transformers-0.3.0.0: Concrete functor and monad transformers

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

Control.Monad.Trans.State.Strict

Contents

- The State monad
- The StateT monad transformer
- State operations
- Lifting other operations
- Examples
  - State monads
  - Counting
  - Labelling trees

Description

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

In this version, sequencing of computations is strict. For a lazy version, see Control.Monad.Trans.State.Lazy, 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)