Because mod :: Integral a => a -> a -> a and sqrt :: Floating a => a -> a, the final type of primes' ends up being :: (Floating a, Integral a) => [a], which doesn't work very well obviously.

The easiest solution is to try
let primes' = 2 : [p | p <- odds, null [d | d <- (takeWhile (<=ceiling (sqrt (fromInteger p))) odds), p `mod` d == 0]]

You can make your own sqrt if you want to clean it up.
let isqrt = ceiling . sqrt . fromInteger

On Fri, Jul 1, 2016 at 9:41 PM, Russ Abbott <russ.abbott@gmail.com> wrote:

I'm trying to define primes using just list comprehension. The following works.

Prelude> odds = [3, 5..]

Prelude> primes = 2 : [p | p <- odds, null [d | d <- take (p `div` 4) odds, p `mod` d == 0]]

But when I replace "take (p `div` 4)" with takeWhile (<=(sqrt p)) as in

Prelude> primes' = 2 : [p | p <- odds, null [d | d <- (takeWhile (<=(sqrt p)) odds), p `mod` d == 0]]

I get no error message on entering the statement, but when I run

Prelude> take 8 primes'

I get an error message that I can't understand.

<interactive>:23:1: error:
• Ambiguous type variable ‘a0’ arising from a use of ‘it’
prevents the constraint ‘(Floating a0)’ from being solved.
Probable fix: use a type annotation to specify what ‘a0’ should be.
These potential instances exist:
instance Floating Double -- Defined in ‘GHC.Float’
instance Floating Float -- Defined in ‘GHC.Float’
• In the first argument of ‘print’, namely ‘it’
In a stmt of an interactive GHCi command: print it

I tried using (ceiling (sqrt p)), and I tried to explicitly declare it an Int, but neither of those helped.

I'd appreciate some help.

Thanks.

P.S. The following runs fine.

Prelude> takeWhile (<= (sqrt 99)) odds

So I'm completely stumped.

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