Haskell: meaning of the error in GHCI

Question

I'm not able to figure out what this error msg means. I want to define the function distance for the data type below... I do NOT want to use any GHC extensions.. even if the code is ugly, want to understand the error better, before I move on to using the extensions. Can someone please let me know what this error means and how I can get rid of this.

class Vector v where

         distance :: v -> v -> Double

-- doesn't make sense, but WTH...    
newtype OneD1 a = OD1 a
         deriving (Show)

instance Vector (Maybe m) where
    distance _ _ = 5.6

instance Vector (OneD1 m) where
   distance (OD1 x1) (OD1 x2) = x2-x1

    Prelude> :reload
[1 of 1] Compiling Main             ( VectorTypeClass.hs, interpreted )

VectorTypeClass.hs:33:33:
    Couldn't match expected type `Double' with actual type `m'
      `m' is a rigid type variable bound by
          the instance declaration
          at C:\Users\byamm\Documents\Programming\Haskell\Lab\Expts\VectorTypeClass\VectorTypeClass.hs:32:10
    Relevant bindings include
      x2 :: m
        (bound at C:\Users\byamm\Documents\Programming\Haskell\Lab\Expts\VectorTypeClass\VectorTypeClass.hs:33:27)
      x1 :: m
        (bound at C:\Users\byamm\Documents\Programming\Haskell\Lab\Expts\VectorTypeClass\VectorTypeClass.hs:33:18)
      distance :: OneD1 m -> OneD1 m -> Double
        (bound at C:\Users\byamm\Documents\Programming\Haskell\Lab\Expts\VectorTypeClass\VectorTypeClass.hs:33:4)
    In the first argument of `(-)', namely `x2'
    In the expression: x2 - x1
Failed, modules loaded: none.
Prelude>

Answer 1

instance Vector (OneD1 m) where

This promises that (OdeD1 m) is a vector, for any m . Including OneD1 String , etc.

   distance (OD1 x1) (OD1 x2) = x2-x1

Here we try to apply - on two values of type m , which could be absolutely anything. There are two issues here:

• m might not be a numeric type -- GHC is not reporting this error, at the moment.
• the result of the difference is again of type m , but distance should produce a Double . This is the error GHC is reporting.

You need to restrict m to some numeric type, so that you can use - , and that type must admit a conversion to Double , otherwise you can't satisfy the distance signature.

One trivial way is:

instance Vector (OneD1 Double) where
   distance (OD1 x1) (OD1 x2) = x2-x1

Another could be:

instance Real m => Vector (OneD1 m) where
   distance (OD1 x1) (OD1 x2) = realToFrac (x2-x1)