbitrary b) => Arbitrary (Combine a b) where
  arbitrary = do
    f <- arbitrary
--  f <- (arbitrary :: Gen (a -> b)) 
--  The line above does not work for
--  reasons not entirely clear to me
    return $ Combine { unCombine = f }

-- (Cannot get Eq instance to work)
-- instance (Eq b) => Eq (Combine a b) where
--  Combine f == Combine g = 
--    unCombine (Combine f) == unCombine (Combine g)
--    This is same as:    f == g
--    Which you can't do? (Because decidability problem?)

-- Sure why not
instance Show (Combine a b) where
  show (Combine _) = "Combine a b"

-- Not sure why this doesn't work
-- if we've already established an
-- Arbitrary instance for Combine a b
-- 
prop_combAssoc :: Property
prop_combAssoc =
  forAll (arbitrary :: Gen (Combine a b))
    $ \f ->
      forAll (arbitrary :: Gen (Combine a b))
        $ \g ->
          forAll (arbitrary :: Gen (Combine a b))
            $ \h ->
              f <> (g <> h) == (f <> g) <> h