Hi, I study opengl and decided to improve the Vertex3 type. data Vertex3 a => Vertex3 a! a! a! a vertex and a vector are same. It is often need to multiple a vector at a scalar or to calculate a scalar production of two vectors. I have realized the Num class for the Vertex3 type: instance (Num a) => Num (Vertex3 a) where (Vertex3 x y z) * (Vertex3 x' y' z') = (Vertex3 (x*x') (y*y') (z*z')) (Vertex3 x y z) + (Vertex3 x' y' z') = (Vertex3 (x+x') (y+y') (z+z')) (Vertex3 x y z) - (Vertex3 x' y' z') = (Vertex3 (x-x') (y-y') (z-z')) abs (Vertex3 x y z) = (Vertex3 (abs x) (abs y) (abs z)) signum (Vertex3 x y z) = (Vertex3 (signum x) (signum y) (signum z)) negate (Vertex3 x y z) = (Vertex3 (-x) (-y) (-z)) instance (Fractional a) => Fractional (Vertex3 a) where (Vertex3 x y z) / (Vertex3 x' y' z') = (Vertex3 (x/x') (y/y') (z/z')) -------------- But I can't instance my own class: class (Num a) => SVect a where (***) :: Num b => a -> b -> a instance (Num t) => SVect (Vertex3 t) where (Vertex3 x y z) *** c = Vertex3 (c*x) (c*y) (c*z) GHC posts about the error: surface.hs:107:36: Couldn't match expected type `b' against inferred type `t' `b' is a rigid type variable bound by the type signature for `***' at surface.hs:103:14 `t' is a rigid type variable bound by the instance declaration at surface.hs:105:14 In the second argument of `(*)', namely `x' In the first argument of `Vertex3', namely `(c * x)' In the expression: Vertex3 (c * x) (c * y) (c * z) ------------------------ I understand the "c" argument must have type as x,y and z, but I don't know what need to do. Daneel Yaitskov.
On 26 Feb 2009, at 09:02, Daneel Yaitskov wrote:
-------------- But I can't instance my own class:
class (Num a) => SVect a where (***) :: Num b => a -> b -> a
instance (Num t) => SVect (Vertex3 t) where (Vertex3 x y z) *** c = Vertex3 (c*x) (c*y) (c*z)
GHC posts about the error:
surface.hs:107:36: Couldn't match expected type `b' against inferred type `t' `b' is a rigid type variable bound by the type signature for `***' at surface.hs:103:14 `t' is a rigid type variable bound by the instance declaration at surface.hs:105:14 In the second argument of `(*)', namely `x' In the first argument of `Vertex3', namely `(c * x)' In the expression: Vertex3 (c * x) (c * y) (c * z) ------------------------
I understand the "c" argument must have type as x,y and z, but I don't know what need to do.
I don't immediately see what is causing your error, but try downloading the VectorSpace package off hackage – it may save you a lot of wheel reinventing here. Bob
Am Donnerstag, 26. Februar 2009 09:12 schrieb Thomas Davie:
On 26 Feb 2009, at 09:02, Daneel Yaitskov wrote:
-------------- But I can't instance my own class:
class (Num a) => SVect a where (***) :: Num b => a -> b -> a
instance (Num t) => SVect (Vertex3 t) where (Vertex3 x y z) *** c = Vertex3 (c*x) (c*y) (c*z)
GHC posts about the error:
surface.hs:107:36: Couldn't match expected type `b' against inferred type `t' `b' is a rigid type variable bound by the type signature for `***' at surface.hs:103:14 `t' is a rigid type variable bound by the instance declaration at surface.hs:105:14 In the second argument of `(*)', namely `x' In the first argument of `Vertex3', namely `(c * x)' In the expression: Vertex3 (c * x) (c * y) (c * z) ------------------------
I understand the "c" argument must have type as x,y and z, but I don't know what need to do.
The problem is that the type signature of (***) promises that it works with *any* Num type, so if v :: Vertex3 Int and c :: Double, v *** c should work. Or if v :: Vertex3 Double, c :: Complex Float, it should work, too. It obviously can't work by simply multiplying every component of v with c. But what you want isn't that general, what you want is that for every vector type a, there is some number type b, *depending on a*, for which (***) is defined. The solution to the problem is a) multiparameter typeclasses (MPTCs) b) functional dependencies (FunDeps) c) flexible instances {-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances #-} data Vec c = V !c !c deriving (Eq, Show) instance (Num c) => Num (Vec c) where (V x y) + (V u v) = V (x+u) (y+v) (V x y) - (V u v) = V (x-u) (y-v) -- I omit the others for brevity -- the SVec type class for a type a of vectors and a type b of scalars -- the type of scalars is uniquely determined by the vector type, -- that is what the "| a -> b" in the class declaration means class (Num a, Num b) => SVec a b | a -> b where (***) :: a -> b -> a -- since the type variable c appears twice in this instance declaration, -- we need the FlexibleInstances extension instance Num c => SVec (Vec c) c where (V x y) *** t = V (t*x) (t*y)
I don't immediately see what is causing your error, but try downloading the VectorSpace package off hackage – it may save you a lot of wheel reinventing here.
That is probably a good idea. While it is instructive to roll your own, avoiding reinvention of wheels is a good thing (and you can compare your wheel with the other, too). Cheers, Daniel
participants (3)
-
Daneel Yaitskov -
Daniel Fischer -
Thomas Davie