Implementation of binary search tree in Haskell

Tree.hs

{- Implementation of BST (binary search tree)
Script is absolutly free/libre, but with no guarantee.
Author: Ondrej Profant -}

import qualified Data.List

{- DEF data structure -}
data (Ord a, Eq a) => Tree a = Nil | Node (Tree a) a (Tree a) 
	deriving Show

{- BASIC Information -}
empty :: (Ord a) => Tree a -> Bool
empty Nil = True
empty  _  = False

contains :: (Ord a) => (Tree a) -> a -> Bool
contains Nil _ = False
contains (Node t1 v t2) x 
	| x == v = True
	| x  < v = contains t1 x 
	| x  > v = contains t2 x

{- BASIC Manipulation -}
insert :: (Ord a) => Tree a -> a -> Tree a
insert Nil x = Node Nil x Nil
insert (Node t1 v t2) x 
	| v == x = Node t1 v t2
	| v  < x = Node t1 v (insert t2 x)
	| v  > x = Node (insert t1 x) v t2

delete :: (Ord a) => Tree a -> a -> Tree a
delete Nil _ = Nil
delete (Node t1 v t2) x  
	| x == v = deleteX (Node t1 v t2)
	| x  < v = Node (delete t1 x) v t2
	| x  > v = Node t1 v (delete t2 x)

-- Delete root (is used on subtree)
deleteX :: (Ord a) => Tree a -> Tree a 
deleteX (Node Nil v t2) = t2
deleteX (Node t1 v Nil) = t1
deleteX (Node t1 v t2) = (Node t1 v2 t2) --(delete t2 v2))
	where 
		v2 = leftistElement t2

-- Return leftist element of tree (is used on subtree)
leftistElement :: (Ord a) => Tree a -> a
leftistElement (Node Nil v _) = v
leftistElement (Node t1 _ _) = leftistElement t1

-- Create tree from list of elemtents
ctree :: (Ord a) => [a] -> Tree a
ctree [] = Nil
ctree (h:t) = ctree2 (Node Nil h Nil) t
	where
		ctree2 tr [] = tr
		ctree2 tr (h:t) = ctree2 (insert tr h) t

-- Create perfect balance BST
ctreePB :: (Ord a) => [a] -> Tree a
ctreePB [] = Nil
ctreePB s = cpb Nil (qsort s) 

cpb :: (Ord a) => Tree a -> [a] -> Tree a
cpb tr [] = tr
cpb tr t = cpb (insert tr e) t2
	where	
		e = middleEl t
		t2 = Data.List.delete e t

-- Element in middle
middleEl :: (Ord a) => [a] -> a
middleEl s = mEl s s 

mEl :: (Ord a) => [a] ->  [a] -> a
mEl    []    (h:s2) = h
mEl (_:[])   (h:s2) = h
mEl (_:_:s1) (_:s2) = mEl s1 s2

{- PRINT -}
inorder :: (Ord a) => Tree a -> [a]
inorder Nil = []
inorder (Node t1 v t2) = inorder t1 ++ [v] ++ inorder t2

preorder :: (Ord a) => Tree a -> [a]
preorder Nil = []
preorder (Node t1 v t2) = [v] ++ preorder t1 ++ preorder t2

postorder :: (Ord a) => Tree a -> [a]
postorder Nil = []
postorder (Node t1 v t2) = postorder t1 ++ postorder t2 ++ [v]

-- from wiki
levelorder :: (Ord a) => Tree a -> [a]
levelorder t = step [t]
	where
		step [] = []
		step ts = concatMap elements ts ++ step (concatMap subtrees ts)
		elements Nil = []
		elements (Node left x right) = [x]
		subtrees Nil = []
		subtrees (Node left x right) = [left,right]

qsort :: (Ord a) => [a] -> [a] 
qsort [] = []
qsort (h:t) = (qsort [x| x<-t, x < h]) ++ [h] ++ (qsort [x| x<-t, x>=h ])

Elements are duplicated after using the delete function. You pull the leftist element out of the right subtree, but you never update the right subtree to get rid of the pulled item! Easy fix.

just a newbie here trying to look for examples to look at.

looks like something changed with datatype contexts so you need "{-# LANGUAGE DatatypeContexts #-}" or to change the setup for that to prevent compilation error with newer versions i think.

This code has been brought up in #haskell on IRC, and I wanted to mention this should not be used as an example of good design for Haskell code. Adding constraints to data type definitions is not a valuable thing to do (data (Ord a, Eq a) => Tree a = ...) because it doesn't help you ensure the invariants you want to, while meaning to have to add those constraints to every single functions which accepts a Tree, for example, the type of size should be Tree a -> Int because it doesn't need to know anything about the elements contained in the tree, but by doing this the type must be size :: (Ord a, Eq a) => Tree a -> Int, even though it makes no use of those constraints. It also does not prevent a user from creating invalid trees, myTree = Node (Node Nil 100 Nil) 1 (Node Nil 20 Nil) is perfectly valid for that type, but does not maintain the invariant you're expecting. (@deeTEEcee this is the reason it fails to compile, it's a feature that has been considered such a misfeature it has been removed from GHC)

Hi,
Looking for a short example of bst, but this one is much more.

I create another gist with only 3 methods (insert, fromArray, toPreorderArray).

Hope you enjoy, thanks.