Haskell Num Instance

Question

I am new to Haskell so I apologize if I am overlooking something basic, but I am creating a Coord type that has three parameters: Position, Vector, and Scalar. Coord must be an instance of Num and must have specific implemented methods in it. I believe I have what I need already, but I'm assuming I'm missing something basic because I get an error based on the Num instance.

My code:

data Position x y = Position (x, y)
data Vector x y = Vector (x, y)
data Scalar n = Scalar n
data Coord x y n = Coord (Position x y, Vector x y, Scalar n)

instance Num Coord where
    negate (Position (x, y)) = Position (-x, -y)
    negate (Vector (x, y)) = Vector (-x, -y)
    (+) (Vector (a, b) Position (x, y)) = Position (x+a, y+b)
    (+) (Vector (a, b) Vector (c, d)) = Vector (c+a, d+b)
    (+) (Scalar x Scalar y) = Scalar (x+y)
    (*) (Vector (a, b) Scalar c) = Vector (a*c, b*c)
    (*) (Position (x1, y1) Position (x2, y2)) = (x1*x2) + (y1*y2)
    (*) (Scalar x Scalar y) = Scalar (x*y)
    (-) (Vector (a, b) Position (x, y)) = Position (x-a, y-b)
    (-) (Position (x1, y1) Position (x2, y2)) = Vector (x2-x1, y2-y1)
    (-) (Scalar x Scalar y) = Scalar (x-y)
    abs (Position (x, y)) = Scalar sqrt((x*x)+(y*y))
    abs (Vector (x, y)) = Scalar sqrt((x*x)+(y*y))
    signum _ = error "undefined"
    fromInteger _ = error "undefined"

The error I get:

Expecting three more arguments to ‘Coord’
The first argument of ‘Num’ should have kind ‘*’,
  but ‘Coord’ has kind ‘* -> * -> * -> *’
In the instance declaration for ‘Num Coord’

Any clarification on how to use Num would be much appreciated (I'm assuming that is what's responsible for the error)

Thank you.

Answer 1

After looking into the suggestions I finally cam up with a solution that works.

data Coord = Position (Double, Double) | Vector (Double, Double) | Scalar Double deriving (Show)

instance Num Coord where
    negate (Position (x, y)) = Position (-x, -y)
    negate (Vector (x, y)) = Vector (-x, -y)
    (+) (Vector (a, b)) (Position (x, y)) = Position (x+a, y+b)
    (+) (Position (x, y)) (Vector (a, b)) = Position (x+a, y+b)
    (+) (Vector (a, b)) (Vector (c, d)) = Vector (c+a, d+b)
    (+) (Scalar x) (Scalar y) = Scalar (x+y)
    (*) (Vector (a, b)) (Scalar c) = Vector (a*c, b*c)
    (*) (Scalar c) (Vector (a, b)) = Vector (a*c, b*c)
    (*) (Position (x1, y1)) (Position (x2, y2)) = Scalar((x1*x2) + (y1*y2))
    (*) (Scalar x) (Scalar y) = Scalar (x*y)
    (-) (Vector (a, b)) (Position (x, y)) = Position (x-a, y-b)
    (-) (Position (x, y)) (Vector (a, b)) = Position (a-x, b-y)
    (-) (Position (x1, y1)) (Position (x2, y2)) = Vector (x2-x1, y2-y1)
    (-) (Scalar x) (Scalar y) = Scalar (x-y)
    abs (Position (x, y)) = Scalar (sqrt((x*x)+(y*y)))
    abs (Vector (x, y)) = Scalar (sqrt((x*x)+(y*y)))
    signum _ = error "undefined"
    fromInteger _ = error "undefined"

Hopefully this helps anyone in the future that is making the same mistakes as me.

Answer 2

Your problem in a word: parentheses.

instead of

negate Position (x, y) = Position (-x, -y)

do

negate (Position (x, y)) = Position (-x, -y)

The former implicitly implies that negate is a function which takes two arguments - the Position value constructor and (x,y) , rather than a single argument of type Position , since it parses it as

((negate Position) (x,y)) = ...

Your other function definitions have the same problem.