--Consider three two-dimensional points a, b, and c. If we look at the angle
--formed by the line segment from a to b and the line segment from b to c,
--it either turns left, turns right, or forms a straight line.
--Define a Direction data type that lets you represent these possibilities.
data Direction a = ToRight
          | ToLeft
          | ToStraight
          | None
            deriving (Eq, Show)

-- Write a function that calculates the turn made by three 2D points and returns a Direction.
dirCalc :: Ord a => Fractional a => Eq a => Num a => (a, a) -> (a, a) -> (a, a) -> Direction a
dirCalc (0,0) (0,0) (0,0) = None
dirCalc (x1, y1) (x2, y2) (x3, y3) = if k1 > k2 then ToRight
                              else if k1 == k2 then ToStraight
                              else ToLeft
                          where k1 = (y2 - y1) / (x2 - x1)
                                k2 = (y3 - y2) / (x3 - x2)