import Control.SetFunctions
import Data.List (nub)

idpair :: a -> (a,a)
idpair x = (x,x)

f :: (Int,Int) -> Int
f (idpair x) = 0  -- <=>
--f (x,x) = 0  <=>
--f (x,y) | x=:=y = 0

zero :: Int -> Int
zero _ = 0

pair :: Int -> Int -> (Int,Int)
pair x y = (x,y)

g :: (Int,Int) -> Int
g (pair (zero x) x) = 0
-- > g (0,x) = 0

-------------------------------------------------------------

-- Permutation with functional patterns:
perm :: Data a => [a] -> [a]
perm []             = []
perm (xs ++ x : ys) = x : perm (xs ++ ys)

-- Contains a list two adjacent element out of order:
someDescending :: [Int] -> Bool
someDescending (_ ++ [x,y] ++ _) | x > y = True

-- A new permutation sort:
sort :: [Int] -> [Int]
sort xs | isEmpty ((set1 someDescending) p) = p
 where p = perm xs


-- Returns the length of the input list until the first repeated element.
lengthUpToRepeat :: [Int] -> Int
-- lengthUpToRepeat [1,2,5,42,41,4,2,5,6]  --> 7
lengthUpToRepeat (ps ++ [r] ++ _)
  | r `elem` ps && nub ps == ps
  = length ps + 1