A function to increment a counter. Taken from the paper
Generalising Monads to Arrows, John
Hughes (http://www.math.chalmers.se/~rjmh/), November 1998:
tick :: State Int Int
tick = do n <- get
put (n+1)
return n
Add one to the given number using the state monad:
plusOne :: Int -> Int
plusOne n = execState tick n
A contrived addition example. Works only with positive numbers:
plus :: Int -> Int -> Int
plus n x = execState (sequence $ replicate n tick) x
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)
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