Haskell prime test

Question

I\'m new to Haskell, and I\'m trying a bit:

isPrime :: Integer->Bool
isPrime x = ([] == [y | y<-[2..floor (sqrt x)], mod x y == 0])

I

Answer 1

1. Because sqrt has the type Floating a => a -> a. This means the input has to be a Floating type and the output will be the same type. In other words x needs to be a Floating type. However you declared x to be of type Integer, which is not a Floating type. In addition floor needs a RealFrac type, so x needs to be that as well.

   The error message suggests that you fix that by making Integer a Floating type (by defining an instance Floating Integer (and the same for RealFrac).

   Of course this is not the correct approach in this case. Rather you should use fromIntegral to convert x to a Real (which is an instance of Floating and RealFrac) and then give that to sqrt.

2. Yes. As soon as == sees that the right operand has at least one element, it knows it is not equal to [] and thus returns False.

   That being said, null is a more idiomatic way to check whether a list is empty than [] ==.