    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Control.Monad.Trans.State.Lazy
    -- Copyright   :  (c) Andy Gill 2001,
    --                (c) Oregon Graduate Institute of Science and Technology, 2001
    -- License     :  BSD-style (see the file LICENSE)
    --
    -- Maintainer  :  ross@soi.city.ac.uk
    -- Stability   :  experimental
    -- Portability :  portable
    --
    -- Lazy state monads, passing an updatable state through a computation.
    -- See below for examples.
    --
    -- In this version, sequencing of computations is lazy.
    -- For a strict version, see "Control.Monad.Trans.State.Strict", which
    -- has the same interface.
    --
    -- Some computations may not require the full power of state transformers:
    --
    -- * For a read-only state, see "Control.Monad.Trans.Reader".
    --
    -- * To accumulate a value without using it on the way, see
    --   "Control.Monad.Trans.Writer".
    -----------------------------------------------------------------------------

    module Control.Monad.Trans.State.Lazy (
        -- * The State monad
        State,
        state,
        runState,
        evalState,
        execState,
        mapState,
        withState,
        -- * The StateT monad transformer
        StateT(..),
        evalStateT,
        execStateT,
        mapStateT,
        withStateT,
        -- * State operations
        get,
        put,
        modify,
        gets,
        -- * Lifting other operations
        liftCallCC,
        liftCallCC',
        liftCatch,
        liftListen,
        liftPass,
        -- * Examples
        -- ** State monads
        -- $examples

        -- ** Counting
        -- $counting

        -- ** Labelling trees
        -- $labelling
      ) where

    import Control.Monad.IO.Class
    import Control.Monad.Trans.Class
    import Data.Functor.Identity

    import Control.Applicative
    import Control.Monad
    import Control.Monad.Fix

    -- ---------------------------------------------------------------------------
    -- | 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.
    type State s = StateT s Identity

    -- | Construct a state monad computation from a function.
    -- (The inverse of 'runState'.)
    state :: Monad m
          => (s -> (a, s))  -- ^pure state transformer
          -> StateT s m a   -- ^equivalent state-passing computation
    state f = StateT (return . f)

    -- | Unwrap a state monad computation as a function.
    -- (The inverse of 'state'.)
    runState :: State s a   -- ^state-passing computation to execute
             -> s           -- ^initial state
             -> (a, s)      -- ^return value and final state
    runState m = runIdentity . runStateT m

    -- | 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)@
    evalState :: State s a  -- ^state-passing computation to execute
              -> s          -- ^initial value
              -> a          -- ^return value of the state computation
    evalState m s = fst (runState m s)

    -- | 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)@
    execState :: State s a  -- ^state-passing computation to execute
              -> s          -- ^initial value
              -> s          -- ^final state
    execState m s = snd (runState m s)

    -- | Map both the return value and final state of a computation using
    -- the given function.
    --
    -- * @'runState' ('mapState' f m) = f . 'runState' m@
    mapState :: ((a, s) -> (b, s)) -> State s a -> State s b
    mapState f = mapStateT (Identity . f . runIdentity)

    -- | @'withState' f m@ executes action @m@ on a state modified by
    -- applying @f@.
    --
    -- * @'withState' f m = 'modify' f >> m@
    withState :: (s -> s) -> State s a -> State s a
    withState = withStateT

    -- ---------------------------------------------------------------------------
    -- | 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.
    newtype StateT s m a = StateT { runStateT :: s -> m (a,s) }

    -- | 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)@
    evalStateT :: (Monad m) => StateT s m a -> s -> m a
    evalStateT m s = do
        ~(a, _) <- runStateT m s
        return a

    -- | 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)@
    execStateT :: (Monad m) => StateT s m a -> s -> m s
    execStateT m s = do
        ~(_, s') <- runStateT m s
        return s'

    -- | Map both the return value and final state of a computation using
    -- the given function.
    --
    -- * @'runStateT' ('mapStateT' f m) = f . 'runStateT' m@
    mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n b
    mapStateT f m = StateT $ f . runStateT m

    -- | @'withStateT' f m@ executes action @m@ on a state modified by
    -- applying @f@.
    --
    -- * @'withStateT' f m = 'modify' f >> m@
    withStateT :: (s -> s) -> StateT s m a -> StateT s m a
    withStateT f m = StateT $ runStateT m . f

    instance (Functor m) => Functor (StateT s m) where
        fmap f m = StateT $ \ s ->
            fmap (\ ~(a, s') -> (f a, s')) $ runStateT m s

    instance (Functor m, Monad m) => Applicative (StateT s m) where
        pure = return
        (<*>) = ap

    instance (Functor m, MonadPlus m) => Alternative (StateT s m) where
        empty = mzero
        (<|>) = mplus

    instance (Monad m) => Monad (StateT s m) where
        return a = state $ \s -> (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 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

    -- | Fetch the current value of the state within the monad.
    get :: (Monad m) => StateT s m s
    get = state $ \s -> (s, s)

    -- | @'put' s@ sets the state within the monad to @s@.
    put :: (Monad m) => s -> StateT s m ()
    put s = state $ \_ -> ((), s)

    -- | @'modify' f@ is an action that updates the state to the result of
    -- applying @f@ to the current state.
    --
    -- * @'modify' f = 'get' >>= ('put' . f)@
    modify :: (Monad m) => (s -> s) -> StateT s m ()
    modify f = state $ \s -> ((), f s)

    -- | Get a specific component of the state, using a projection function
    -- supplied.
    --
    -- * @'gets' f = 'liftM' f 'get'@
    gets :: (Monad m) => (s -> a) -> StateT s m a
    gets f = state $ \s -> (f s, s)

    -- | Uniform lifting of a @callCC@ operation to the new monad.
    -- This version rolls back to the original state on entering the
    -- continuation.
    liftCallCC :: ((((a,s) -> m (b,s)) -> m (a,s)) -> m (a,s)) ->
        ((a -> StateT s m b) -> StateT s m a) -> StateT s m a
    liftCallCC callCC f = StateT $ \s ->
        callCC $ \c ->
        runStateT (f (\a -> StateT $ \ _ -> c (a, s))) s

    -- | In-situ lifting of a @callCC@ operation to the new monad.
    -- This version uses the current state on entering the continuation.
    -- It does not satisfy the laws of a monad transformer.
    liftCallCC' :: ((((a,s) -> m (b,s)) -> m (a,s)) -> m (a,s)) ->
        ((a -> StateT s m b) -> StateT s m a) -> StateT s m a
    liftCallCC' callCC f = StateT $ \s ->
        callCC $ \c ->
        runStateT (f (\a -> StateT $ \s' -> c (a, s'))) s

    -- | Lift a @catchError@ operation to the new monad.
    liftCatch :: (m (a,s) -> (e -> m (a,s)) -> m (a,s)) ->
        StateT s m a -> (e -> StateT s m a) -> StateT s m a
    liftCatch catchError m h =
        StateT $ \s -> runStateT m s `catchError` \e -> runStateT (h e) s

    -- | Lift a @listen@ operation to the new monad.
    liftListen :: Monad m =>
        (m (a,s) -> m ((a,s),w)) -> StateT s m a -> StateT s m (a,w)
    liftListen listen m = StateT $ \s -> do
        ~((a, s'), w) <- listen (runStateT m s)
        return ((a, w), s')

    -- | Lift a @pass@ operation to the new monad.
    liftPass :: Monad m =>
        (m ((a,s),b) -> m (a,s)) -> StateT s m (a,b) -> StateT s m a
    liftPass pass m = StateT $ \s -> pass $ do
        ~((a, f), s') <- runStateT m s
        return ((a, s'), f)

    {- $examples

    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))

    -}

    {- $counting

    A function to increment a counter.
    Taken from the paper \"Generalising Monads to Arrows\",
    John Hughes (<http://www.cse.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

    -}

    {- $labelling

    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)

    -}