content: {-# LANGUAGE CPP #-}
  {-# LANGUAGE MultiParamTypeClasses #-}
  {-# LANGUAGE FunctionalDependencies #-}
  {-# LANGUAGE FlexibleContexts #-}
  {-# LANGUAGE FlexibleInstances #-}
  {-# LANGUAGE UndecidableInstances #-}
  {-# LANGUAGE ScopedTypeVariables #-}
  {-# LANGUAGE RankNTypes #-}
  {-# LANGUAGE TypeFamilies #-}
  {-# LANGUAGE KindSignatures #-}
  {-# LANGUAGE Trustworthy #-}
  #if !MIN_VERSION_base(4, 9, 0)
  {-# LANGUAGE DataKinds #-}
  #endif
  
  -- This is needed because ErrorT is deprecated.
  {-# OPTIONS_GHC -fno-warn-warnings-deprecations #-}
  
  
  {- |
  Module      :  Lens.Micro.Mtl.Internal
  Copyright   :  (C) 2013-2016 Edward Kmett, 2015-2016 Artyom Kazak, 2018 Monadfix
  License     :  BSD-style (see the file LICENSE)
  
  This module lets you define your own instances of 'Zoom' and 'Magnify'.
  
  The warning from "Lens.Micro.Internal" applies to this module as well. Don't export functions that have 'Zoom' or 'Magnify' in their type signatures. If you absolutely need to define an instance (e.g. for internal use), only do it for your own types, because otherwise I might add an instance to one of the microlens packages later and if our instances are different it might lead to subtle bugs.
  -}
  module Lens.Micro.Mtl.Internal
  (
    -- * Classes
    Zoomed,
    Zoom(..),
    Magnified,
    Magnify(..),
  
    -- * Focusing (used for 'Zoom')
    Focusing(..),
    FocusingWith(..),
    FocusingPlus(..),
    FocusingOn(..),
    FocusingMay(..),
    FocusingErr(..),
  
    -- * Effect (used for 'Magnify')
    Effect(..),
    EffectRWS(..),
  
    -- * Utilities
    May(..),
    Err(..),
  )
  where
  
  
  import Control.Applicative
  #if MIN_VERSION_mtl(2, 3, 0)
  import Control.Monad (liftM, liftM2)
  #else
  #endif
  import Control.Monad.Reader as Reader
  import Control.Monad.State as State
  import Control.Monad.Trans.State.Lazy as Lazy
  import Control.Monad.Trans.State.Strict as Strict
  import Control.Monad.Trans.Writer.Lazy as Lazy
  import Control.Monad.Trans.Writer.Strict as Strict
  import Control.Monad.Trans.RWS.Lazy as Lazy
  import Control.Monad.Trans.RWS.Strict as Strict
  #if !MIN_VERSION_transformers(0, 6, 0)
  import Control.Monad.Trans.Error
  import Control.Monad.Trans.List
  #endif
  import Control.Monad.Trans.Except
  import Control.Monad.Trans.Identity
  import Control.Monad.Trans.Maybe
  -- microlens
  import Lens.Micro
  import Lens.Micro.Internal
  
  #if __GLASGOW_HASKELL__ < 710
  import Data.Monoid
  #endif
  
  #if MIN_VERSION_base(4,9,0)
  import Data.Kind (Type)
  #endif
  
  
  ------------------------------------------------------------------------------
  -- Zoomed
  ------------------------------------------------------------------------------
  
  -- | This type family is used by 'Zoom' to describe the common effect type.
  #if MIN_VERSION_base(4,9,0)
  type family Zoomed (m :: Type -> Type) :: Type -> Type -> Type
  #else
  type family Zoomed (m :: * -> *) :: * -> * -> *
  #endif
  type instance Zoomed (Strict.StateT s z) = Focusing z
  type instance Zoomed (Lazy.StateT s z) = Focusing z
  type instance Zoomed (ReaderT e m) = Zoomed m
  type instance Zoomed (IdentityT m) = Zoomed m
  type instance Zoomed (Strict.RWST r w s z) = FocusingWith w z
  type instance Zoomed (Lazy.RWST r w s z) = FocusingWith w z
  type instance Zoomed (Strict.WriterT w m) = FocusingPlus w (Zoomed m)
  type instance Zoomed (Lazy.WriterT w m) = FocusingPlus w (Zoomed m)
  #if !MIN_VERSION_transformers(0, 6, 0)
  type instance Zoomed (ListT m) = FocusingOn [] (Zoomed m)
  type instance Zoomed (ErrorT e m) = FocusingErr e (Zoomed m)
  #endif
  type instance Zoomed (MaybeT m) = FocusingMay (Zoomed m)
  type instance Zoomed (ExceptT e m) = FocusingErr e (Zoomed m)
  
  ------------------------------------------------------------------------------
  -- Focusing
  ------------------------------------------------------------------------------
  
  -- | Used by 'Zoom' to 'zoom' into 'Control.Monad.State.StateT'.
  newtype Focusing m s a = Focusing { unfocusing :: m (s, a) }
  
  instance Monad m => Functor (Focusing m s) where
    fmap f (Focusing m) = Focusing $ do
       (s, a) <- m
       return (s, f a)
    {-# INLINE fmap #-}
  
  instance (Monad m, Monoid s) => Applicative (Focusing m s) where
    pure a = Focusing (return (mempty, a))
    {-# INLINE pure #-}
    Focusing mf <*> Focusing ma = Focusing $ do
      (s, f) <- mf
      (s', a) <- ma
      return (mappend s s', f a)
    {-# INLINE (<*>) #-}
  
  ------------------------------------------------------------------------------
  -- FocusingWith
  ------------------------------------------------------------------------------
  
  -- | Used by 'Zoom' to 'zoom' into 'Control.Monad.RWS.RWST'.
  newtype FocusingWith w m s a = FocusingWith { unfocusingWith :: m (s, a, w) }
  
  instance Monad m => Functor (FocusingWith w m s) where
    fmap f (FocusingWith m) = FocusingWith $ do
       (s, a, w) <- m
       return (s, f a, w)
    {-# INLINE fmap #-}
  
  instance (Monad m, Monoid s, Monoid w) => Applicative (FocusingWith w m s) where
    pure a = FocusingWith (return (mempty, a, mempty))
    {-# INLINE pure #-}
    FocusingWith mf <*> FocusingWith ma = FocusingWith $ do
      (s, f, w) <- mf
      (s', a, w') <- ma
      return (mappend s s', f a, mappend w w')
    {-# INLINE (<*>) #-}
  
  ------------------------------------------------------------------------------
  -- FocusingPlus
  ------------------------------------------------------------------------------
  
  -- | Used by 'Zoom' to 'zoom' into 'Control.Monad.Writer.WriterT'.
  newtype FocusingPlus w k s a = FocusingPlus { unfocusingPlus :: k (s, w) a }
  
  instance Functor (k (s, w)) => Functor (FocusingPlus w k s) where
    fmap f (FocusingPlus as) = FocusingPlus (fmap f as)
    {-# INLINE fmap #-}
  
  instance Applicative (k (s, w)) => Applicative (FocusingPlus w k s) where
    pure = FocusingPlus . pure
    {-# INLINE pure #-}
    FocusingPlus kf <*> FocusingPlus ka = FocusingPlus (kf <*> ka)
    {-# INLINE (<*>) #-}
  
  ------------------------------------------------------------------------------
  -- FocusingOn
  ------------------------------------------------------------------------------
  
  -- | Used by 'Zoom' to 'zoom' into 'Control.Monad.Trans.Maybe.MaybeT' or 'Control.Monad.Trans.List.ListT'.
  newtype FocusingOn f k s a = FocusingOn { unfocusingOn :: k (f s) a }
  
  instance Functor (k (f s)) => Functor (FocusingOn f k s) where
    fmap f (FocusingOn as) = FocusingOn (fmap f as)
    {-# INLINE fmap #-}
  
  instance Applicative (k (f s)) => Applicative (FocusingOn f k s) where
    pure = FocusingOn . pure
    {-# INLINE pure #-}
    FocusingOn kf <*> FocusingOn ka = FocusingOn (kf <*> ka)
    {-# INLINE (<*>) #-}
  
  ------------------------------------------------------------------------------
  -- May
  ------------------------------------------------------------------------------
  
  -- | Make a 'Monoid' out of 'Maybe' for error handling.
  newtype May a = May { getMay :: Maybe a }
  
  instance Monoid a => Monoid (May a) where
    mempty = May (Just mempty)
    {-# INLINE mempty #-}
  #if !MIN_VERSION_base(4,11,0)
    May Nothing `mappend` _ = May Nothing
    _ `mappend` May Nothing = May Nothing
    May (Just a) `mappend` May (Just b) = May (Just (mappend a b))
    {-# INLINE mappend #-}
  #else
  instance Semigroup a => Semigroup (May a) where
    May Nothing <> _ = May Nothing
    _ <> May Nothing = May Nothing
    May (Just a) <> May (Just b) = May (Just (a <> b))
    {-# INLINE (<>) #-}
  #endif
  
  ------------------------------------------------------------------------------
  -- FocusingMay
  ------------------------------------------------------------------------------
  
  -- | Used by 'Zoom' to 'zoom' into 'Control.Monad.Error.ErrorT'.
  newtype FocusingMay k s a = FocusingMay { unfocusingMay :: k (May s) a }
  
  instance Functor (k (May s)) => Functor (FocusingMay k s) where
    fmap f (FocusingMay as) = FocusingMay (fmap f as)
    {-# INLINE fmap #-}
  
  instance Applicative (k (May s)) => Applicative (FocusingMay k s) where
    pure = FocusingMay . pure
    {-# INLINE pure #-}
    FocusingMay kf <*> FocusingMay ka = FocusingMay (kf <*> ka)
    {-# INLINE (<*>) #-}
  
  ------------------------------------------------------------------------------
  -- Err
  ------------------------------------------------------------------------------
  
  -- | Make a 'Monoid' out of 'Either' for error handling.
  newtype Err e a = Err { getErr :: Either e a }
  
  instance Monoid a => Monoid (Err e a) where
    mempty = Err (Right mempty)
    {-# INLINE mempty #-}
  #if !MIN_VERSION_base(4,11,0)
    Err (Left e) `mappend` _ = Err (Left e)
    _ `mappend` Err (Left e) = Err (Left e)
    Err (Right a) `mappend` Err (Right b) = Err (Right (mappend a b))
    {-# INLINE mappend #-}
  #else
  instance Semigroup a => Semigroup (Err e a) where
    Err (Left e) <> _ = Err (Left e)
    _ <> Err (Left e) = Err (Left e)
    Err (Right a) <> Err (Right b) = Err (Right (a <> b))
    {-# INLINE (<>) #-}
  #endif
  
  ------------------------------------------------------------------------------
  -- FocusingErr
  ------------------------------------------------------------------------------
  
  -- | Used by 'Zoom' to 'zoom' into 'Control.Monad.Error.ErrorT'.
  newtype FocusingErr e k s a = FocusingErr { unfocusingErr :: k (Err e s) a }
  
  instance Functor (k (Err e s)) => Functor (FocusingErr e k s) where
    fmap f (FocusingErr as) = FocusingErr (fmap f as)
    {-# INLINE fmap #-}
  
  instance Applicative (k (Err e s)) => Applicative (FocusingErr e k s) where
    pure = FocusingErr . pure
    {-# INLINE pure #-}
    FocusingErr kf <*> FocusingErr ka = FocusingErr (kf <*> ka)
    {-# INLINE (<*>) #-}
  
  ------------------------------------------------------------------------------
  -- Zoom
  ------------------------------------------------------------------------------
  
  infixr 2 `zoom`
  
  class (MonadState s m, MonadState t n) => Zoom m n s t | m -> s, n -> t, m t -> n, n s -> m where
    {- |
  When you're in a state monad, this function lets you operate on a part of your state. For instance, if your state was a record containing a @position@ field, after zooming @position@ would become your whole state (and when you modify it, the bigger structure would be modified as well).
  
  (Your 'Lazy.State' \/ 'Lazy.StateT' or 'Lazy.RWS' \/ 'Lazy.RWST' can be anywhere in the stack, but you can't use 'zoom' with arbitrary 'MonadState' because it doesn't provide any methods to change the type of the state. See <https://github.com/ekmett/lens/issues/316 this issue> for details.)
  
  For the sake of the example, let's define some types first:
  
  @
  data Position = Position {
    _x, _y :: Int }
  
  data Player = Player {
    _position :: Position,
    ... }
  
  data Game = Game {
    _player :: Player,
    _obstacles :: [Position],
    ... }
  
  concat \<$\> mapM makeLenses [''Position, ''Player, ''Game]
  @
  
  Now, here's an action that moves the player north-east:
  
  @
  moveNE :: 'Lazy.State' Game ()
  moveNE = do
    player.position.x 'Lens.Micro.Mtl.+=' 1
    player.position.y 'Lens.Micro.Mtl.+=' 1
  @
  
  With 'zoom', you can use @player.position@ to focus just on a part of the state:
  
  @
  moveNE :: 'Lazy.State' Game ()
  moveNE = do
    'zoom' (player.position) $ do
      x 'Lens.Micro.Mtl.+=' 1
      y 'Lens.Micro.Mtl.+=' 1
  @
  
  You can just as well use it for retrieving things out of the state:
  
  @
  getCoords :: 'Lazy.State' Game (Int, Int)
  getCoords = 'zoom' (player.position) ((,) '<$>' 'Lens.Micro.Mtl.use' x '<*>' 'Lens.Micro.Mtl.use' y)
  @
  
  Or more explicitly:
  
  @
  getCoords = 'zoom' (player.position) $ do
    x' <- 'Lens.Micro.Mtl.use' x
    y' <- 'Lens.Micro.Mtl.use' y
    return (x', y')
  @
  
  When you pass a traversal to 'zoom', it'll work as a loop. For instance, here we move all obstacles:
  
  @
  moveObstaclesNE :: 'Lazy.State' Game ()
  moveObstaclesNE = do
    'zoom' (obstacles.'each') $ do
      x 'Lens.Micro.Mtl.+=' 1
      y 'Lens.Micro.Mtl.+=' 1
  @
  
  If the action returns a result, all results would be combined with '<>' – the same way they're combined when '^.' is passed a traversal. In this example, @moveObstaclesNE@ returns a list of old coordinates of obstacles in addition to moving them:
  
  @
  moveObstaclesNE = do
    xys <- 'zoom' (obstacles.'each') $ do
      -- Get old coordinates.
      x' <- 'Lens.Micro.Mtl.use' x
      y' <- 'Lens.Micro.Mtl.use' y
      -- Update them.
      x 'Lens.Micro.Mtl..=' x' + 1
      y 'Lens.Micro.Mtl..=' y' + 1
      -- Return a single-element list with old coordinates.
      return [(x', y')]
    ...
  @
  
  Finally, you might need to write your own instances of 'Zoom' if you use @newtype@d transformers in your monad stack. This can be done as follows:
  
  @
  import "Lens.Micro.Mtl.Internal"
  
  type instance 'Zoomed' (MyStateT s m) = 'Zoomed' (StateT s m)
  
  instance Monad m =\> 'Zoom' (MyStateT s m) (MyStateT t m) s t where
      'zoom' l (MyStateT m) = MyStateT ('zoom' l m)
  @
    -}
    zoom :: LensLike' (Zoomed m c) t s -> m c -> n c
  
  instance Monad z => Zoom (Strict.StateT s z) (Strict.StateT t z) s t where
    zoom l (Strict.StateT m) = Strict.StateT $ unfocusing #. l (Focusing #. m)
    {-# INLINE zoom #-}
  
  instance Monad z => Zoom (Lazy.StateT s z) (Lazy.StateT t z) s t where
    zoom l (Lazy.StateT m) = Lazy.StateT $ unfocusing #. l (Focusing #. m)
    {-# INLINE zoom #-}
  
  instance Zoom m n s t => Zoom (ReaderT e m) (ReaderT e n) s t where
    zoom l (ReaderT m) = ReaderT (zoom l . m)
    {-# INLINE zoom #-}
  
  instance Zoom m n s t => Zoom (IdentityT m) (IdentityT n) s t where
    zoom l (IdentityT m) = IdentityT (zoom l m)
    {-# INLINE zoom #-}
  
  instance (Monoid w, Monad z) => Zoom (Strict.RWST r w s z) (Strict.RWST r w t z) s t where
    zoom l (Strict.RWST m) = Strict.RWST $ \r -> unfocusingWith #. l (FocusingWith #. m r)
    {-# INLINE zoom #-}
  
  instance (Monoid w, Monad z) => Zoom (Lazy.RWST r w s z) (Lazy.RWST r w t z) s t where
    zoom l (Lazy.RWST m) = Lazy.RWST $ \r -> unfocusingWith #. l (FocusingWith #. m r)
    {-# INLINE zoom #-}
  
  instance (Monoid w, Zoom m n s t) => Zoom (Strict.WriterT w m) (Strict.WriterT w n) s t where
    zoom l = Strict.WriterT . zoom (\afb -> unfocusingPlus #. l (FocusingPlus #. afb)) . Strict.runWriterT
    {-# INLINE zoom #-}
  
  instance (Monoid w, Zoom m n s t) => Zoom (Lazy.WriterT w m) (Lazy.WriterT w n) s t where
    zoom l = Lazy.WriterT . zoom (\afb -> unfocusingPlus #. l (FocusingPlus #. afb)) . Lazy.runWriterT
    {-# INLINE zoom #-}
  
  #if !MIN_VERSION_mtl(2, 3, 0) && !MIN_VERSION_transformers(0, 6, 0)
  instance Zoom m n s t => Zoom (ListT m) (ListT n) s t where
    zoom l = ListT . zoom (\afb -> unfocusingOn . l (FocusingOn . afb)) . runListT
    {-# INLINE zoom #-}
  
  instance (Error e, Zoom m n s t) => Zoom (ErrorT e m) (ErrorT e n) s t where
    zoom l = ErrorT . liftM getErr . zoom (\afb -> unfocusingErr #. l (FocusingErr #. afb)) . liftM Err . runErrorT
    {-# INLINE zoom #-}
  #endif
  
  instance Zoom m n s t => Zoom (MaybeT m) (MaybeT n) s t where
    zoom l = MaybeT . liftM getMay . zoom (\afb -> unfocusingMay #. l (FocusingMay #. afb)) . liftM May . runMaybeT
    {-# INLINE zoom #-}
  
  instance Zoom m n s t => Zoom (ExceptT e m) (ExceptT e n) s t where
    zoom l = ExceptT . liftM getErr . zoom (\afb -> unfocusingErr #. l (FocusingErr #. afb)) . liftM Err . runExceptT
    {-# INLINE zoom #-}
  
  -- TODO: instance Zoom m m a a => Zoom (ContT r m) (ContT r m) a a where
  
  ------------------------------------------------------------------------------
  -- Magnified
  ------------------------------------------------------------------------------
  
  -- | This type family is used by 'Magnify' to describe the common effect type.
  #if MIN_VERSION_base(4,9,0)
  type family Magnified (m :: Type -> Type) :: Type -> Type -> Type
  #else
  type family Magnified (m :: * -> *) :: * -> * -> *
  #endif
  type instance Magnified (ReaderT b m) = Effect m
  type instance Magnified ((->)b) = Const
  type instance Magnified (Strict.RWST a w s m) = EffectRWS w s m
  type instance Magnified (Lazy.RWST a w s m) = EffectRWS w s m
  type instance Magnified (IdentityT m) = Magnified m
  
  ------------------------------------------------------------------------------
  -- Magnify
  ------------------------------------------------------------------------------
  
  infixr 2 `magnify`
  
  class (MonadReader b m, MonadReader a n) => Magnify m n b a | m -> b, n -> a, m a -> n, n b -> m where
    {- |
  This is an equivalent of 'Reader.local' which lets you apply a getter to your environment instead of merely applying a function (and it also lets you change the type of the environment).
  
  @
  'Reader.local'   :: (r -> r)   -> 'Reader.Reader' r a -> 'Reader.Reader' r a
  'magnify' :: Getter r x -> 'Reader.Reader' x a -> 'Reader.Reader' r a
  @
  
  'magnify' works with 'Reader.Reader' \/ 'Reader.ReaderT', 'Lazy.RWS' \/ 'Lazy.RWST', and @(->)@.
  
  Here's an example of 'magnify' being used to work with a part of a bigger config. First, the types:
  
  @
  data URL = URL {
    _protocol :: Maybe String,
    _path :: String }
  
  data Config = Config {
    _base :: URL,
    ... }
  
  makeLenses ''URL
  makeLenses ''Config
  @
  
  Now, let's define a function which returns the base url:
  
  @
  getBase :: 'Reader.Reader' Config String
  getBase = do
    protocol \<- 'Data.Maybe.fromMaybe' \"https\" '<$>' 'Lens.Micro.Mtl.view' (base.protocol)
    path     \<- 'Lens.Micro.Mtl.view' (base.path)
    return (protocol ++ path)
  @
  
  With 'magnify', we can factor out @base@:
  
  @
  getBase = 'magnify' base $ do
    protocol \<- 'Data.Maybe.fromMaybe' \"https\" '<$>' 'Lens.Micro.Mtl.view' protocol
    path     \<- 'Lens.Micro.Mtl.view' path
    return (protocol ++ path)
  @
  
  This concludes the example.
  
  Finally, you should know writing instances of 'Magnify' for your own types can be done as follows:
  
  @
  import "Lens.Micro.Mtl.Internal"
  
  type instance 'Magnified' (MyReaderT r m) = 'Magnified' (ReaderT r m)
  
  instance Monad m =\> 'Magnify' (MyReaderT r m) (MyReaderT t m) r t where
      'magnify' l (MyReaderT m) = MyReaderT ('magnify' l m)
  @
    -}
    magnify :: LensLike' (Magnified m c) a b -> m c -> n c
  
  instance Monad m => Magnify (ReaderT b m) (ReaderT a m) b a where
    magnify l (ReaderT m) = ReaderT $ getEffect #. l (Effect #. m)
    {-# INLINE magnify #-}
  
  instance Magnify ((->) b) ((->) a) b a where
    magnify l f = Reader.asks (getConst #. l (Const #. f))
    {-# INLINE magnify #-}
  
  instance (Monad m, Monoid w) => Magnify (Strict.RWST b w s m) (Strict.RWST a w s m) b a where
    magnify l (Strict.RWST m) = Strict.RWST $ getEffectRWS #. l (EffectRWS #. m)
    {-# INLINE magnify #-}
  
  instance (Monad m, Monoid w) => Magnify (Lazy.RWST b w s m) (Lazy.RWST a w s m) b a where
    magnify l (Lazy.RWST m) = Lazy.RWST $ getEffectRWS #. l (EffectRWS #. m)
    {-# INLINE magnify #-}
  
  instance Magnify m n b a => Magnify (IdentityT m) (IdentityT n) b a where
    magnify l (IdentityT m) = IdentityT (magnify l m)
    {-# INLINE magnify #-}
  
  -----------------------------------------------------------------------------
  --- Effect
  -------------------------------------------------------------------------------
  
  -- | Wrap a monadic effect with a phantom type argument.
  newtype Effect m r a = Effect { getEffect :: m r }
  -- type role Effect representational nominal phantom
  
  instance Functor (Effect m r) where
    fmap _ (Effect m) = Effect m
    {-# INLINE fmap #-}
  
  instance (Monad m, Monoid r) => Monoid (Effect m r a) where
    mempty = Effect (return mempty)
    {-# INLINE mempty #-}
  #if !MIN_VERSION_base(4,11,0)
    Effect ma `mappend` Effect mb = Effect (liftM2 mappend ma mb)
    {-# INLINE mappend #-}
  #else
  instance (Monad m, Semigroup r) => Semigroup (Effect m r a) where
    Effect ma <> Effect mb = Effect (liftM2 (<>) ma mb)
    {-# INLINE (<>) #-}
  #endif
  
  instance (Monad m, Monoid r) => Applicative (Effect m r) where
    pure _ = Effect (return mempty)
    {-# INLINE pure #-}
    Effect ma <*> Effect mb = Effect (liftM2 mappend ma mb)
    {-# INLINE (<*>) #-}
  
  ------------------------------------------------------------------------------
  -- EffectRWS
  ------------------------------------------------------------------------------
  
  -- | Wrap a monadic effect with a phantom type argument. Used when magnifying 'Control.Monad.RWS.RWST'.
  newtype EffectRWS w st m s a = EffectRWS { getEffectRWS :: st -> m (s,st,w) }
  
  instance Functor (EffectRWS w st m s) where
    fmap _ (EffectRWS m) = EffectRWS m
    {-# INLINE fmap #-}
  
  instance (Monoid s, Monoid w, Monad m) => Applicative (EffectRWS w st m s) where
    pure _ = EffectRWS $ \st -> return (mempty, st, mempty)
    {-# INLINE pure #-}
    EffectRWS m <*> EffectRWS n = EffectRWS $ \st -> m st >>= \ (s,t,w) -> n t >>= \ (s',u,w') -> return (mappend s s', u, mappend w w')
    {-# INLINE (<*>) #-}
  