https://youtu.be/WuGlElBjwVA

solutions.hs

import Data.List hiding (insert)
import Test.QuickCheck

data Tree a = Leaf | Node (Tree a) a (Tree a)
    deriving Show

-- Exercise 1
inv_tup_tree = aux (0,0)
 where
  aux (l,r) = Node (aux $ (l+1,r)) (l,r) (aux $ (l,r+1))
  
cut :: Integer -> Tree a -> Tree a
cut 0 _ = Leaf
cut n Leaf = Leaf
cut n (Node l v r) = Node (cut (n-1) l) v (cut (n-1) r)

-- Exercise 2
insert :: (Ord a) => a -> Tree a -> Tree a
insert v Leaf = Node Leaf v Leaf
insert v (Node l vt r)
 | v <= vt = Node (insert v l) vt r
 | v > vt  = Node l vt (insert v r)
 
inorder :: Tree a -> [a]
inorder Leaf = []
inorder (Node l v r) = (inorder l) ++ [v] ++ (inorder r)

prop_IIS xs = length xs > 5 ==> sort xs === xs'
 where 
  types = xs :: [Int]
  xs' = inorder $ foldr insert Leaf xs