Recursive mathematical and list functions in Haskell

module Gyak05 where


sumTo :: Integer -> Integer
sumTo x 
 | x <= 0 = 0
 | otherwise = x + sumTo (x-1)


sumBetweenHelper :: Integer -> Integer -> Integer
sumBetweenHelper n m 
 | n == m = n
 | otherwise = sumBetweenHelper n (m-1) + m


sumBetween :: Integer -> Integer -> Integer
sumBetween n m
 | n > m = sumBetweenHelper m n
 | otherwise = sumBetweenHelper n m


sumSquaresFromTo :: Integer -> Integer -> Integer
sumSquaresFromTo n m
 | n > m = 0
 | n == m = n ^ 2
 | otherwise = n^2 + sumSquaresFromTo (n+1) m


sqr :: Integer -> Integer
sqr x = x ^ 2


powerN :: Integer -> Integer -> Integer 
powerN x 0 = 0
powerN x n = x * powerN x (n-1)


pwr :: Integer -> Integer -> Integer
pwr x n
 | n == 0 = 1
 | odd n = x * pwr x (n-1)
 | otherwise = sqr (pwr x (n `div` 2))

pwr2 :: Integer -> Integer -> Integer
pwr2 x n
 | n == 0 = 1
 | odd n = x * pwr x (n-1)
 | otherwise = pwr x (n `div` 2) * pwr x (n `div` 2)



--Listak

divByNHelper :: Integer -> Integer -> [Integer]
divByNHelper n x = ((n*x) : divByNHelper n (x+1))


divByN :: Integer -> [Integer]
divByN n = divByNHelper n 0


isNull :: [Integer] -> Bool
isNull [] = True
isNull _ = False

isNull2 :: [a] -> Bool
isNull2 (x:xs) = False
isNull2 _ = True


isNull3 :: [a] -> Bool
isNull3 (_:_) = False
isNull3 _ = True


hd :: [Integer] -> Integer 
hd (x:xs) = x


thrd :: [Integer] -> Integer
thrd (x:y:z:xs) = z