[Haskell-cafe] Functional dependencies and incoherent instances

[Joel Björnson]

Hi,

On Wed, Oct 8, 2008 at 2:31 PM, Tobias Bexelius
<tobias.bexelius at avalanchestudios.se> wrote:
> Hi,
>
> Im trying to overload a multiplication operator for scalars and vectors,
> but keep running into the error message "Functional dependencies
> conflict". What I think is going on is that the dependency check doesn't
> work with incoherent (or overlapping) instances. In the example below,
> the two instances of Mult are overlapping. What I want is the vector
> version to be used for vectors and the scalar version used for numbers,
> even if a vector-type is an instance of the Num-class (I believe
> -fallow-incoherent-instances would make that kind of choise for me,
> right?).
>
> Im using the Visual Studio plugin Visual Haskell, and thus GHC version
> 6.6. Otherwise I think associated types might have worked better for
> this...
>
>
> {-# OPTIONS_GHC -fglasgow-exts -fallow-undecidable-instances
> -fallow-incoherent-instances #-}
>
> data V2 a = V2 a a
>
> class Vec v a where
>    dot :: v a -> v a -> a
> instance Num a => Vec V2 a where
>    V2 a1 a2 `dot` V2 b1 b2 = a1*b1+a2*b2
>
> class Mult a b c | a b -> c where
>        (*.) :: a -> b -> c
> instance (Num x) => Mult x x x where (*.) = (*)
> instance (Vec a x) => Mult (a x) (a x) x where (*.) = dot

According to the definition of Mult the parameter 'c' from above
should be uniquely determined by a pair of types 'a' and 'b'. Now,
lets say we have a type NumVec that instantiates both the Vec class
and the Num as in

instance Num (NumVec a) where
instance Vec NumVec a where

Then according to the instance declaration

instance (Num x) => Mult x x x where ...

(NumVec a)  (NumVec a) (NumVec a) instantiates the class. On the other
hand looking at the instance declaration:

instance (Vec a x) => Mult (a x) (a x) x where ...

(NumVec a) (NumVec a)  a , is also an instance why the fun dep (a b ->
c) is violated.

Regards,
Joel