Haskell, "Is Prime" function

Question

I am new to Haskell and I couldnt understand the "Null $ filter" thing.

isPrime n
  | n < 2 = error "Zu kleine Zahl fuer Primzahltest"
  | otherwise = null $ filter (\k -> n `mod` k == 0) [2.. n-1]

Answer 1

The ($) :: (a -> b) -> a -> b operator applies the left operand to the right operand. Because it has a low precedence, it is used as a way to "group" expressions. The expression is thus equivalent to:

-- null $ filter (\k -> n `mod` k == 0) [2.. n-1]
   null ( filter (\k -> n `mod` k == 0) [2.. n-1] )

null :: Foldable f => f a -> Bool is a function that checks whether a Foldable has no elements. So for a list, it will return True if the list is empty, and False otherwise.

The list contains the integers k between 2 and n-1 in ascending order where n `mod` k is 0, hence the divisors of n. By using null we thus check that the number n has no divisors, and if that is the case we return True; otherwise we return False.