[Haskell-cafe] using "default" declaration for overloaded numeric operations

[TP]

Hi,

I try to develop an embedded domain specific language in Haskell.
I don't want to type "::Rational" all the time, so I try to use a default 
declaration for my types.

This works correctly in this simple example:

------------------------------------------
default (Integer, Double) -- "default default"

mag :: Float -> Float -> Float
mag x y = sqrt( x^2 + y^2 )

main = do

print $ mag 1 1
------------------------------------------

Indeed we obtain sqrt(2) as a result. If we replace the default declaration 
by:
default ()
, we obtain errors at compilation as expected: the type of `2` is ambiguous.

Now let us consider a more complicated example:

------------------------------------------
{-# LANGUAGE FlexibleInstances #-}
import Prelude hiding ((^^))
import Data.Ratio

default (Integer, Rational, Double)

class (Num a) => Foo a where
    (^^) :: Num b => b -> a -> b

instance Foo Rational where
    (^^) x r = x ^ n
        where n = 2*numerator r -- dummy calculation

instance Foo Integer where
    (^^) x n = x ^ n

mag :: Float -> Float -> Float
mag x y = sqrt( x ^^ 2 + y ^^ 2 )

main = do
print $ mag 1 1
------------------------------------------

I would expect it to work correctly, but we obtain errors concerning the 
ambiguous type of `2`.
Why?
How to make my default declaration work?
And if I want to give the priority to `Rational` instead of `Integer`? 
Indeed, this should be possible because we don't get any error below.

$ ghci
> import Data.Ratio
> 2::Rational
2 % 1

Thanks in advance,

TP