    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Control.Monad.Trans.Writer.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
    --
    -- The lazy 'WriterT' monad transformer, which adds collection of
    -- outputs (such as a count or string output) to a given monad.
    --
    -- This version builds its output lazily; for a strict version, see
    -- "Control.Monad.Trans.Writer.Strict", which has the same interface.
    --
    -- This monad transformer provides only limited access to the output
    -- during the computation.  For more general access, use
    -- "Control.Monad.Trans.State" instead.
    -----------------------------------------------------------------------------

    module Control.Monad.Trans.Writer.Lazy (
        -- * The Writer monad
        Writer,
        writer,
        runWriter,
        execWriter,
        mapWriter,
        -- * The WriterT monad transformer
        WriterT(..),
        execWriterT,
        mapWriterT,
        -- * Writer operations
        tell,
        listen,
        listens,
        pass,
        censor,
        -- * Lifting other operations
        liftCallCC,
        liftCatch,
      ) 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
    import Data.Foldable (Foldable(foldMap))
    import Data.Monoid
    import Data.Traversable (Traversable(traverse))

    -- ---------------------------------------------------------------------------
    -- | A writer monad parameterized by the type @w@ of output to accumulate.
    --
    -- The 'return' function produces the output 'mempty', while @>>=@
    -- combines the outputs of the subcomputations using 'mappend'.
    type Writer w = WriterT w Identity

    -- | Construct a writer computation from a (result, output) pair.
    -- (The inverse of 'runWriter'.)
    writer :: Monad m => (a, w) -> WriterT w m a
    writer = WriterT . return

    -- | Unwrap a writer computation as a (result, output) pair.
    -- (The inverse of 'writer'.)
    runWriter :: Writer w a -> (a, w)
    runWriter = runIdentity . runWriterT

    -- | Extract the output from a writer computation.
    --
    -- * @'execWriter' m = 'snd' ('runWriter' m)@
    execWriter :: Writer w a -> w
    execWriter m = snd (runWriter m)

    -- | Map both the return value and output of a computation using
    -- the given function.
    --
    -- * @'runWriter' ('mapWriter' f m) = f ('runWriter' m)@
    mapWriter :: ((a, w) -> (b, w')) -> Writer w a -> Writer w' b
    mapWriter f = mapWriterT (Identity . f . runIdentity)

    -- ---------------------------------------------------------------------------
    -- | A writer monad parameterized by:
    --
    --   * @w@ - the output to accumulate.
    --
    --   * @m@ - The inner monad.
    --
    -- The 'return' function produces the output 'mempty', while @>>=@
    -- combines the outputs of the subcomputations using 'mappend'.
    newtype WriterT w m a = WriterT { runWriterT :: m (a, w) }

    -- | Extract the output from a writer computation.
    --
    -- * @'execWriterT' m = 'liftM' 'snd' ('runWriterT' m)@
    execWriterT :: Monad m => WriterT w m a -> m w
    execWriterT m = do
        ~(_, w) <- runWriterT m
        return w

    -- | Map both the return value and output of a computation using
    -- the given function.
    --
    -- * @'runWriterT' ('mapWriterT' f m) = f ('runWriterT' m)@
    mapWriterT :: (m (a, w) -> n (b, w')) -> WriterT w m a -> WriterT w' n b
    mapWriterT f m = WriterT $ f (runWriterT m)

    instance (Functor m) => Functor (WriterT w m) where
        fmap f = mapWriterT $ fmap $ \ ~(a, w) -> (f a, w)

    instance (Monoid w, Applicative m) => Applicative (WriterT w m) where
        pure a  = WriterT $ pure (a, mempty)
        f <*> v = WriterT $ liftA2 k (runWriterT f) (runWriterT v)
          where k ~(a, w) ~(b, w') = (a b, w `mappend` w')

    instance (Monoid w, Alternative m) => Alternative (WriterT w m) where
        empty   = WriterT empty
        m <|> n = WriterT $ runWriterT m <|> runWriterT n

    instance (Monoid w, Monad m) => Monad (WriterT w m) where
        return a = writer (a, mempty)
        m >>= k  = WriterT $ do
            ~(a, w)  <- runWriterT m
            ~(b, w') <- runWriterT (k a)
            return (b, w `mappend` w')
        fail msg = WriterT $ fail msg

    instance (Monoid w, MonadPlus m) => MonadPlus (WriterT w m) where
        mzero       = WriterT mzero
        m `mplus` n = WriterT $ runWriterT m `mplus` runWriterT n

    instance (Monoid w, MonadFix m) => MonadFix (WriterT w m) where
        mfix m = WriterT $ mfix $ \ ~(a, _) -> runWriterT (m a)

    instance (Monoid w) => MonadTrans (WriterT w) where
        lift m = WriterT $ do
            a <- m
            return (a, mempty)

    instance (Monoid w, MonadIO m) => MonadIO (WriterT w m) where
        liftIO = lift . liftIO

    instance Foldable f => Foldable (WriterT w f) where
        foldMap f (WriterT a) = foldMap (f . fst) a

    instance Traversable f => Traversable (WriterT w f) where
        traverse f (WriterT a) = WriterT <$> traverse f' a where
           f' (a, b) = fmap (\c -> (c, b)) (f a)

    -- | @'tell' w@ is an action that produces the output @w@.
    tell :: (Monoid w, Monad m) => w -> WriterT w m ()
    tell w = writer ((), w)

    -- | @'listen' m@ is an action that executes the action @m@ and adds its
    -- output to the value of the computation.
    --
    -- * @'runWriterT' ('listen' m) = 'liftM' (\\(a, w) -> ((a, w), w)) ('runWriterT' m)@
    listen :: (Monoid w, Monad m) => WriterT w m a -> WriterT w m (a, w)
    listen m = WriterT $ do
        ~(a, w) <- runWriterT m
        return ((a, w), w)

    -- | @'listens' f m@ is an action that executes the action @m@ and adds
    -- the result of applying @f@ to the output to the value of the computation.
    --
    -- * @'listens' f m = 'liftM' (id *** f) ('listen' m)@
    --
    -- * @'runWriterT' ('listens' f m) = 'liftM' (\\(a, w) -> ((a, f w), w)) ('runWriterT' m)@
    listens :: (Monoid w, Monad m) => (w -> b) -> WriterT w m a -> WriterT w m (a, b)
    listens f m = WriterT $ do
        ~(a, w) <- runWriterT m
        return ((a, f w), w)

    -- | @'pass' m@ is an action that executes the action @m@, which returns
    -- a value and a function, and returns the value, applying the function
    -- to the output.
    --
    -- * @'runWriterT' ('pass' m) = 'liftM' (\\((a, f), w) -> (a, f w)) ('runWriterT' m)@
    pass :: (Monoid w, Monad m) => WriterT w m (a, w -> w) -> WriterT w m a
    pass m = WriterT $ do
        ~((a, f), w) <- runWriterT m
        return (a, f w)

    -- | @'censor' f m@ is an action that executes the action @m@ and
    -- applies the function @f@ to its output, leaving the return value
    -- unchanged.
    --
    -- * @'censor' f m = 'pass' ('liftM' (\\x -> (x,f)) m)@
    --
    -- * @'runWriterT' ('censor' f m) = 'liftM' (\\(a, w) -> (a, f w)) ('runWriterT' m)@
    censor :: (Monoid w, Monad m) => (w -> w) -> WriterT w m a -> WriterT w m a
    censor f m = WriterT $ do
        ~(a, w) <- runWriterT m
        return (a, f w)

    -- | Lift a @callCC@ operation to the new monad.
    liftCallCC :: (Monoid w) => ((((a,w) -> m (b,w)) -> m (a,w)) -> m (a,w)) ->
        ((a -> WriterT w m b) -> WriterT w m a) -> WriterT w m a
    liftCallCC callCC f = WriterT $
        callCC $ \c ->
        runWriterT (f (\a -> WriterT $ c (a, mempty)))

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