+++ /dev/null
--- from the Glasgow Haskell Compiler sources (/Control/Monad/State/Strict.hs)
-
--- An example from /The Craft of Functional Programming/, Simon
--- Thompson (<http://www.cs.kent.ac.uk/people/staff/sjt/>),
--- 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)