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-- Search for -fallow-undecidable-instances to see why this is needed
-----------------------------------------------------------------------------
-- |
-- Module : Control.Monad.State
-- Copyright : (c) Andy Gill 2001,
-- (c) Oregon Graduate Institute of Science and Technology, 2001
-- License : BSD-style (see the file libraries/base/LICENSE)
--
-- Maintainer : libraries@haskell.org
-- Stability : experimental
-- Portability : non-portable (multi-param classes, functional dependencies)
--
-- State monads.
--
-- This module is inspired by the paper
-- /Functional Programming with Overloading and
-- Higher-Order Polymorphism/,
-- Mark P Jones (<http://www.cse.ogi.edu/~mpj/>)
-- Advanced School of Functional Programming, 1995.
--
-- See below for examples.
-----------------------------------------------------------------------------
module Control.Monad.State (
-- * MonadState class
MonadState(..),
modify,
gets,
-- * The State Monad
State(..),
evalState,
execState,
mapState,
withState,
-- * The StateT Monad
StateT(..),
evalStateT,
execStateT,
mapStateT,
withStateT,
module Control.Monad,
module Control.Monad.Fix,
module Control.Monad.Trans,
-- * Examples
-- $examples
) where
import Prelude
import Control.Monad
import Control.Monad.Fix
import Control.Monad.Trans
import Control.Monad.Reader
import Control.Monad.Writer
-- ---------------------------------------------------------------------------
-- | /get/ returns the state from the internals of the monad.
--
-- /put/ replaces the state inside the monad.
class (Monad m) => MonadState s m | m -> s where
get :: m s
put :: 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 ()
modify f = do
s <- get
put (f s)
-- | Gets specific component of the state, using a projection function
-- supplied.
gets :: (MonadState s m) => (s -> a) -> m a
gets f = do
s <- get
return (f s)
-- ---------------------------------------------------------------------------
-- | A parameterizable state monad where /s/ is the type of the state
-- to carry and /a/ is the type of the /return value/.
newtype State s a = State { runState :: s -> (a, s) }
-- The State Monad structure is parameterized over just the state.
instance Functor (State s) where
fmap f m = State $ \s -> let
(a, s') = runState m s
in (f a, s')
instance Monad (State s) where
return a = State $ \s -> (a, s)
m >>= k = State $ \s -> let
(a, s') = runState m s
in runState (k a) s'
instance MonadFix (State s) where
mfix f = State $ \s -> let (a, s') = runState (f a) s in (a, s')
instance MonadState s (State s) where
get = State $ \s -> (s, s)
put s = State $ \_ -> ((), s)
-- |Evaluate this state monad with the given initial state,throwing
-- away the final state. Very much like @fst@ composed with
-- @runstate@.
evalState :: State s a -- ^The state to evaluate
-> s -- ^An initial value
-> a -- ^The return value of the state application
evalState m s = fst (runState m s)
-- |Execute this state and return the new state, throwing away the
-- return value. Very much like @snd@ composed with
-- @runstate@.
execState :: State s a -- ^The state to evaluate
-> s -- ^An initial value
-> s -- ^The new state
execState m s = snd (runState m s)
-- |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
mapState :: ((a, s) -> (b, s)) -> State s a -> State s b
mapState f m = State $ f . runState m
-- |Apply this function to this state and return the resulting state.
withState :: (s -> s) -> State s a -> State s a
withState f m = State $ runState m . f
-- ---------------------------------------------------------------------------
-- | 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 Indentity 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))
newtype StateT s m a = StateT { runStateT :: s -> m (a,s) }
instance (Monad m) => Functor (StateT s m) where
fmap f m = StateT $ \s -> do
(x, s') <- runStateT m s
return (f x, s')
instance (Monad m) => Monad (StateT s m) where
return a = StateT $ \s -> return (a, s)
m >>= k = StateT $ \s -> do
(a, s') <- runStateT m s
runStateT (k a) s'
fail str = StateT $ \_ -> fail str
instance (MonadPlus m) => MonadPlus (StateT s m) where
mzero = StateT $ \_ -> mzero
m `mplus` n = StateT $ \s -> runStateT m s `mplus` runStateT n s
instance (MonadFix m) => MonadFix (StateT s m) where
mfix f = StateT $ \s -> mfix $ \ ~(a, _) -> runStateT (f a) s
instance (Monad m) => MonadState s (StateT s m) where
get = StateT $ \s -> return (s, s)
put s = StateT $ \_ -> return ((), s)
instance MonadTrans (StateT s) where
lift m = StateT $ \s -> do
a <- m
return (a, s)
instance (MonadIO m) => MonadIO (StateT s m) where
liftIO = lift . liftIO
-- Needs -fallow-undecidable-instances
instance (MonadReader r m) => MonadReader r (StateT s m) where
ask = lift ask
local f m = StateT $ \s -> local f (runStateT m s)
-- Needs -fallow-undecidable-instances
instance (MonadWriter w m) => MonadWriter w (StateT s m) where
tell = lift . tell
listen m = StateT $ \s -> do
((a, s'), w) <- listen (runStateT m s)
return ((a, w), s')
pass m = StateT $ \s -> pass $ do
((a, f), s') <- runStateT m s
return ((a, s'), f)
-- |Similar to 'evalState'
evalStateT :: (Monad m) => StateT s m a -> s -> m a
evalStateT m s = do
(a, _) <- runStateT m s
return a
-- |Similar to 'execState'
execStateT :: (Monad m) => StateT s m a -> s -> m s
execStateT m s = do
(_, s') <- runStateT m s
return s'
-- |Similar to 'mapState'
mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n b
mapStateT f m = StateT $ f . runStateT m
-- |Similar to 'withState'
withStateT :: (s -> s) -> StateT s m a -> StateT s m a
withStateT f m = StateT $ runStateT m . f
-- ---------------------------------------------------------------------------
-- MonadState instances for other monad transformers
-- Needs -fallow-undecidable-instances
instance (MonadState s m) => MonadState s (ReaderT r m) where
get = lift get
put = lift . put
-- Needs -fallow-undecidable-instances
instance (Monoid w, MonadState s m) => MonadState s (WriterT w m) where
get = lift get
put = lift . put
-- ---------------------------------------------------------------------------
-- $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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