Filtering an infinite list in Haskell

Question

I have the following code that implements the Sieve of Eratosthenes:

primes :: [Int]
primes = primes' [2..]

primes' :: [Int] -> [Int]
primes' [] = []
primes' (p:ps) = p:(primes' [p' | p' <- ps, not (p' `isMultiple` p)])

a `isMultiple` b = (a `mod` b) == 0

main = print (sum (primes' [2..100000]))

I would like to change main to something like

main = print (sum [p | p <- primes, p < 100000]))

Not surprisingly, this hangs because it must compare p against every element of the infinite list primes. Since I know that primes is in increasing order, how do I truncate the infinite list as soon as I find an element that exceeds my upper limit?

p.s. In theory, primes' filters the input list to return a list of primes. I know there will be some issues if I start the list at something other than 2. I'm still working on how to address this issue on my own, so please no spoilers. Thanks ;-)

Answer 1

In cases like this where you know that once the predicate returns false for an element, it won't ever return true for a later element, you can replace filter with takeWhile, which stops taking elements as soon as the predicate returns false for the first time.