Copyright	(c) Andy Gill 2001, (c) Oregon Graduate Institute of Science and Technology, 2001
License	BSD-style (see the file LICENSE)
Maintainer	[email protected]
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell98

The State monad

type State s = StateT s Identity Source

A state monad parameterized by the type s of the state to carry.

The return function leaves the state unchanged, while >>= uses the final state of the first computation as the initial state of the second.

state Source

Construct a state monad computation from a function. (The inverse of runState.)

runState Source

Unwrap a state monad computation as a function. (The inverse of state.)

evalState Source

Evaluate a state computation with the given initial state and return the final value, discarding the final state.

• evalState m s = fst (runState m s)

execState Source

Evaluate a state computation with the given initial state and return the final state, discarding the final value.

• execState m s = snd (runState m s)

mapState :: ((a, s) -> (b, s)) -> State s a -> State s b Source

Map both the return value and final state of a computation using the given function.

• runState (mapState f m) = f . runState m

withState :: (s -> s) -> State s a -> State s a Source

withState f m executes action m on a state modified by applying f.

• withState f m = modify f >> m

The StateT monad transformer

newtype StateT s m a Source

A state transformer monad parameterized by:

• s - The state.
• m - The inner monad.

The return function leaves the state unchanged, while >>= uses the final state of the first computation as the initial state of the second.

evalStateT :: Monad m => StateT s m a -> s -> m a Source

Evaluate a state computation with the given initial state and return the final value, discarding the final state.

• evalStateT m s = liftM fst (runStateT m s)

execStateT :: Monad m => StateT s m a -> s -> m s Source

Evaluate a state computation with the given initial state and return the final state, discarding the final value.

• execStateT m s = liftM snd (runStateT m s)

mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n b Source

Map both the return value and final state of a computation using the given function.

• runStateT (mapStateT f m) = f . runStateT m

withStateT :: (s -> s) -> StateT s m a -> StateT s m a Source

withStateT f m executes action m on a state modified by applying f.

• withStateT f m = modify f >> m

State operations

get :: Monad m => StateT s m s Source

Fetch the current value of the state within the monad.

put :: Monad m => s -> StateT s m () Source

put s sets the state within the monad to s.

modify :: Monad m => (s -> s) -> StateT s m () Source

modify f is an action that updates the state to the result of applying f to the current state.

• modify f = get >>= (put . f)

modify' :: Monad m => (s -> s) -> StateT s m () Source

A variant of modify in which the computation is strict in the new state.

• modify' f = get >>= (($!) put . f)

gets :: Monad m => (s -> a) -> StateT s m a Source

Get a specific component of the state, using a projection function supplied.

• gets f = liftM f get

Lifting other operations

liftCallCC :: CallCC m (a, s) (b, s) -> CallCC (StateT s m) a b Source

Uniform lifting of a callCC operation to the new monad. This version rolls back to the original state on entering the continuation.

liftCallCC' :: CallCC m (a, s) (b, s) -> CallCC (StateT s m) a b Source

In-situ lifting of a callCC operation to the new monad. This version uses the current state on entering the continuation. It does not satisfy the laws of a monad transformer.

liftCatch :: Catch e m (a, s) -> Catch e (StateT s m) a Source

Lift a catchE operation to the new monad.

liftListen :: Monad m => Listen w m (a, s) -> Listen w (StateT s m) a Source

Lift a listen operation to the new monad.

liftPass :: Monad m => Pass w m (a, s) -> Pass w (StateT s m) a Source

Lift a pass operation to the new monad.

Examples

State monads

Parser from ParseLib with Hugs:

type Parser a = StateT String [] a
   ==> StateT (String -> [(a,String)])

For example, item can be written as:

item = do (x:xs) <- get
       put xs
       return x

type BoringState s a = StateT s Identity a
     ==> StateT (s -> Identity (a,s))

type StateWithIO s a = StateT s IO a
     ==> StateT (s -> IO (a,s))

type StateWithErr s a = StateT s Maybe a
     ==> StateT (s -> Maybe (a,s))

Counting

A function to increment a counter. Taken from the paper "Generalising Monads to Arrows", John Hughes (http://www.cse.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

Labelling trees

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
        case elemIndex x table of
            Nothing -> do
                put (table ++ [x])
                return (length table)
            Just i -> return i

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