    -- |
    -- Module      :  Data.Functor.Reverse
    -- Copyright   :  (c) Russell O'Connor 2009
    -- License     :  BSD-style (see the file LICENSE)
    --
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  experimental
    -- Portability :  portable
    --
    -- Making functors whose elements are notionally in the reverse order
    -- from the original functor.

    module Data.Functor.Reverse where

    import Control.Applicative.Backwards

    import Prelude hiding (foldr, foldr1, foldl, foldl1)
    import Control.Applicative
    import Data.Foldable
    import Data.Traversable
    import Data.Monoid

    -- | The same functor, but with 'Foldable' and 'Traversable' instances
    -- that process the elements in the reverse order.
    newtype Reverse f a = Reverse { getReverse :: f a }

    -- | Derived instance.
    instance (Functor f) => Functor (Reverse f) where
        fmap f (Reverse a) = Reverse (fmap f a)

    -- | Derived instance.
    instance (Applicative f) => Applicative (Reverse f) where
        pure a = Reverse (pure a)
        Reverse f <*> Reverse a = Reverse (f <*> a)

    -- | Derived instance.
    instance (Alternative f) => Alternative (Reverse f) where
        empty = Reverse empty
        Reverse x <|> Reverse y = Reverse (x <|> y)

    -- | Fold from right to left.
    instance (Foldable f) => Foldable (Reverse f) where
        foldMap f (Reverse t) = getDual (foldMap (Dual . f) t)
        foldr f z (Reverse t) = foldl (flip f) z t
        foldl f z (Reverse t) = foldr (flip f) z t
        foldr1 f (Reverse t) = foldl1 (flip f) t
        foldl1 f (Reverse t) = foldr1 (flip f) t

    -- | Traverse from right to left.
    instance (Traversable f) => Traversable (Reverse f) where
        traverse f (Reverse t) =
            fmap Reverse . forwards $ traverse (Backwards . f) t
        sequenceA (Reverse t) =
            fmap Reverse . forwards $ sequenceA (fmap Backwards t)