What is wrong with this class/instance?

Question

I have this:

data Vector3 t = Vector3 { ax, ay, az :: t }
data Point3 t = Point3 { x, y, z :: t }
data Ray3 t = Ray3 { ori :: Point3 t, dir :: Vector3 t }
data Sphere t = Sphere { center :: Point3 t, radius :: t }

I want a Shape type class, so I did this:

class Shape s where
      distance :: s -> Ray3 t -> t

distance takes a shape and a ray and computes the distance to the shape along the given ray. When I try to create an instance, it doesn't work. This is what I have so far:

instance Shape (Sphere t) where
         distance (Sphere center radius) ray = -- some value of type t --

How do I create an instance of Shape? I've tried everything I can think of, and I'm getting all kind of errors.

Answer 1

The problem is that the type variable t in Sphere t is not the same as the one in the type signature of distance. Your current types are saying that if I have a Sphere t1, I can check it against a Ray3 t2. However, you probably want these to be the same type. To solve this, I would change the Shape class to

class Shape s where
    distance :: s t -> Ray3 t -> t

Now the dependency on t is explicit, so if you write your instance as

instance Shape Sphere where
    distance (Sphere center radius) ray = ...

the types should line up nicely, although you'll probably need to add in some numeric constraints on t to do any useful calculations.