import Test.QuickCheck
import Data.List( sort, insert )


--

ordered :: Ord a => [a] -> Bool
ordered (x:y:xs) = x <= y && ordered (y:xs)
ordered _        = True

-- try 1, does not work

prop_Insert1 :: Int -> [Int] -> Bool
prop_Insert1 x xs =
  ordered (insert x xs)

-- try 2, works badly

prop_Insert2 :: Int -> [Int] -> Property
prop_Insert2 x xs =
  collect (length xs) $
    ordered xs ==> ordered (insert x xs)

-- try 3, works better

orderedList :: Gen [Int]
orderedList =
  do xs <- arbitrary
     return (sort xs)

data OrderedList = Ordered [Int]
  deriving ( Show )

instance Arbitrary OrderedList where
  arbitrary =
    do xs <- orderedList
       return (Ordered xs)

prop_Insert3 :: Int -> OrderedList -> Bool
prop_Insert3 x (Ordered xs) =
  ordered (insert x xs)