-- Topic about lists

fact :: Int -> Int
fact n = product [1..n]

hasElements :: [Int] -> Bool
hasElements [] = False
hasElements n = n /= []

hasElements' :: [Int] -> Bool
hasElements' [] = False
hasElements' n = length n /= 0

hasElements'' :: [Int] -> Bool
hasElements'' [] = False
hasElements'' n = not $ null n

hasElementsButWithMagic :: [Int] -> Bool
hasElementsButWithMagic = not . null

myLengthPM :: [Int] -> Int
myLengthPM [] = 0
myLengthPM (_:xs) = 1 + myLength xs

myLengthNonPM :: [Int] -> Int
myLengthNonPM [] = 0
myLengthNonPM xs
    | null xs = 0
    | otherwise = 1 + (myLength $ tail xs)

getClosedInterval :: Int -> Int -> [Int]
getClosedInterval x y = [min x y .. max x y]

isInside :: Int -> Int -> Int -> [Int]
isInside x y n = n `elem` [min x y .. max x y]

removeFirst :: Int -> [Int] -> [Int]
removeFirst n (x:xs)
    | x == n = removeFirst n xs
    | otherwise = removeFirst n xs

removeAllRec :: Int -> [Int] -> [Int]
removeAllRec n (x:xs)
    | x == n = removeAllRec n xs
    | otherwise = x : removeAllRec n xs

removeAllHOF :: Int -> [Int] -> [Int]
removeAllHOF n xs = filter (\x -> x == n) xs

incrementByLC :: Int -> [Int] -> [Int]
incrementByLC n xs = [n + x | x <- xs]

incrementByHOF :: Int -> [Int] -> [Int]
incrementByHOF n xs = map (+n) xs

rev = read . reverse . show
rev' n = read $ reverse $ show n

sumDivs n = sum [d | d <- [1..n], mod n d == 0]

isPrime n = n > 2 && [1, n] == [d | d <- [1..n], mod n d == 0]

sumDig = sum . map digitToInt . show
sumDig' n = sum $ map digitToInt $ show n

getPrimesLC :: Int -> Int -> [Int]
getPrimesLC x y = [d | d <- [min x y .. max x y], isPrime d && elem '7' $ show d]

getPrimesHOF :: Int -> Int -> [Int]
getPrimesHOF x y = filter (\d -> isPrime d && elem '7' $ show d) [min x y .. max x y]