Control.Monad.State.Lazy

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.

MonadState class

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

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

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)

(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.

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)

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)

MonadCont m => MonadCont (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

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)