You should look at functional dependencies. They allow you to write things like: class HasTimes a b c | a b -> c where (*) :: a -> b -> c this means "a and b determine c", which is more or less what you want. This, especially as related to numeric operations, has been discussed a lot on this list; it's probably worth reading up. On Thu, 6 Nov 2003, David Sankel wrote:

Hello All,

I'm trying to create a generic function (*) using classes. I've been playing with ghc extensions but haven't found what I need yet.

class HasTimes a b c where (*) :: a -> b -> c

This doesn't work because it can't figure out what the return types are for a general expression a*(b*c). This kinda makes sense since someone could overload HasTimes Float Float Int and HasTimes Float Float Float.

What about:

class HasTimes a b where (*) :: a -> b -> c

This would sort of imply that c is the only possible result of a (*) for types a and b. But I'm pretty sure this functionality hasn't been implemented.

Why is this important? I'm trying to reduce ugliness of code using the following library:

data Matrix = Matrix ((Float,Float),(Float,Float)) data HVec = HVec Float Float data VVec = VVec Float Float

idMatrix = Matrix ((1.0,0.0),(0.0,1.0))

vhVecMult (VVec a b) (HVec c d) = Matrix ((a*c,a*d),(b*c,b*d))

matMult (Matrix ((a,b),(c,d))) (Matrix ((e,f),(g,h))) = Matrix (((a*e+b*g),(a*f+b*h)),((c*e+d*g),(c*f+d*h)))

matVVecMult (Matrix ((c,d),(e,f))) (VVec a b) = VVec (a*c + b*d) (a*e + b*f)

hVecMatMult (HVec a b) (Matrix ((c,d),(e,f))) = HVec (c*c+b*e) (a*d+b*f)

vVecMinus (VVec a b) (VVec c d) = VVec (a-c) (b-d)

vVecPlus (VVec a b) (VVec c d) = VVec (a+c) (b+d)

matMinus (Matrix ((a,b),(c,d))) (Matrix ((e,f),(g,h))) = Matrix ((a-e,b-f),(c-g,d-h))

hvVecMult (HVec a b) (VVec c d) = a*c + b*d

scalHVecMult :: Float -> HVec -> HVec scalHVecMult i (HVec a b ) = HVec (i*a) (i*b)

Thanks,

David J. Sankel

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