Portability	portable
Stability	experimental
Maintainer	ross@soi.city.ac.uk
Safe Haskell	Safe-Infered

Control.Monad.Trans.State.Lazy

Contents

The State monad
The StateT monad transformer
State operations
Lifting other operations
Examples

Description

Lazy state monads, passing an updatable state through a computation. See below for examples.

In this version, sequencing of computations is lazy. For a strict version, see Control.Monad.Trans.State.Strict, which has the same interface.

Some computations may not require the full power of state transformers:

For a read-only state, see Control.Monad.Trans.Reader.
To accumulate a value without using it on the way, see Control.Monad.Trans.Writer.

Synopsis

type State s = StateT s Identity
state :: Monad m => (s -> (a, s)) -> StateT s m 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 {
- runStateT :: s -> m (a, s)
}
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

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

Arguments

:: Monad m

=> (s -> (a, s))

pure state transformer

-> StateT s m a

equivalent state-passing computation

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

runState Source

Arguments

:: 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 .)

evalState Source

Arguments

:: 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.

```
evalState  m s = fst  (runState  m s)
```

execState Source

Arguments

:: 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.

```
execState  m s = snd  (runState  m s)
```

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

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 aSource

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.

Constructors

StateT

Fields

runStateT :: s -> m (a, s)

Instances

MonadTrans (StateT s)

Monad m => Monad (StateT s m)

Functor m => Functor (StateT s m)

MonadFix m => MonadFix (StateT s m)

MonadPlus m => MonadPlus (StateT s m)

(Functor m, Monad m) => Applicative (StateT s m)

(Functor m, MonadPlus m) => Alternative (StateT s m)

MonadIO m => MonadIO (StateT s m)

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

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 sSource

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 bSource

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 aSource

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 sSource

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)
```

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

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

```
gets  f = liftM  f get 
```

Lifting other operations

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

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

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

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 :: (m (a, s) -> (e -> m (a, s)) -> m (a, s)) -> StateT s m a -> (e -> StateT s m a) -> StateT s m aSource

Lift a catchError operation to the new monad.

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

Lift a listen operation to the new monad.

liftPass :: Monad m => (m ((a, s), b) -> m (a, s)) -> StateT s m (a, b) -> StateT s m aSource

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
 (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)