Illegal instance declaraion when using tuples

Question

Messing around in Haskell getting to know type classes more intimately, but I've hit a bit of a roadblock. For whatever reason I'm not allowed to make an instance of my Vector class. I'm being told that it's an illegal instance declaration because I don't have distinct type variables? What's going on here?

class Vector v where
  vplus :: v -> v -> v
  vmult :: Num a => v -> a -> v

instance Num a => Vector (a, a) where
  (a, b) `vplus` (c, d) = (a + c, b + d)
  (a, b) `vmult` m = (a * m, b * m)

leftaroundabout leftaroundabout · Accepted Answer · 2015-12-22T13:42:13

a in you (a,a) instance will be one arbitrary Num instance. The a in vmult :: Num a => v -> a -> v knows nothing about this, i.e. this may be any other Num instance.

To make the class work you need to either

ensure that the number types can be converted into each other. For instance,

class Vector v where
  vplus :: v -> v -> v
  vmult :: RealFrac a => v -> a -> v

instance RealFrac a => Vector (a, a) where
  (a, b) `vplus` (c, d) = (a + c, b + d)
  (a, b) `vmult` m' = (a * m, b * m)
    where m = realToFrac m'

make sure the scalar multiplicators are actually the same type as the vector components. This is how the vector-space library does it. For your code, it would take on the form

{-# LANGUAGE TypeFamilies, FlexibleInstances #-}

class Vector v where
  type Scalar v :: *
  vplus :: v -> v -> v
  vmult :: v -> Scalar v -> v

instance Num a => Vector (a, a) where
  type Scalar (a,a) = a
  (a, b) `vplus` (c, d) = (a + c, b + d)
  (a, b) `vmult` m = (a * m, b * m)

Illegal instance declaraion when using tuples

1 Answers