Scott, Here's a type families solution (see below). *Main> ((2,3) :: (Int, Int)) <+> (10,10) (12,13) *Main> I think TypeSynonymInstances are best avoided if possible, otherwise the two types are not really interchangeable. It's certainly not needed for this, anyway. Steve {-# LANGUAGE TypeFamilies, FlexibleInstances, FlexibleContexts #-} infixl 6 <+> infixl 6 <-> infixl 7 *> infixl 7 <* class Num (Elt v) => BasicVector v where type Elt v :: * (<+>) :: v -> v -> v (<->) :: v -> v -> v (*>) :: Elt v -> v -> v (<*) :: v -> Elt v -> v v1 <-> v2 = v1 <+> fromInteger (-1) *> v2 v1 <* c = c *> v1 c *> v1 = v1 <* c type Vector2D a = (a,a) instance Num a => BasicVector (a, a) where type Elt (a, a) = a (ax,ay) <+> (bx,by) = (ax+bx,ay+by) c *> (ax,ay) = (c*ax,c*ay) On 21/05/10 03:30, Brent Yorgey wrote:
On Thu, May 20, 2010 at 06:35:34AM -0400, Walck, Scott wrote:
Hi folks,
NewVectorShort.hs:19:0: Type synonym `Vector2D' should have 1 argument, but has been given 0 In the instance declaration for `BasicVector Vector2D' Failed, modules loaded: none.
The problem is simply that type synonyms must always be fully applied, so given
type Vector2D a = (a,a)
you cannot declare an instance for Vector2D, since Vector2D is not applied to an argument. The solution is to make Vector2D a newtype:
newtype Vector2D a = V2D (a,a)
Of course, this means you'll need to wrap and unwrap V2D constructors in various places, which can be a bit annoying, but such is the price of progress.
For another take on encoding vector stuff in Haskell, see the vector-space package on Hackage.
-Brent
I don't understand how what I'm trying to do is different from, say, the Monad instance for Maybe. (Maybe a) is a type, and (Vector2D a) is a type.
Thanks,
Scott
{-# LANGUAGE TypeSynonymInstances #-}
infixl 6 <+> infixl 6 <-> infixl 7 *> infixl 7 <*
class BasicVector v where (<+>) :: v a -> v a -> v a (<->) :: v a -> v a -> v a (*>) :: Num a => a -> v a -> v a (<*) :: Num a => v a -> a -> v a v1 <-> v2 = v1 <+> fromInteger (-1) *> v2 v1 <* c = c *> v1 c *> v1 = v1 <* c
type Vector2D a = (a,a)
instance BasicVector Vector2D where (ax,ay) <+> (bx,by) = (ax+bx,ay+by) c *> (ax,ay) = (c*ax,c*ay)
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