Question

I’ve been struggling with this for over half an hour. I know it’s something simple, but I am awful at types in Haskell, and even after reading the accepted answers to problems very similar to mine, I still cannot solve my problem – let alone understand it!

The code:

p108 = [filter (\[a,b] -> a>0 && b>0) (diophantinepairs n) | n <- [1..]]

diophantinepairs :: Integer -> [[Integer]]
diophantinepairs n = nub$map sort b
    where
        a = divisors n
        b = [[(n-d), n - (n^2)/d] | d <- a]

The error :

249:39:
    No instance for (Fractional Integer)
      arising from a use of `/'
    Possible fix: add an instance declaration for (Fractional Integer)
    In the second argument of `(-)', namely `(n ^ 2) / d'
    In the expression: n - (n ^ 2) / d
    In the expression: [(n - d), n - (n ^ 2) / d]

Thanks,
Sam.

Answer 1

Here’s how you read these kind of errors:

No instance for (Fractional Integer)

Translation: your program has an Integer, but you are using one of the methods of the Fractional class on it.

arising from a use of `/'

Translation: The method involved is /, which is part of the Fractional class. Integer is not Fractional, so you cannot apply / to an integer.

Solution: Use div or quot instead.

I can get the same error in ghci easily enough:

Prelude> (1 :: Integer) / (2 :: Integer)

<interactive>:2:16:
    No instance for (Fractional Integer)
      arising from a use of `/'
    Possible fix: add an instance declaration for (Fractional Integer)
    In the expression: (1 :: Integer) / (2 :: Integer)
    In an equation for `it': it = (1 :: Integer) / (2 :: Integer)

Alternate fix: use a Fractional type such as a Rational instead of Integer:

Prelude> (1 :: Integer) `div` (2 :: Integer)
0
Prelude> :m + Data.Ratio
Prelude Data.Ratio> (1 :: Rational) / (2 :: Rational)
1 % 2