Факториалы Haskell

-- Задача №1
factorial1 :: Int -> Int
factorial1 x = if x == 0 then 1 else x * factorial1 (x - 1)

-- Задача №2
factorial2 :: Int -> Int
factorial2 0 = 1
factorial2 x =  x * factorial2 (x - 1)

-- Задача №3
doubleFact :: Int -> Int
doubleFact x = if x <= 2 then max 1 x else x * doubleFact (x - 2)

-- Задача №4
factorial4 :: Int -> Int
factorial4 0 = 1
factorial4 x = if x < 0 then error "arg must be >=0" else x * factorial4 (x - 1)

-- Задача №5

--1-ый способ:
factorial51 :: Int -> Int
factorial51 x
    | x >= 0 = if x == 0 then 1 else x * factorial51 (x - 1)
    | otherwise = error "arg must be >=0"

--2-ой способ:
factorial52 :: Int -> Int
factorial52 x
    | x > 0 = x * factorial52 (x - 1)
    | x == 0 = 1
    | otherwise = error "arg must be >=0"

-- Задача №6

--1-ый способ:
factorial61 :: Int -> Int
factorial61 x
    | x > 0 = doubleFact x * doubleFact (x - 1)
    | x == 0 = 1
    | otherwise = error "arg must be >=0"

--2-ой способ:
factorial62 :: Int -> Int
factorial62 x | x >= 0 = helper 1 x
              | otherwise = error "arg must be >=0"

helper :: Int -> Int -> Int
helper acc 0 = acc
helper acc x = helper (acc * x) (x - 1)

--3-ий способ:
factorial63 :: Int -> Int
factorial63 n = aux n 1
    where
        aux n acc
            | n <= 1 = acc
            | otherwise = aux (n - 1) (n * acc)