Doing weird things with types.

[Hal Daume III]

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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-- 
 Hal Daume III                                   | hdaume at isi.edu
 "Arrest this man, he talks in maths."           | www.isi.edu/~hdaume