Q29.hs

module Main where

newtype Identity a = Id a deriving Show
data DoubleF a   = DoubleF a a deriving Show

instance Functor Identity where
  fmap f (Id a) = Id (f a)

instance Functor DoubleF where
  fmap f (DoubleF x y) = DoubleF (f x) (f y)

-- it is isomorphic to
-- diag :: a -> (a, a)
-- diag x = (x, x)
diag :: Identity a -> DoubleF a
diag (Id x) = DoubleF x x

x :: Identity Int
x = Id 10

-- Part (a)
-- (diag . fmap f) x == (fmap f . diag) x
-- diag $ fmap f x == fmap f (diag x)
-- diag $ (f x)  == fmap f (x,x)
-- (f x, f x) == (f x, f x)

main = do
  print $ (diag . fmap show) x
  print $ (fmap show . diag) x