haskell - List of different types?

Question

data Plane = Plane { point :: Point, normal :: Vector Double }
data Sphere = Sphere { center :: Point, radius :: Double }

class Shape s where
    intersect :: s -> Ray -> Maybe Point
    surfaceNormal :: s -> Point -> Vector Double

I have also made both Plane and Sphere instances of Shape.

I'm trying to store spheres and planes in the same list, but it doesn't work. I understand that it shouldn't work because Sphere and Plane are two different types, but they are both instances of Shape, so shouldn't it work? How would I store shapes and planes in a list?

shapes :: (Shape t) => [t]
shapes = [ Sphere { center = Point [0, 0, 0], radius = 2.0 },
         Plane { point = Point [1, 2, 1], normal = 3 |> [0.5, 0.6, 0.2] }
         ]

Answer 1

This problem represents a turning point between object-oriented and functional thinking. Sometimes even sophisticated Haskellers are still in this mental transition, and their designs often fall into the existential typeclass pattern, mentioned in Thomas's answer.

A functional solution to this problem involves reifying the typeclass into a data type (usually once this is done, the need for the typeclass vanishes):

data Shape = Shape {
    intersect :: Ray -> Maybe Point,
    surfaceNormal :: Point -> Vector Double
}

Now you can easily construct a list of Shapes, because it is a monomorphic type. Because Haskell does not support downcasting, no information is lost by removing the representational distinction between Planes and Spheres. The specific data types become functions that construct Shapes:

plane :: Point -> Vector Double -> Shape
sphere :: Point -> Double -> Shape

If you cannot capture everything you need to know about a shape in the Shape data type, you can enumerate the cases with an algebraic data type, as Thomas suggested. But I would recommend against that if possible; instead, try to find the essential characteristics of a shape that you need rather than just listing off examples.