{-# LANGUAGE Rank2Types, FlexibleInstances, FlexibleContexts, TypeOperators, CPP, ConstraintKinds #-}
#if __GLASGOW_HASKELL__ >= 707
{-# LANGUAGE DeriveDataTypeable #-}
#endif
-----------------------------------------------------------------------------
-- |
-- Module      :  Control.Object
-- Copyright   :  (c) Fumiaki Kinoshita 2014
-- License     :  BSD3
--
-- Maintainer  :  Fumiaki Kinoshita <fumiexcel@gmail.com>
-- Stability   :  experimental
-- Portability :  non-portable
--
-- Stateful effect transducer: The Mealy machine for effects.
--
-----------------------------------------------------------------------------
module Control.Object (
  -- * Construction
  Object(..),
  (@-),
  liftO,
  echo,
  oneshot,
  stateful,
  variable,
  Variable,
  unfoldO,
  unfoldOM,
  foldP,
  foldP',
  sharing,
  animate,
  transit,
  -- * Composition
  (@>>@),
  (@>>^),
  (^>>@),
  (@**@),
  (@||@),
  loner,
  (@|>@),
  transObject,
  adaptObject,
  -- * Stream
  ($$),
  ($$!),
  (!$$),
  (!$$!),
  -- * Monads
  (@!),
  (@!!),
  sequential,
  sequentialT,
  iterObject,
  iterTObject,
  iterative,
  iterativeT,
  -- * Patterns
  flyweight,
  flyweight',
  announce,
  announceMaybe,
  announceMaybeT,
  Process(..),
  _Process,
  Mortal(..),
  runMortal,
  )
where

import Control.Applicative
import Control.Arrow as A
import Control.Elevator
import Control.Monad
import Control.Monad.Free
import Control.Monad.Operational.Mini
import Control.Monad.Trans.Class
import Control.Monad.Trans.Maybe
import Control.Monad.Trans.State.Strict
import Control.Monad.Trans.Writer.Strict
import Data.Functor.Day
import Data.Functor.PushPull
import Data.Functor.Request
import Data.Functor.Sum as F
import Data.Hashable
import Data.Monoid
import Data.OpenUnion1.Clean
import Data.Profunctor
import Data.Typeable
import Data.Witherable
import qualified Control.Category as C
import qualified Control.Monad.Trans.Free as T
import qualified Control.Monad.Trans.Operational.Mini as T
import qualified Data.HashMap.Strict as HM
import qualified Data.Map.Strict as Map
import qualified Data.Traversable as T
import Control.Monad.Trans.Either as E
import Unsafe.Coerce

import Data.Functor.Rep
import Data.Functor.Adjunction

-- | The type @Object f g@ represents objects which can handle messages @f@, perform actions in the environment @g@.
-- It can be thought of as an automaton that converts effects.
-- 'Object's can be composed just like functions using '@>>@'; the identity element is 'echo'.
-- Objects are morphisms of the category of functors
newtype Object f g = Object { runObject :: forall x. f x -> g (x, Object f g) }
#if __GLASGOW_HASKELL__ >= 707
  deriving (Typeable)
#else
instance (Typeable1 f, Typeable1 g) => Typeable (Object f g) where
  typeOf t = mkTyConApp objectTyCon [typeOf1 (f t), typeOf1 (g t)] where
    f :: Object f g -> f a
    f = undefined
    g :: Object f g -> g a
    g = undefined

objectTyCon :: TyCon
#if __GLASGOW_HASKELL__ < 704
objectTyCon = mkTyCon "Control.Object.Object"
#else
objectTyCon = mkTyCon3 "object" "Control.Object" "Object"
#endif
{-# NOINLINE objectTyCon #-}
#endif

-- | An alias for 'runObject'.
(@-) :: Object f g -> f x -> g (x, Object f g)
(@-) = runObject
{-# INLINE (@-) #-}
infixr 5 @-

-- | The identity object
echo :: Functor f => Object f f
echo = Object (fmap (\x -> (x, echo)))

-- | Object-object composition
(@>>@) :: Functor h => Object f g -> Object g h -> Object f h
Object m @>>@ Object n = Object $ \e -> fmap (\((x, m'), n') -> (x, m' @>>@ n')) $ n (m e)
infixr 1 @>>@

-- | Object-function composition
(@>>^) :: Functor h => Object f g -> (forall x. g x -> h x) -> Object f h
m0 @>>^ g = go m0 where go (Object m) = Object $ fmap (fmap go) . g . m
infixr 1 @>>^

-- | Function-object composition
(^>>@) :: Functor h => (forall x. f x -> g x) -> Object g h -> Object f h
f ^>>@ m0 = go m0 where go (Object m) = Object $ fmap (fmap go) . m . f
infixr 1 ^>>@

(@**@) :: Applicative m => Object f m -> Object g m -> Object (Day f g) m
a @**@ b = Object $ \(Day f g r) -> (\(x, a') (y, b') -> (r x y, a' @**@ b')) <$> runObject a f <*> runObject b g
infixr 3 @**@

(@||@) :: Functor m => Object f m -> Object g m -> Object (F.Sum f g) m
a @||@ b = Object $ \r -> case r of
  InL f -> fmap (fmap (@||@b)) (runObject a f)
  InR g -> fmap (fmap (a@||@)) (runObject b g)
infixr 2 @||@

-- | Lift a natural transformation into an object.
liftO :: Functor g => (forall x. f x -> g x) -> Object f g
liftO f = go where go = Object $ fmap (\x -> (x, go)) . f
{-# INLINE liftO #-}

-- | Change the workspace of the object.
transObject :: Functor g => (forall x. f x -> g x) -> Object e f -> Object e g
transObject f = (@>>^f)

-- | Apply a function to the messages coming into the object.
adaptObject :: Functor m => (forall x. g x -> f x) -> Object f m -> Object g m
adaptObject f = (f^>>@)

-- | Build an object using continuation passing style.
oneshot :: (Functor f, Monad m) => (forall a. f (m a) -> m a) -> Object f m
oneshot m = go where
  go = Object $ \e -> m (fmap return e) >>= \a -> return (a, go)
{-# INLINE oneshot #-}

-- | Build a stateful object.
--
-- @stateful t s = t ^>>@ variable s@
stateful :: Monad m => (forall a. f a -> StateT s m a) -> s -> Object f m
stateful h = go where
  go s = Object $ liftM (\(a, s') -> (a, go s')) . flip runStateT s . h
{-# INLINE stateful #-}

-- | The unwrapped analog of 'stateful'
--     @unfoldO runObject = id@
--     @unfoldO runSequential = sequential@
--     @unfoldO iterObject = iterable@
unfoldO :: Functor g => (forall a. r -> f a -> g (a, r)) -> r -> Object f g
unfoldO h = go where go r = Object $ fmap (fmap go) . h r
{-# INLINE unfoldO #-}

unfoldOM :: Monad m => (forall a. r -> f a -> m (a, r)) -> r -> Object f m
unfoldOM h = go where go r = Object $ liftM (fmap go) . h r
{-# INLINE unfoldOM #-}

type Variable s = forall m. Monad m => Object (StateT s m) m

-- | A mutable variable.
variable :: s -> Variable s
variable s = Object $ \m -> liftM (fmap variable) $ runStateT m s

-- | Build a stateful object, sharing out the state.
sharing :: Monad m => (forall a. f a -> StateT s m a) -> s -> Object (State s |> f |> Nil) m
sharing m = go where
  go s = Object $ \k -> liftM (fmap go) $ ($k)
    $ (\n -> return $ runState n s)
    ||> (\e -> runStateT (m e) s)
    ||> exhaust
{-# INLINE sharing #-}

-- | An object that won't accept any messages.
loner :: Functor f => Object Nil f
loner = liftO exhaust

-- | Extend an object by adding another independent object.
(@|>@) :: Functor g => Object f g -> Object (Union s) g -> Object (f |> Union s) g
p @|>@ q = Object $ fmap (fmap (@|>@q)) . runObject p ||> fmap (fmap (p @|>@)) . runObject q
infixr 3 @|>@

-- | The flyweight pattern.
flyweight :: (Monad m, Ord k) => (k -> m a) -> Object (Request k a) m
flyweight f = go Map.empty where
  go m = Object $ \(Request k cont) -> case Map.lookup k m of
    Just a -> return (cont a, go m)
    Nothing -> f k >>= \a -> return (cont a, go $ Map.insert k a m)

-- | Like 'flyweight', but it uses 'Data.HashMap.Strict' internally.
flyweight' :: (Monad m, Eq k, Hashable k) => (k -> m a) -> Object (Request k a) m
flyweight' f = go HM.empty where
  go m = Object $ \(Request k cont) -> case HM.lookup k m of
    Just a -> return (cont a, go m)
    Nothing -> f k >>= \a -> return (cont a, go $ HM.insert k a m)

(@!) :: Monad m => Object e m -> ReifiedProgram e a -> m (a, Object e m)
obj @! Return a = return (a, obj)
obj @! (e :>>= cont) = runObject obj e >>= \(a, obj') -> obj' @! cont a
infixr 5 @!

(@!!) :: Monad m => Object e m -> T.ReifiedProgramT e m a -> m (a, Object e m)
obj @!! T.Return a = return (a, obj)
obj @!! T.Lift m cont = m >>= (obj @!!) . cont
obj @!! (e T.:>>= cont) = runObject obj e >>= \(a, obj') -> obj' @!! cont a
infixr 5 @!!

iterObject :: Monad m => Object f m -> Free f a -> m (a, Object f m)
iterObject obj (Pure a) = return (a, obj)
iterObject obj (Free f) = runObject obj f >>= \(cont, obj') -> iterObject obj' cont

iterTObject :: Monad m => Object f m -> T.FreeT f m a -> m (a, Object f m)
iterTObject obj m = T.runFreeT m >>= \r -> case r of
  T.Pure a -> return (a, obj)
  T.Free f -> runObject obj f >>= \(cont, obj') -> iterTObject obj' cont

-- | Let object handle sequential methods.
sequential :: Monad m => Object e m -> Object (ReifiedProgram e) m
sequential = unfoldOM (@!)

-- | Let object handle sequential methods.
sequentialT :: Monad m => Object e m -> Object (T.ReifiedProgramT e m) m
sequentialT = unfoldOM (@!!)

iterative :: Monad m => Object f m -> Object (Free f) m
iterative = unfoldOM iterObject

iterativeT :: Monad m => Object f m -> Object (T.FreeT f m) m
iterativeT = unfoldOM iterTObject

foldP :: Applicative f => (a -> r -> f r) -> r -> Object (PushPull a r) f
foldP f = go where
  go r = Object $ \pp -> case pp of
    Push a c -> fmap (\z -> (c, z `seq` go z)) (f a r)
    Pull cont -> pure (cont r, go r)
{-# INLINE foldP #-}

foldP' :: Applicative f => (a -> r -> r) -> r -> Object (PushPull a r) f
foldP' f = go where
  go r = Object $ \pp -> case pp of
    Push a c -> let z = f a r in pure (c, z `seq` go z)
    Pull cont -> pure (cont r, go r)
{-# INLINE foldP' #-}

animate :: (Applicative m, Num t) => (t -> m a) -> Object (Request t a) m
animate f = go 0 where
  go t = Object $ \(Request dt cont) -> (\x -> (cont x, go (t + dt))) <$> f t

transit :: (Alternative m, Fractional t, Ord t) => t -> (t -> m a) -> Object (Request t a) m
transit len f = go 0 where
  go t
    | t >= len = Object $ const empty
    | otherwise = Object $ \(Request dt cont) -> (\x -> (cont x, go (t + dt))) <$> f (t / len)

announce :: (T.Traversable t, Monad m, Elevate (State (t (Object f g))) m, Elevate g m) => f a -> m [a]
announce f = do
  t <- elevate get
  (t', Endo e) <- runWriterT $ T.mapM (\obj -> (lift . elevate) (runObject obj f)
      >>= \(x, obj') -> writer (obj', Endo (x:))) t
  elevate (put t')
  return (e [])

announceMaybe :: (Witherable t, Monad m, Elevate (State (t (Object f Maybe))) m) => f a -> m [a]
announceMaybe f = elevate $ state
  $ \t -> let (t', Endo e) = runWriter
                $ witherM (\obj -> case runObject obj f of
                  Just (x, obj') -> lift $ writer (obj', Endo (x:))
                  Nothing -> mzero) t in (e [], t')

announceMaybeT :: (Witherable t, Monad m, State (t (Object f (MaybeT g))) ∈ Floors1 m, g ∈ Floors1 m, Tower m) => f a -> m [a]
announceMaybeT f = do
  t <- elevate get
  (t', Endo e) <- runWriterT $ witherM (\obj -> mapMaybeT (lift . elevate) (runObject obj f)
      >>= \(x, obj') -> lift (writer (obj', Endo (x:)))) t
  elevate (put t')
  return (e [])

-- | An object which is specialized to be a Mealy machine
newtype Process m a b = Process { unProcess :: Object (Request a b) m }

-- | @_Process :: Iso' (Object (Request a b) m) (Process m a b)@
_Process :: (Profunctor p, Functor f) => p (Process m a b) (f (Process m a b)) -> p (Object (Request a b) m) (f (Object (Request a b) m))
_Process = dimap Process (fmap unProcess)

instance Functor f => Functor (Process f a) where
  fmap f (Process o0) = Process $ go o0 where
    go o = Object $ \(Request a cont) -> fmap (cont *** go) $ runObject o (Request a f)

instance Applicative f => Applicative (Process f a) where
  pure a = Process go where
    go = Object $ \(Request _ cont) -> pure (cont a, go)
  Process f0 <*> Process a0 = Process $ go f0 a0 where
    go mf ma = Object $ \(Request a cont) -> (\(f, mf') (x, ma') -> (cont (f x), go mf' ma'))
      <$> runObject mf (Request a id)
      <*> runObject ma (Request a id)

instance (Applicative f, Monoid b) => Monoid (Process f a b) where
  mempty = pure mempty
  mappend = liftA2 mappend

instance Monad m => C.Category (Process m) where
  id = arr id
  Process g0 . Process f0 = Process $ go f0 g0 where
    go f g = Object $ \(Request a cont) -> runObject f (Request a id)
      >>= \(b, f') -> liftM (\(c, g') -> (cont c, go f' g')) $ runObject g (Request b id)

instance Monad m => Arrow (Process m) where
  arr f = Process go where
    go = Object $ \(Request a cont) -> return (cont (f a), go)
  first (Process f0) = Process $ go f0 where
    go f = Object $ \(Request (a, c) cont) -> liftM (\(b, f') -> (cont (b, c), go f')) $ runObject f (Request a id)
  second (Process f0) = Process $ go f0 where
    go f = Object $ \(Request (a, c) cont) -> liftM (\(d, f') -> (cont (a, d), go f')) $ runObject f (Request c id)

instance Monad m => ArrowChoice (Process m) where
  left (Process f0) = Process $ go f0 where
    go f = Object $ \(Request e cont) -> case e of
      Left a -> liftM (\(b, f') -> (cont (Left b), go f')) $ runObject f (Request a id)
      Right c -> return (cont (Right c), go f)
  right (Process f0) = Process $ go f0 where
    go f = Object $ \(Request e cont) -> case e of
      Right a -> liftM (\(b, f') -> (cont (Right b), go f')) $ runObject f (Request a id)
      Left c -> return (cont (Left c), go f)

instance Monad m => Profunctor (Process m) where
  dimap f g (Process f0) = Process (go f0) where
    go m = Object $ \(Request a cont) -> liftM (\(b, m') -> (cont (g b), go m')) $ runObject m (Request (f a) id)
  {-# INLINE dimap #-}

instance Monad m => Strong (Process m) where
  first' = first
  {-# INLINE first' #-}
  second' = second
  {-# INLINE second' #-}

instance Monad m => Choice (Process m) where
  left' = A.left
  {-# INLINE left' #-}
  right' = A.right
  {-# INLINE right' #-}

instance (Applicative m, Num o) => Num (Process m i o) where
  (+) = liftA2 (+)
  {-# INLINE (+) #-}
  (-) = liftA2 (-)
  {-# INLINE (-) #-}
  (*) = liftA2 (*)
  {-# INLINE (*) #-}
  abs = fmap abs
  {-# INLINE abs #-}
  signum = fmap signum
  {-# INLINE signum #-}
  fromInteger = pure . fromInteger
  {-# INLINE fromInteger #-}

instance (Applicative m, Fractional o) => Fractional (Process m i o) where
  (/) = liftA2 (/)
  {-# INLINE (/) #-}
  recip = fmap recip
  fromRational = pure . fromRational

-- | Object with a final result.
--
-- @Object f g ≡ Mortal f g Void@
--
newtype Mortal f g a = Mortal { unMortal :: Object f (EitherT a g) }

instance (Functor m, Monad m) => Functor (Mortal f m) where
  fmap f (Mortal obj) = Mortal (obj @>>^ bimapEitherT f id)

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

instance Monad m => Monad (Mortal f m) where
  return a = Mortal $ Object $ const $ E.left a
  Mortal obj >>= k = unsafeCoerce $ \f -> lift (runEitherT (runObject obj f)) >>= \r -> case r of
    Left a -> runObject (unMortal (k a)) f
    Right (x, obj') -> return (x, unMortal (Mortal obj' >>= k))

runMortal :: Monad m => Mortal f m a -> f x -> m (Either a (x, Mortal f m a))
runMortal = unsafeCoerce runObject

-- | For every adjunction f ⊣ g, we can "connect" @Object g m@ and @Object f m@ permanently.
($$) :: (Monad m, Adjunction f g) => Object g m -> Object f m -> m x
a $$ b = do
  (x, a') <- runObject a askRep
  ((), b') <- runObject b (unit () `index` x)
  a' $$ b'
infix 0 $$

-- | Like '$$', but kept until the right 'Mortal' dies.
($$!) :: (Monad m, Adjunction f g) => Object g m -> Mortal f m a -> m (Object g m, a)
o $$! m = do
  (x, o') <- runObject o askRep
  r <- runMortal m (unit () `index` x)
  case r of
    Left a -> return (o', a)
    Right ((), m') -> o' $$! m'
infix 0 $$!

-- | Like '$$', but kept until the left 'Mortal' dies.
(!$$) :: (Monad m, Adjunction f g) => Mortal g m a -> Object f m -> m (a, Object f m)
m !$$ o = do
  r <- runMortal m askRep
  case r of
    Left a -> return (a, o)
    Right (x, m') -> do
      ((), o') <- runObject o (unit () `index` x)
      m' !$$ o'
infix 0 !$$

-- | Connect two 'Mortal's.
(!$$!) :: (Monad m, Adjunction f g) => Mortal g m a -> Mortal f m b -> m (Either (a, Mortal f m b) (Mortal g m a, b))
m !$$! n = do
  r <- runMortal m askRep
  case r of
    Left a -> return (Left (a, n))
    Right (x, m') -> do
      s <- runMortal n (unit () `index` x)
      case s of
        Left b -> return (Right (m', b))
        Right ((), n') -> m' !$$! n'

infix 0 !$$!