This module is inspired by the paper Functional Programming with Overloading and Higher-Order Polymorphism, Mark P Jones (http://www.cse.ogi.edu/~mpj/) Advanced School of Functional Programming, 1995.
See below for examples.
|class Monad m => MonadState s m | m -> s where|
|modify :: MonadState s m => (s -> s) -> m ()|
Monadic state transformer.
Maps an old state to a new state inside a state monad. The old state is thrown away.
Main> :t modify ((+1) :: Int -> Int) modify (...) :: (MonadState Int a) => a ()
This says that modify (+1) acts over any Monad that is a member of the MonadState class, with an Int state.
|gets :: MonadState s m => (s -> a) -> m a|
|Gets specific component of the state, using a projection function supplied.|
|The State Monad|
|newtype State s a|
|mapState :: ((a, s) -> (b, s)) -> State s a -> State s b|
Map a stateful computation from one (return value, state) pair to another. For instance, to convert numberTree from a function that returns a tree to a function that returns the sum of the numbered tree (see the Examples section for numberTree and sumTree) you may write:
sumNumberedTree :: (Eq a) => Tree a -> State (Table a) Int sumNumberedTree = mapState (\ (t, tab) -> (sumTree t, tab)) . numberTree
|withState :: (s -> s) -> State s a -> State s a|
|Apply this function to this state and return the resulting state.|
|The StateT Monad|
|newtype StateT s m a|
|evalStateT :: Monad m => StateT s m a -> s -> m a|
|Similar to evalState|
|execStateT :: Monad m => StateT s m a -> s -> m s|
|Similar to execState|
|mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n b|
|Similar to mapState|
|withStateT :: (s -> s) -> StateT s m a -> StateT s m a|
|Similar to withState|
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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