По заданным точками A, B, C, D определить, является ли четырехугольник ABCD квадратом

import Data.List
 
dist (x1,y1) (x2,y2) = (x1-x2)^2+(y1-y2)^2
 
isSquare :: [(Int,Int)] -> Bool
isSquare cs = (length d == 2) && (length (d !! 0) == 4) && ((d !! 1) !! 0) `div` ((d !! 0) !! 0) == 2 
        where d = group $ sort $ [dist c1 c2 | c1 <- cs, c2 <- cs, c1 < c2]
              
main = do
       let a1 = isSquare [(1,1),(2,2),(1,2),(2,1)]
       print a1
       let a2 = isSquare [(1,1),(2,2),(1,2),(2,-1)]
       print a2

type Point2D = (Double,Double)
 
dist :: Point2D -> Point2D -> Double
dist (x1,y1) (x2,y2) = (x1-x2)^2+(y1-y2)^2
 
(~=) :: Double -> Double -> Bool
x ~= y = abs (x-y) < 1e-5
infix 4 ~=
 
isSquare :: Point2D -> Point2D -> Point2D -> Point2D -> Bool
isSquare a b c d 
    | ab ~= h = chk b c d
    | ac ~= h = chk c b d 
    | ad ~= h = chk d b c
    | otherwise = False
    where ab = dist a b
          ac = dist a c
          ad = dist a d
          l = min ab ac
          h = l*2
          chk2 x y = l ~= dist x y
          chk x y z = chk3 a && chk3 x 
            where chk3 p = chk2 p y && chk2 p z
            
main :: IO ()
main = do
    print $ isSquare (1,1) (2,2) (1,2) (2,1)
    print $ isSquare (1,1) (2,2) (1,2) (2,-1)