Hi, The Graham Scan function I wrote, looks like running well. But when I put it in QuickCheck, it just failed in some case. Anyone can show me some clues about the problem? Thanks. When I test it in ghci with some example, it returns the right result. *Main> let xs = [Point {x = 1.0, y = 1.0},Point {x = 0.0, y = 4.0},Point {x = 0.0, y = 6.0},Point {x = 3.0, y = 5.0},Point {x = 4.0, y = 4.0},Point {x = 4.0, y = 1.0},Point {x = 3.0, y = 3.0},Point {x = 2.0, y = 2.0},Point {x = 5.0, y = 5.0}] *Main> grahamScan xs [Point {x = 1.0, y = 1.0},Point {x = 4.0, y = 1.0},Point {x = 5.0, y = 5.0},Point {x = 0.0, y = 6.0},Point {x = 0.0, y = 4.0}] *Main> grahamScan it [Point {x = 1.0, y = 1.0},Point {x = 4.0, y = 1.0},Point {x = 5.0, y = 5.0},Point {x = 0.0, y = 6.0},Point {x = 0.0, y = 4.0}] However, QuickCheck find some points which can fail it. Could it be a data type overflow problem? prop_scan_idempotent xs = not (null xs) ==> (grahamScan . grahamScan) xs == grahamScan xs *Main> quickCheck prop_scan_idempotent *** Failed! Falsifiable (after 13 tests and 4 shrinks): [Point {x = -6.29996952110807, y = -91.37172300100718},Point {x = 9.353314917365527, y = 64.35532141764591},Point {x = -23.826685687218355, y = 60.32049750442556},Point {x = -1.4281411275074123, y = 31.54197550020998},Point {x = -2.911218918860731, y = 15.564623822256719}] === code === module GrahamScan (grahamScan, Point(..)) where import Data.List import Data.Ratio data Point = Point { x :: Double, y :: Double } deriving (Eq, Show) instance Ord Point where compare (Point x1 y1) (Point x2 y2) = compare (y1, x1) (y2, x2) data Vector = Vector { start :: Point, end :: Point } deriving (Eq) cosine :: Vector -> Double cosine (Vector (Point x1 y1) (Point x2 y2)) = (x2 - x1) / ((x2 - x1) ^ 2 + (y2 - y1) ^ 2) instance Ord Vector where compare a b = compare (f a) (f b) where f = negate . cosine sort' :: [Point] -> [Point] sort' xs = pivot : fmap end sortedVectors where sortedVectors = sort . fmap (Vector pivot) . delete pivot $ xs pivot = minimum xs counterClockwise :: Point -> Point -> Point -> Bool counterClockwise (Point x1 y1) (Point x2 y2) (Point x3 y3) = (x2 - x1) * (y3 - y1) > (y2 - y1) * (x3 - x1) scan :: [Point] -> [Point] scan (p1 : p2 : p3 : xs) | counterClockwise p1 p2 p3 = p1 : scan (p2 : p3 : xs) | otherwise = scan (p1 : p3 : xs) scan xs = xs grahamScan :: [Point] -> [Point] grahamScan = scan . sort' . nub === code === Best regards, Zhi-Qiang Lei zhiqiang.lei@gmail.com