Data/Functor/Reverse.hs

-- |
-- 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)