Why it is impossible to divide Integer number in Haskell?

Question

This code

(4 :: Integer) / 2

will lead to error:

  No instance for (Fractional Integer) arising from a use of ‘/’
    In the expression: (4 :: Integer) / 2
    In an equation for ‘it’: it = (4 :: Integer) / 2

Why?

I need to specify

fromIntegral(4 :: Integer) / 2

to get a result. But what if I need a real number and not 2.0?

Answer 1

Because the Integer type has no Fractional instance.

The type for (/) is Fractional a => a -> a -> a. Consider what happens when a = Integer. You'd have Integer -> Integer -> Integer. But 1/2 is not an integer, it's 0.5. So the only way to fit the division operator would be to round the result. But there is not a single way to round, and the best choice depends on the application, hence it was decided to not provide that instance.

If you want to perform integer division use the div or quot functions (they use different rounding). Otherwise convert to something that supports a well-defined division operation like Rational (this is what the fromIntegral is doing).