--
-- pairs of Int
--

data Pair = P Int Int deriving (Show, Eq)

pairFst (P x y ) = x
pairSnd (P x y ) = y

instance Ord Pair where
  compare (P x1 y1) (P x2 y2) = 
    case compare x1 x2 of EQ -> compare y1 y2
                          LT -> LT
                          GT -> GT
--
-- pairs of things of type a
--

data Pair a = P a a deriving (Show, Eq)

pairFst (P x y ) = x
pairSnd (P x y ) = y

-- ordering on same kinds of pairs pairs of the same type of thing

instance Ord a => Ord (Pair a) where
  compare (P x1 y1) (P x2 y2) = 
    case compare x1 x2 of EQ -> compare y1 y2
                          LT -> LT
                          GT -> GT
--
-- pairs of things of type a and b
--

data Pair a b = P a b deriving (Show, Eq)

pairFst (P x y ) = x
pairSnd (P x y ) = y

-- ordering on same kinds of pairs pairs of the same type of thing

instance (Ord a, Ord b) => Ord (Pair a b) where
  compare (P x1 y1) (P x2 y2) = 
    case compare x1 x2 of EQ -> compare y1 y2
                          LT -> LT
                          GT -> GT
--
-- pairs of things of type a and b, automatic deriving
--

data Pair a b = P a b deriving (Show, Eq, Ord)

pairFst (P x y ) = x
pairSnd (P x y ) = y

:t (<) P 1 2
:t (<) P 1 'a'
:t (<) P 1 "a"


--
-- fancier data types
--

data Fn1 = Fn1 (Int -> Int)
exec1 (Fn1 f) = f 0

data Fn2 a = Fn2 (a -> a)
exec2 (Fn2 f) = f 0

-- Fn1 2
-- :t (Fn2 (\x -> x ++ "hello"))

--
-- type synonyms
--

type Inc = Int -> Int

inc1 :: Inc
inc1 x = x + 1

inc2 :: Inc
inc2 x = x + 2

twice :: Inc -> Int -> Int
twice i x = (i (i x))

nof :: Inc -> Int -> Int -> Int
nof i 0 x = x
nof i n x = (i (nof i (n-1) x))

-- :t nof (\x -> x + 3)

data Wrapper = Wrap Inc
unwrap :: Wrapper -> Inc
unwrap (Wrap x) = x

apply :: Wrapper -> Int -> Int
apply (Wrap f) x = f x