[Haskell-cafe] Functional dependencies and incoherent instances
Joel Björnson
joel.bjornson at gmail.com
Wed Oct 8 09:50:10 EDT 2008
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
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