Doing weird things with types.

[David Sankel]

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