{-# LANGUAGE CPP #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}

{-# LANGUAGE Trustworthy #-}

-----------------------------------------------------------------------------
-- |
-- Copyright   :  (C) 2011-2015 Edward Kmett,
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  provisional
-- Portability :  portable
--
-- For a good explanation of profunctors in Haskell see Dan Piponi's article:
--
-- <http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html>
--
-- For more information on strength and costrength, see:
--
-- <http://comonad.com/reader/2008/deriving-strength-from-laziness/>
----------------------------------------------------------------------------
module Data.Profunctor.Types
  ( Profunctor(dimap, lmap, rmap)
  , Star(..)
  , Costar(..)
  , WrappedArrow(..)
  , Forget(..)
  , (:->)
  ) where

import Control.Applicative hiding (WrappedArrow(..))
import Control.Arrow
import Control.Category
import Control.Comonad
import Control.Monad (MonadPlus(..), (>=>))
import Data.Coerce (Coercible, coerce)
import Data.Distributive
import Data.Foldable
import Data.Monoid hiding (Product)
import Data.Profunctor.Unsafe
import Data.Traversable
import Prelude hiding (id,(.))

infixr 0 :->
type p :-> q = forall a b. p a b -> q a b

------------------------------------------------------------------------------
-- Star
------------------------------------------------------------------------------

-- | Lift a 'Functor' into a 'Profunctor' (forwards).
newtype Star f d c = Star { runStar :: d -> f c }

instance Functor f => Profunctor (Star f) where
  dimap ab cd (Star bfc) = Star (fmap cd . bfc . ab)
  {-# INLINE dimap #-}
  lmap k (Star f) = Star (f . k)
  {-# INLINE lmap #-}
  rmap k (Star f) = Star (fmap k . f)
  {-# INLINE rmap #-}
  -- We cannot safely overload (#.) because we didn't write the 'Functor'.
  p .# _ = coerce p
  {-# INLINE (.#) #-}

instance Functor f => Functor (Star f a) where
  fmap = rmap
  {-# INLINE fmap #-}

instance Applicative f => Applicative (Star f a) where
  pure a = Star $ \_ -> pure a
  Star ff <*> Star fx = Star $ \a -> ff a <*> fx a
  Star ff  *> Star fx = Star $ \a -> ff a  *> fx a
  Star ff <*  Star fx = Star $ \a -> ff a <*  fx a

instance Alternative f => Alternative (Star f a) where
  empty = Star $ \_ -> empty
  Star f <|> Star g = Star $ \a -> f a <|> g a

instance Monad f => Monad (Star f a) where
#if __GLASGOW_HASKELL__ < 710
  return a = Star $ \_ -> return a
#endif
  Star m >>= f = Star $ \ e -> do
    a <- m e
    runStar (f a) e

instance MonadPlus f => MonadPlus (Star f a) where
  mzero = Star $ \_ -> mzero
  Star f `mplus` Star g = Star $ \a -> f a `mplus` g a

instance Distributive f => Distributive (Star f a) where
  distribute fs = Star $ \a -> collect (($ a) .# runStar) fs

instance Monad f => Category (Star f) where
  id = Star return
  Star f . Star g = Star $ g >=> f

------------------------------------------------------------------------------
-- Costar
------------------------------------------------------------------------------

-- | Lift a 'Functor' into a 'Profunctor' (backwards).
newtype Costar f d c = Costar { runCostar :: f d -> c }

instance Functor f => Profunctor (Costar f) where
  dimap ab cd (Costar fbc) = Costar (cd . fbc . fmap ab)
  {-# INLINE dimap #-}
  lmap k (Costar f) = Costar (f . fmap k)
  {-# INLINE lmap #-}
  rmap k (Costar f) = Costar (k . f)
  {-# INLINE rmap #-}
  (#.) _ = coerce (\x -> x :: b) :: forall a b. Coercible b a => a -> b
  {-# INLINE (#.) #-}
  -- We cannot overload (.#) because we didn't write the 'Functor'.

instance Distributive (Costar f d) where
  distribute fs = Costar $ \gd -> fmap (($ gd) .# runCostar) fs

instance Functor (Costar f a) where
  fmap k (Costar f) = Costar (k . f)
  {-# INLINE fmap #-}
  a <$ _ = Costar $ \_ -> a
  {-# INLINE (<$) #-}

instance Applicative (Costar f a) where
  pure a = Costar $ \_ -> a
  Costar ff <*> Costar fx = Costar $ \a -> ff a (fx a)
  _ *> m = m
  m <* _ = m

instance Monad (Costar f a) where
  return = pure
  Costar m >>= f = Costar $ \ x -> runCostar (f (m x)) x

------------------------------------------------------------------------------
-- Wrapped Profunctors
------------------------------------------------------------------------------

-- | Wrap an arrow for use as a 'Profunctor'.
newtype WrappedArrow p a b = WrapArrow { unwrapArrow :: p a b }

instance Category p => Category (WrappedArrow p) where
  WrapArrow f . WrapArrow g = WrapArrow (f . g)
  {-# INLINE (.) #-}
  id = WrapArrow id
  {-# INLINE id #-}

instance Arrow p => Arrow (WrappedArrow p) where
  arr = WrapArrow . arr
  {-# INLINE arr #-}
  first = WrapArrow . first . unwrapArrow
  {-# INLINE first #-}
  second = WrapArrow . second . unwrapArrow
  {-# INLINE second #-}
  WrapArrow a *** WrapArrow b = WrapArrow (a *** b)
  {-# INLINE (***) #-}
  WrapArrow a &&& WrapArrow b = WrapArrow (a &&& b)
  {-# INLINE (&&&) #-}

instance ArrowZero p => ArrowZero (WrappedArrow p) where
  zeroArrow = WrapArrow zeroArrow
  {-# INLINE zeroArrow #-}

instance ArrowChoice p => ArrowChoice (WrappedArrow p) where
  left = WrapArrow . left . unwrapArrow
  {-# INLINE left #-}
  right = WrapArrow . right . unwrapArrow
  {-# INLINE right #-}
  WrapArrow a +++ WrapArrow b = WrapArrow (a +++ b)
  {-# INLINE (+++) #-}
  WrapArrow a ||| WrapArrow b = WrapArrow (a ||| b)
  {-# INLINE (|||) #-}

instance ArrowApply p => ArrowApply (WrappedArrow p) where
  app = WrapArrow $ app . arr (first unwrapArrow)
  {-# INLINE app #-}

instance ArrowLoop p => ArrowLoop (WrappedArrow p) where
  loop = WrapArrow . loop . unwrapArrow
  {-# INLINE loop #-}

instance Arrow p => Profunctor (WrappedArrow p) where
  lmap = (^>>)
  {-# INLINE lmap #-}
  rmap = (^<<)
  {-# INLINE rmap #-}
  -- We cannot safely overload (#.) or (.#) because we didn't write the 'Arrow'.

------------------------------------------------------------------------------
-- Forget
------------------------------------------------------------------------------

newtype Forget r a b = Forget { runForget :: a -> r }

instance Profunctor (Forget r) where
  dimap f _ (Forget k) = Forget (k . f)
  {-# INLINE dimap #-}
  lmap f (Forget k) = Forget (k . f)
  {-# INLINE lmap #-}
  rmap _ (Forget k) = Forget k
  {-# INLINE rmap #-}

instance Functor (Forget r a) where
  fmap _ (Forget k) = Forget k
  {-# INLINE fmap #-}

instance Foldable (Forget r a) where
  foldMap _ _ = mempty
  {-# INLINE foldMap #-}

instance Traversable (Forget r a) where
  traverse _ (Forget k) = pure (Forget k)
  {-# INLINE traverse #-}