monads-fd-0.0.0.0: Monad classes, using functional dependenciesSource codeContentsIndex
Control.Monad.State.Lazy
Portabilitynon-portable (multi-param classes, functional dependencies)
Stabilityexperimental
Maintainerlibraries@haskell.org
Contents
MonadState class
The State monad
The StateT monad transformer
Examples
Description

Lazy 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 ()
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)
}
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 whereSource

get returns the state from the internals of the monad.

put replaces the state inside the monad.

Methods
get :: m sSource
put :: s -> m ()Source
show/hide Instances
MonadState s m => MonadState s (ListT 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)
(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 ()Source

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.

gets :: MonadState s m => (s -> a) -> m aSource
Gets specific component of the state, using a projection function supplied.
The State monad
type State s = StateT s IdentitySource
A parameterizable state monad where s is the type of the state to carry and a is the type of the return value.
runState :: State s a -> s -> (a, s)Source
evalStateSource
::
=> State s aAn initial value
-> sThe return value of the state application
-> a
Evaluate this state monad with the given initial state,throwing away the final state. Very much like fst composed with runstate.
execStateSource
::
=> State s aAn initial value
-> sThe new state
-> s
Execute this state and return the new state, throwing away the return value. Very much like snd composed with runstate.
mapState :: ((a, s) -> (b, s)) -> State s a -> State s bSource

Map a stateful computation from one (return value, state) pair to another. For instance, to convert numberTree from a function that returns a tree to a function that returns the sum of the numbered tree (see the Examples section for numberTree and sumTree) you may write:

sumNumberedTree :: (Eq a) => Tree a -> State (Table a) Int sumNumberedTree = mapState (\ (t, tab) -> (sumTree t, tab)) . numberTree
withState :: (s -> s) -> State s a -> State s aSource
Apply this function to this state and return the resulting state.
The StateT monad transformer
newtype StateT s m a Source

A parameterizable state monad for encapsulating an inner monad.

The StateT Monad structure is parameterized over two things:

  • s - The state.
  • m - The inner monad.

Here are some examples of use:

(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))
Constructors
StateT
runStateT :: s -> m (a, s)
show/hide Instances
evalStateT :: Monad m => StateT s m a -> s -> m aSource
Similar to evalState
execStateT :: Monad m => StateT s m a -> s -> m sSource
Similar to execState
mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n bSource
Similar to mapState
withStateT :: (s -> s) -> StateT s m a -> StateT s m aSource
Similar to withState
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)
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