If you can't change a variable's value in Haskell, how do you create data structures?

Question

As per the title.

I have the following code which creates a binary search tree, but if I want it created and changed dynamically with user input, how would I do that if

Answer 1

The idea behind purely functional data structures is to compute new values instead of changing them and to pass them (recursively) in parameters instead of storing them globally.

So given a function

insert :: Ord a => Node a -> a -> Node a

your programm could look like this

-- Let the user enter k values that are stored in a tree structure
addTreeItems :: Int -> Node Int -> IO (Node Int)
addTreeItems 0 tree = return tree
addTreeItems k tree = do
    putStr "Enter new item: "
    item <- readLn
    addTreeItems (k - 1) (insert tree item) -- Recursively pass the tree

main = do
    tree <- addTreeItems 10 Empty
    -- ...

Using monadic helper functions, this could be simplified to things like

(foldl insert Empty) `liftM` (sequence $ replicate k (putStr "Enter new item: " >> readLn))

If you want to update values at a certain position, you'll need more advanced datastructures like a zipper, that are nevertheless still purely functional!