On Sat, Apr 03, 2004 at 01:35:44PM +0200, Henning Thielemann wrote:
(I like to omit -fallow-undecidable-instances before knowing what it means)
There's a nice section in the GHC user's manual on it. I can't add anything to that.
-- a classical linear space class VectorSpace v a where zero :: v add :: v -> v -> v scale :: a -> v -> v
You might want to add a functional dependency, if you only have one type of scalars per vertor space:
class VectorSpace v a | v -> awhere zero :: v add :: v -> v -> v scale :: a -> v -> v
But then again, you might not.
instance Num a => VectorSpace a a where zero = 0 add = (+) scale = (*)
Here the compiler complains the first time:
VectorSpace.lhs:27: Illegal instance declaration for `VectorSpace a a' (There must be at least one non-type-variable in the instance head Use -fallow-undecidable-instances to permit this) In the instance declaration for `VectorSpace a a'
Well, you know how to fix this... Another way to fix it is to add a dummy type constructor:
newtype Vector a = Vector a
instance Num a => VectorSpace (Vector a) a
Later:
instance Num a => VectorSpace [a] a where
By the way, depending how you resolve the issue above, you might want instead
instance (RealFloat a, VectorSpace b a) => VectorSpace [b] a where ...
Now I introduce a new datatype for a vector valued quantity. The 'show' function in this simplified example may show the vector with the magnitude separated from the vector components. ... The problem which arises here is that the type 'a' is used for internal purposes of 'show' only. Thus the compiler can't decide which instance of 'Normed' to use if I call 'show':
This is exactly what is fixed by adding the functional dependency above. Alternatively, if you want to consider varying the scalars, you can add 'a' as a dummy type variable to 'Quantity':
data Quantity v a = Quantity v
instance (Show v, Fractional a, Normed v a) => Show (Quantity v a) where show (Quantity v) = let nv::a = norm v in (show (scale (1/nv) v)) ++ "*" ++ (show nv)
GHC still won't accept this without prompting, but now at least you can provide a complete type: *VectorSpace> show (Quantity [1,2,3] :: Quantity [Double] Double) "[0.16666666666666666,0.3333333333333333,0.5]*6.0" Note that this makes sense semantically: if you have a vector space over both, say, the reals and the complexes, you need to know which base field to work over when you normalize.
So I tried the approach which is more similar to what I tried before with a single-parameter type class: I use a type constructor 'v' instead of a vector type 'v' ...
data QuantityC v a = QuantityC (v a)
instance (Fractional a, NormedC v a, Show (v a)) => Show (QuantityC v a) where show (QuantityC v) = let nv = normC v in (show (scaleC (1/nv) v)) ++ "*" ++ (show nv)
It lead the compiler eventually fail with: VectorSpace.lhs:138: Non-type variables in constraint: Show (v a) (Use -fallow-undecidable-instances to permit this) In the context: (Fractional a, NormedC v a, Show (v a)) While checking the context of an instance declaration In the instance declaration for `Show (QuantityC v a)'
Hmm, I don't know how to fix up this version. Peace, Dylan