    {-# LANGUAGE Rank2Types #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Either.Validation
    -- Copyright   :  (c) 2014 Chris Allen, Edward Kmett
    -- License     :  BSD-style
    --
    -- Maintainer  :  ekmett@gmail.com
    -- Stability   :  provisional
    -- Portability :  portable
    --
    -- Monoidal 'Validation' sibling to 'Either'.
    --
    -----------------------------------------------------------------------------

    module Data.Either.Validation
      ( Validation(..)
      , _Success
      , _Failure
      , eitherToValidation
      , validationToEither
      , _Validation
      ) where

    import Control.Applicative
    import Data.Bifoldable(Bifoldable(bifoldr))
    import Data.Bifunctor(Bifunctor(bimap))
    import Data.Bitraversable(Bitraversable(bitraverse))
    import Data.Foldable (Foldable(foldr))
    import Data.Functor.Alt (Alt((<!>)))
    import Data.Monoid (Monoid(mappend, mempty))
    import Data.Profunctor
    import Data.Semigroup (Semigroup((<>)))
    import Data.Traversable (Traversable(traverse))
    import Prelude hiding (foldr)

    -- | 'Validation' is 'Either' with a Left that is a 'Monoid'
    data Validation e a
      = Failure e
      | Success a
      deriving (Eq, Ord, Show)

    instance Functor (Validation e) where
       fmap _ (Failure e) = Failure e
       fmap f (Success a) = Success (f a)

    instance Semigroup e => Applicative (Validation e) where
      pure = Success
      Failure e1 <*> Failure e2 = Failure (e1 <> e2)
      Failure e1 <*> Success _  = Failure e1
      Success _  <*> Failure e2 = Failure e2
      Success f  <*> Success a  = Success (f a)

    instance Alt (Validation e) where
      Failure _ <!> x = x
      Success a <!> _ = Success a

    instance (Semigroup e, Monoid e) => Alternative (Validation e) where
      empty = Failure mempty
      (<|>) = (<!>)

    instance Foldable (Validation e) where
      foldr f x (Success a) = f a x
      foldr _ x (Failure _) = x

    instance Traversable (Validation e) where
      traverse f (Success a) = Success <$> f a
      traverse _ (Failure e) = pure (Failure e)

    instance Bifunctor Validation where
      bimap f _ (Failure e) = Failure (f e)
      bimap _ g (Success a) = Success (g a)

    instance Bifoldable Validation where
      bifoldr _ g x (Success a) = g a x
      bifoldr f _ x (Failure e) = f e x

    instance Bitraversable Validation where
      bitraverse _ g (Success a) = Success <$> g a
      bitraverse f _ (Failure e) = Failure <$> f e

    instance Semigroup e => Semigroup (Validation e a) where
      Failure e1 <> Failure e2 = Failure (e1 <> e2)
      Failure _  <> Success a2 = Success a2
      Success a1 <> Failure _  = Success a1
      Success a1 <> Success _  = Success a1

    instance Monoid e => Monoid (Validation e a) where
      mempty = Failure mempty
      Failure e1 `mappend` Failure e2 = Failure (e1 `mappend` e2)
      Failure _  `mappend` Success a2 = Success a2
      Success a1 `mappend` Failure _  = Success a1
      Success a1 `mappend` Success _  = Success a1

    type Prism s t a b = forall p f. (Choice p, Applicative f) => p a (f b) -> p s (f t)

    prism :: (b -> t) -> (s -> Either t a) -> Prism s t a b
    prism bt seta = dimap seta (either pure (fmap bt)) . right'
    {-# INLINE prism #-}

    _Failure :: Prism (Validation a c) (Validation b c) a b
    _Failure = prism
               (\ x -> Failure x)
               (\ x
                -> case x of
                  Failure y -> Right y
                  Success y -> Left (Success y))
    {-# INLINE _Failure #-}

    _Success :: Prism (Validation c a) (Validation c b) a b
    _Success = prism
               (\ x -> Success x)
               (\ x
                -> case x of
                  Failure y -> Left (Failure y)
                  Success y -> Right y)
    {-# INLINE _Success #-}

    type Iso s t a b = (Profunctor p, Functor f) => p a (f b) -> p s (f t)

    iso :: (s -> a) -> (b -> t) -> Iso s t a b
    iso sa bt = dimap sa (fmap bt)
    {-# INLINE iso #-}

    validationToEither :: Validation e a -> Either e a
    validationToEither x = case x of
      Failure e -> Left e
      Success a -> Right a
    {-# INLINE validationToEither #-}

    eitherToValidation :: Either e a -> Validation e a
    eitherToValidation x = case x of
      Left e -> Failure e
      Right a -> Success a
    {-# INLINE eitherToValidation #-}

    -- | 'Validation' is isomorphic to 'Either'
    _Validation :: Iso (Validation e a) (Validation g b) (Either e a) (Either g b)
    _Validation = iso validationToEither eitherToValidation
    {-# INLINE _Validation #-}