f :: a -> a
f = \ x -> x

f' :: a -> a
f' x = x 


-- Bool
data MyBoolean = T | F
  deriving (Show)

-- Unit
data MyUnit = U
  deriving (Show)

-- Either a b 
data MyEither a b = Left' a | Right' b
  deriving (Show)

-- Empty
data Empty 

abort :: Empty -> a
abort x = error "abort"

g :: Either (a -> Empty) b -> (a -> b)
g x y =
  case x of
    Left z -> abort (z y)
    Right h -> h

safeDiv :: Integer -> Integer -> Either String Integer
safeDiv x y =
  if y == 0 then
    Left "div by zero"
  else Right (div x y)

-- Product


-- List


-- Recursion.
-- add' :: Int -> Int -> Int

add1 :: Integer -> Integer -> Integer
add1 0 y = y
add1 x y | x > 0 = (add1 (x-1) y) + 1

add2 :: Integer -> Integer -> Integer
add2 x y =
  if x == 0 then y
  else (add2 (x-1) y) + 1

add3 :: Integer -> Integer -> Integer
add3 x y =
  case x == 0 of
    True -> y
    False -> (add3 (x-1) y) + 1

-- n! = n * (n-1) ... * 1
fac :: Integer -> Integer
fac n =
  if n == 0 then 1
  else n * fac (n-1)

fac' :: Int -> Int
fac' n =
  if n == 0 then 1
  else n * fac' (n-1)

-- "Monad" 
-- Computation types and do-notation.
hello :: IO ()
hello = do
  putStrLn "welcome to haskell, what is your name?"
  l <- getLine
  putStrLn $ "welcome " ++ l ++ "!"
  return ()
  
hello' :: IO ()
hello' = do 
  putStrLn "welcome to haskell, what is your name?"
  l <- getLine
  putStrLn $ "welcome " ++ l ++ "!"
  hello'
  
main :: IO ()
main = hello'