module Example9 where

data Tree = Leaf Int | Tree :^: Tree deriving Show

-- fmr: "find min and replace"
fmr :: Int -> Tree -> (Tree, Int)
fmr m (Leaf i) = (Leaf m, i)
fmr m (l :^: r) = (l' :^: r', min ml mr)
    where
	(l', ml) = fmr m l
        (r', mr) = fmr m r


replaceByMin :: Tree -> Tree
replaceByMin t = t'
    where
	-- Tying the recursive knot.
        (t', m) = fmr m t


aSmallTree = Leaf 3 :^: Leaf 1


aLargerTree = (Leaf 7 :^: Leaf 3) :^: (Leaf 1 :^: (Leaf 2 :^: Leaf 9))