Ok. I was hoping that there was a common ancestor of Integral and Fractional. Now I realize that I can be more precise about what I wanted: avg :: (FractionalOrIntegral a) => [a] -> a avg xs = sum (map fromFractionalOrIntegral xs) / (fromIntegral (length xs)) But although it there may be a sound type system supporting this it looks a little weird... thanks, matthias On Sat, Apr 01, 2006 at 06:10:48PM -0500, Cale Gibbard wrote:

To: Matthias Fischmann Cc: haskell-cafe@haskell.org From: Cale Gibbard Date: Sat, 1 Apr 2006 18:10:48 -0500 Subject: Re: [Haskell-cafe] casting numerical types

Arbitrary numerical types don't support division. (They're rings, not fields.) The (Fractional a) => [a] -> a type is the best you can do.

- Cale

On 01/04/06, Matthias Fischmann wrote:

...

hi all,

this should be a quick one (for now I would be happy with a "that's impossible", just want to make sure I don't miss anything). I want to compute the average from a list of arbitrary numerical element type. I wanted to do this:

avg :: (Num a) => [a] -> a avg xs = sum (map fromNum xs) / (fromIntegral (length xs))

but it doesn't compile. All I could get to work is this:

avg :: (Fractional a) => [a] -> a avg xs = sum xs / (fromIntegral (length xs))

avgI :: (Integral a) => [a] -> Float avgI = avg . map fromIntegral

The two function names for the same thing are tolerable, but not very elegant. Is there another option?

Thanks, Matthias

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On Sun, Apr 02, 2006 at 10:53:02AM +0100, Malcolm Wallace wrote:

To: haskell-cafe@haskell.org From: Malcolm Wallace Date: Sun, 2 Apr 2006 10:53:02 +0100 Subject: Re: [Haskell-cafe] casting numerical types

Matthias Fischmann writes:

...

avg :: (FractionalOrIntegral a) => [a] -> a avg xs = sum (map fromFractionalOrIntegral xs) / (fromIntegral (length xs))

Your condition is probably too strong. For one thing, there is no need to convert every element of the list being summed, just its result. Also, does the final result need to be the same type as the elements?

avg :: (Num a, Fractional b) => [a] -> b avg xs = fromRational (sum xs % toInteger (length xs))

you are right, your version looks better, and i managed to make ghc eat these variants: avg' :: (RealFrac a, Fractional b) => [a] -> b avg' xs = fromRational (round (sum xs) % toInteger (length xs)) avg'' :: (RealFrac a, Fractional b) => a -> [a] -> b avg'' epsilon xs = fromRational ((1 % toInteger (length xs)) * approxRational (sum xs) epsilon) But the problem is that (%) requests integral types, and I do not want to round my input. Also, I have the same problem as above that Integral types are not RealFrac, so these do not accept [Int] as input. When I try yours, however, I get: Couldn't match the rigid variable `a' against `Integer' `a' is bound by the type signature for `avg' Expected type: a Inferred type: Integer In the application `toInteger (length xs)' In the second argument of `(%)', namely `toInteger (length xs)' So do I need 'toNum' now? m.