transformers-0.3.0.0: Concrete functor and monad transformers

Copyright | (c) Andy Gill 2001, (c) Oregon Graduate Institute of Science and Technology, 2001
License | BSD-style (see the file LICENSE)
Maintainer | ross@soi.city.ac.uk
Stability | experimental
Portability | portable
Safe Haskell | Safe-Inferred
Language | Haskell98

Control.Monad.Trans.State.Lazy

Contents

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

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

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

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

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

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

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 b

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

``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

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

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

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

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

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

``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

Fetch the current value of the state within the monad.

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

``put` s` sets the state within the monad to `s`.

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

``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 a

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 a

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 a

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 a

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)

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 a

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)