    {-# OPTIONS -fallow-undecidable-instances #-}
    -- Search for -fallow-undecidable-instances to see why this is needed

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Control.Monad.State.Lazy
    -- 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)
    --
    -- 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.
    --
    -- See below for examples.

    -----------------------------------------------------------------------------

    module Control.Monad.State.Lazy (
        module Control.Monad.State.Class,
        -- * 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 Control.Monad
    import Control.Monad.Cont.Class
    import Control.Monad.Error.Class
    import Control.Monad.Fix
    import Control.Monad.Reader.Class
    import Control.Monad.State.Class
    import Control.Monad.Trans
    import Control.Monad.Writer.Class

    -- ---------------------------------------------------------------------------
    -- | 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) }

    -- |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

    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)

    -- ---------------------------------------------------------------------------
    -- | 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) }

    -- |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

    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)

    -- ---------------------------------------------------------------------------
    -- Instances for other mtl transformers

    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

    instance (MonadCont m) => MonadCont (StateT s m) where
        callCC f = StateT $ \s ->
            callCC $ \c ->
            runStateT (f (\a -> StateT $ \s' -> c (a, s'))) s

    instance (MonadError e m) => MonadError e (StateT s m) where
        throwError       = lift . throwError
        m `catchError` h = StateT $ \s -> runStateT m s
            `catchError` \e -> runStateT (h e) s

    -- 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)

    -- ---------------------------------------------------------------------------
    -- $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)