Question

I’m trying to find all the primes less than some integer n as concisely as possible, using list comprehensions. I’m learning Haskell, and this is just an exercise. I’d like to write something like:

isqrt :: Integral a => a -> a   
isqrt = floor . sqrt . fromIntegral

primes :: Integral a => a -> [a]  
primes n = [i | i <- [1,3..n], mod i k /= 0 | k <- primes (isqrt i)]

which of course doesn’t work. Is there a way to have a list comprehension inside a list comprehension?

Here is the error I’m getting:

exercise-99-1.hs:138:39: Not in scope: `k'

exercise-99-1.hs:138:46:
    Illegal parallel list comprehension: use -XParallelListComp

exercise-99-1.hs:138:68: Not in scope: `i'

BUT – I wasn’t really expecting the syntax to even be legit 🙂

The intent was to translate as directly as possible: ” primes n = the set of odd integers i less than n such that i is not divisible by any k, for all k in the set: primes (isqrt i)“ – more or less. (I hope I got that right?)

Thanks!

Answer 1

I made some progress with the following:

primes :: Integral a => a -> [a]  
primes 2 = [2]  
primes n = 2:[i | i <- [3,5..n], all (\k -> if (mod i k /= 0) then True else False) 
                                     (primes (isqrt i))]

Is there a shorter way to write the lambda predicate?

edit: Yes, there is, thanks to the remarks in the comments!

primes :: Integral a => a -> [a]  
primes 2 = [2]  
primes n = 2:[i | i <- [3,5..n], all ((/= 0) . mod i) (primes (isqrt i))]