Control.Monad.State.Strict

mtl-2.2.1: Monad classes, using functional dependencies

Copyright | (c) Andy Gill 2001, (c) Oregon Graduate Institute of Science and Technology, 2001
License | BSD-style (see the file LICENSE)
Maintainer | libraries@haskell.org
Stability | experimental
Portability | non-portable (multi-param classes, functional dependencies)
Safe Haskell | Safe
Language | Haskell98

Control.Monad.State.Strict

Contents

- MonadState class
- The State monad
- The StateT monad transformer
- Examples

Description

Strict state monads.

This module is inspired by the paper Functional Programming with Overloading and Higher-Order Polymorphism, Mark P Jones (http://web.cecs.pdx.edu/~mpj/) Advanced School of Functional Programming, 1995.

Synopsis

- class Monad m => MonadState s m | m -> s where
  - get :: m s
  - put :: s -> m ()
  - state :: (s -> (a, s)) -> m a
- modify :: MonadState s m => (s -> s) -> m ()
- modify' :: MonadState s m => (s -> s) -> m ()
- gets :: MonadState s m => (s -> a) -> m a
- type State s = StateT s Identity
- 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)
  }
- runStateT :: StateT s m a -> 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
- module Control.Monad
- module Control.Monad.Fix
- module Control.Monad.Trans

# MonadState class

class Monad m => MonadState s m | m -> s where

Minimal definition is either both of `get` and `put` or just `state`

Minimal complete definition

state | get, put

Methods

get :: m s

Return the state from the internals of the monad.

put :: s -> m ()

Replace the state inside the monad.

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

Embed a simple state action into the monad.

Instances

MonadState s m => MonadState s (MaybeT m) |
MonadState s m => MonadState s (ListT m) |
MonadState s m => MonadState s (IdentityT m) |
(Monoid w, MonadState s m) => MonadState s (WriterT w m) |
(Monoid w, MonadState s m) => MonadState s (WriterT w m) |
MonadState s m => MonadState s (ReaderT r m) |
MonadState s m => MonadState s (ExceptT e m) |
(Error e, MonadState s m) => MonadState s (ErrorT e m) |
MonadState s m => MonadState s (ContT r m) |
Monad m => MonadState s (StateT s m) |
Monad m => MonadState s (StateT s m) |
(Monad m, Monoid w) => MonadState s (RWST r w s m) |
(Monad m, Monoid w) => MonadState s (RWST r w s m) |

modify :: MonadState s m => (s -> s) -> m ()

Monadic state transformer.

Maps an old state to a new state inside a state monad. The old state is thrown away.

         Main> :t modify ((+1) :: Int -> Int)
         modify (...) :: (MonadState Int a) => a ()

This says that `modify (+1)` acts over any Monad that is a member of the `MonadState` class, with an `Int` state.

modify' :: MonadState s m => (s -> s) -> m ()

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

gets :: MonadState s m => (s -> a) -> m a

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

# 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.

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

MonadWriter w m => MonadWriter w (StateT s m) |
Monad m => MonadState s (StateT s m) |
MonadReader r m => MonadReader r (StateT s m) |
MonadError e m => MonadError e (StateT s m) |
MonadTrans (StateT s) |
Monad m => Monad (StateT s m) |
Functor m => Functor (StateT s m) |
MonadFix m => MonadFix (StateT s m) |
(Functor m, Monad m) => Applicative (StateT s m) |
(Functor m, MonadPlus m) => Alternative (StateT s m) |
MonadPlus m => MonadPlus (StateT s m) |
MonadIO m => MonadIO (StateT s m) |
MonadCont m => MonadCont (StateT s m) |

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

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

module Control.Monad

module Control.Monad.Fix

module Control.Monad.Trans

# Examples

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

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)