-- from the Glasgow Haskell Compiler sources (/Control/Monad/State/Strict.hs) -- An example from /The Craft of Functional Programming/, Simon -- Thompson (), -- Addison-Wesley 1999: \"Given an arbitrary tree, transform it to a -- tree of integers in which the original elements are replaced by -- natural numbers, starting from 0. The same element has to be -- replaced by the same number at every occurrence, and when we meet -- an as-yet-unvisited element we have to find a \'new\' number to match -- it with:\" -- -- > data Tree a = Nil | Node a (Tree a) (Tree a) deriving (Show, Eq) -- > type Table a = [a] -- -- > numberTree :: Eq a => Tree a -> State (Table a) (Tree Int) -- > numberTree Nil = return Nil -- > numberTree (Node x t1 t2) -- > = do num <- numberNode x -- > nt1 <- numberTree t1 -- > nt2 <- numberTree t2 -- > return (Node num nt1 nt2) -- > where -- > numberNode :: Eq a => a -> State (Table a) Int -- > numberNode x -- > = do table <- get -- > (newTable, newPos) <- return (nNode x table) -- > put newTable -- > return newPos -- > nNode:: (Eq a) => a -> Table a -> (Table a, Int) -- > nNode x table -- > = case (findIndexInList (== x) table) of -- > Nothing -> (table ++ [x], length table) -- > Just i -> (table, i) -- > findIndexInList :: (a -> Bool) -> [a] -> Maybe Int -- > findIndexInList = findIndexInListHelp 0 -- > findIndexInListHelp _ _ [] = Nothing -- > findIndexInListHelp count f (h:t) -- > = if (f h) -- > then Just count -- > else findIndexInListHelp (count+1) f t -- -- numTree applies numberTree with an initial state: -- -- > numTree :: (Eq a) => Tree a -> Tree Int -- > numTree t = evalState (numberTree t) [] -- -- > testTree = Node "Zero" (Node "One" (Node "Two" Nil Nil) (Node "One" (Node "Zero" Nil Nil) Nil)) Nil -- > numTree testTree => Node 0 (Node 1 (Node 2 Nil Nil) (Node 1 (Node 0 Nil Nil) Nil)) Nil -- -- sumTree is a little helper function that does not use the State monad: -- -- > sumTree :: (Num a) => Tree a -> a -- > sumTree Nil = 0 -- > sumTree (Node e t1 t2) = e + (sumTree t1) + (sumTree t2)