Interval Ariphmetic on free types

I had already post about interval arithmetic, so here is only additional example of 2nd algorithm, based on analizing of sorted edges of the interval:

But now implementation will be in Haskell and shows how to do interval arithmetic with not integers only, but any other type (which can have some metric, i.e. be ordering):

{-# LANGUAGE ExistentialQuantification #-}
import Data.List

data Iv e = Ord e => Iv e e

makeIv e1 e2 =
  Iv e1' e2' where [e1', e2'] = sort [e1, e2]

ivFst (Iv e _) = e
ivSnd (Iv _ e) = e
iv2List (Iv e1 e2) = [e1, e2]

mergeIv :: Ord e => Iv e -> Iv e -> [Iv e]
mergeIv i1 i2 =
  let sx = sort $ (iv2List i1) ++ (iv2List i2)
      [isx1, isx2] = sortBy (\x y->compare (ivSnd x) (ivSnd y)) [i1, i2] in
    case (ivSnd isx1) `compare` (ivFst isx2) of
      LT -> [Iv (sx!!0) (sx!!1), Iv (sx!!2) (sx!!3)]
      _ -> [Iv (sx!!0) (sx!!3)]


-- Examples:
data Color = Red|Orange|Yellow|Green|Blue|Indigo|Violet deriving (Eq, Ord, Show)

main = do
  print $ map iv2List $ mergeIv (makeIv 20 1) (makeIv (-1) 10)
  print $ map iv2List $ mergeIv (makeIv Red Blue) (makeIv Orange Indigo)

You see example with colors: merging of [Red; Blue] interval with [Orange; Indigo] gives us result as [Red; Indigo] interval :-)