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Control.Monad.Trans.State.Strict | Portability | portable | Stability | experimental | Maintainer | libraries@haskell.org |
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Description |
Strict state monads, passing an updateable state through a computation.
See below for examples.
In this version, sequencing of computations is strict in the state.
For a lazy version, see Control.Monad.Trans.Writer.Lazy, which
has the same interface.
Some computations may not require the full power of state transformers:
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Synopsis |
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type State s = StateT s Identity | | state :: (s -> (a, s)) -> State s a | | runState :: State s a -> s -> (a, s) | | evalState :: State s a -> s -> a | | execState :: State s a -> s -> s | | mapState :: ((a, s) -> (b, s)) -> State s a -> State s b | | withState :: (s -> s) -> State s a -> State s a | | newtype StateT s m a = StateT {} | | evalStateT :: Monad m => StateT s m a -> s -> m a | | execStateT :: Monad m => StateT s m a -> s -> m s | | mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n b | | withStateT :: (s -> s) -> StateT s m a -> StateT s m a | | get :: Monad m => StateT s m s | | put :: Monad m => s -> StateT s m () | | modify :: Monad m => (s -> s) -> StateT s m () | | gets :: Monad m => (s -> a) -> StateT s m a | | liftCallCC :: ((((a, s) -> m (b, s)) -> m (a, s)) -> m (a, s)) -> ((a -> StateT s m b) -> StateT s m a) -> StateT s m a | | liftCallCC' :: ((((a, s) -> m (b, s)) -> m (a, s)) -> m (a, s)) -> ((a -> StateT s m b) -> StateT s m a) -> StateT s m a | | liftCatch :: (m (a, s) -> (e -> m (a, s)) -> m (a, s)) -> StateT s m a -> (e -> StateT s m a) -> StateT s m a | | liftListen :: Monad m => (m (a, s) -> m ((a, s), w)) -> StateT s m a -> StateT s m (a, w) | | liftPass :: Monad m => (m ((a, s), b) -> m (a, s)) -> StateT s m (a, b) -> StateT s m a |
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The State monad
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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.
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:: s -> (a, s) | pure state transformer
| -> State s a | equivalent state-passing computation
| Construct a state monad computation from a function.
(The inverse of runState.)
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:: State s a | state-passing computation to execute
| -> s | initial state
| -> (a, s) | return value and final state
| Unwrap a state monad computation as a function.
(The inverse of state.)
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:: State s a | state-passing computation to execute
| -> s | initial value
| -> a | return value of the state computation
| Evaluate a state computation with the given initial state
and return the final value, discarding the final state.
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:: State s a | state-passing computation to execute
| -> s | initial value
| -> s | final state
| Evaluate a state computation with the given initial state
and return the final state, discarding the final value.
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Map both the return value and final state of a computation using
the given function.
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withState f m executes action m on a state modified by
applying f.
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The StateT monad transformer
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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.
| Constructors | StateT | | runStateT :: s -> m (a, s) | |
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Evaluate a state computation with the given initial state
and return the final value, discarding the final state.
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Evaluate a state computation with the given initial state
and return the final state, discarding the final value.
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Map both the return value and final state of a computation using
the given function.
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withStateT f m executes action m on a state modified by
applying f.
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State operations
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Fetch the current value of the state within the monad.
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put s sets the state within the monad to s.
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modify f is an action that updates the state to the result of
applying f to the current state.
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Get a specific component of the state, using a projection function
supplied.
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Lifting other operations
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liftCallCC :: ((((a, s) -> m (b, s)) -> m (a, s)) -> m (a, s)) -> ((a -> StateT s m b) -> StateT s m a) -> StateT s m a | Source |
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Uniform lifting of a callCC operation to the new monad.
This version rolls back to the original state on entering the
continuation.
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liftCallCC' :: ((((a, s) -> m (b, s)) -> m (a, s)) -> m (a, s)) -> ((a -> StateT s m b) -> StateT s m a) -> StateT s m a | Source |
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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.
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Lift a catchError operation to the new monad.
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Lift a listen operation to the new monad.
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Lift a pass operation to the new monad.
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Examples
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State monads
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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))
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Counting
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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
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Labelling trees
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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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