-- `fact0 n` returns the factorial of n
fact0 :: Integer -> Integer
fact0 n = if n == 0 then 1 else n * fact0(n-1)

{-
  `fact1 n` also returns the factorial of n.
  However, it's written using pattern matching.
-}
fact1 :: Integer -> Integer
fact1 0 = 1
fact1 n = n * fact1 (n-1)

-- `fact2` is also the factorial function; it uses builtin functions
fact2 :: Integer -> Integer
fact2 n = product [1..n]

-- `fib n` returns the nth Fibonacci number
fib :: Int -> Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)

-- `sum list` returns the sum of all numbers in list
sum' :: [Integer] -> Integer
sum' [] = 0
sum' (x:xs) = x + sum' xs

-- `isMember x list` returns True iff x is a member of list
isMember :: Eq a => a -> [a] -> Bool
isMember x list =
  if null list then False
  else if x == (head list) then True
  else isMember x (tail list)

{-
  `isMember' x list` still returns True iff x is a member of list.
  However, it's written using pattern matching.
-}
isMember' :: Eq a => a -> [a] -> Bool
isMember' _ [] = False
isMember' y (x:xs) = if y == x then True else isMember' y xs

{-
 `take'` works exactly the same as the prelude `take`
-}
take' :: Int -> [a] -> [a]
take' _ [] = []
take' 0 _ = []
take' n (x:xs) = x:(take' (n-1) xs)