    {-# LANGUAGE CPP #-}
    #if __GLASGOW_HASKELL__ >= 702
    {-# LANGUAGE Safe #-}
    {-# LANGUAGE DeriveGeneric #-}
    #endif
    #if __GLASGOW_HASKELL__ >= 706
    {-# LANGUAGE PolyKinds #-}
    #endif
    #if __GLASGOW_HASKELL__ >= 710 && __GLASGOW_HASKELL__ < 802
    {-# LANGUAGE AutoDeriveTypeable #-}
    #endif
    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Control.Applicative.Backwards
    -- Copyright   :  (c) Russell O'Connor 2009
    -- License     :  BSD-style (see the file LICENSE)
    --
    -- Maintainer  :  R.Paterson@city.ac.uk
    -- Stability   :  experimental
    -- Portability :  portable
    --
    -- Making functors with an 'Applicative' instance that performs actions
    -- in the reverse order.
    -----------------------------------------------------------------------------

    module Control.Applicative.Backwards (
        Backwards(..),
      ) where

    #if MIN_VERSION_base(4,18,0)
    import Data.Foldable1 (Foldable1(foldMap1))
    #endif
    import Data.Functor.Classes
    #if MIN_VERSION_base(4,12,0)
    import Data.Functor.Contravariant
    #endif
    #if __GLASGOW_HASKELL__ >= 704
    import GHC.Generics
    #endif

    import Prelude hiding (foldr, foldr1, foldl, foldl1, null, length)
    import Control.Applicative
    import Data.Foldable
    #if !(MIN_VERSION_base(4,8,0))
    import Data.Traversable (Traversable(traverse, sequenceA))
    #endif

    -- | The same functor, but with an 'Applicative' instance that performs
    -- actions in the reverse order.
    newtype Backwards f a = Backwards { forall {k} (f :: k -> *) (a :: k). Backwards f a -> f a
    forwards :: f a }
    #if __GLASGOW_HASKELL__ >= 710
        deriving ((forall x. Backwards f a -> Rep (Backwards f a) x)
    -> (forall x. Rep (Backwards f a) x -> Backwards f a)
    -> Generic (Backwards f a)
    forall x. Rep (Backwards f a) x -> Backwards f a
    forall x. Backwards f a -> Rep (Backwards f a) x
    forall a.
    (forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
    forall k (f :: k -> *) (a :: k) x.
    Rep (Backwards f a) x -> Backwards f a
    forall k (f :: k -> *) (a :: k) x.
    Backwards f a -> Rep (Backwards f a) x
    $cfrom :: forall k (f :: k -> *) (a :: k) x.
    Backwards f a -> Rep (Backwards f a) x
    from :: forall x. Backwards f a -> Rep (Backwards f a) x
    $cto :: forall k (f :: k -> *) (a :: k) x.
    Rep (Backwards f a) x -> Backwards f a
    to :: forall x. Rep (Backwards f a) x -> Backwards f a
    Generic, (forall (a :: k). Backwards f a -> Rep1 (Backwards f) a)
    -> (forall (a :: k). Rep1 (Backwards f) a -> Backwards f a)
    -> Generic1 (Backwards f)
    forall (a :: k). Rep1 (Backwards f) a -> Backwards f a
    forall (a :: k). Backwards f a -> Rep1 (Backwards f) a
    forall k (f :: k -> *).
    (forall (a :: k). f a -> Rep1 f a)
    -> (forall (a :: k). Rep1 f a -> f a) -> Generic1 f
    forall k (f :: k -> *) (a :: k).
    Rep1 (Backwards f) a -> Backwards f a
    forall k (f :: k -> *) (a :: k).
    Backwards f a -> Rep1 (Backwards f) a
    $cfrom1 :: forall k (f :: k -> *) (a :: k).
    Backwards f a -> Rep1 (Backwards f) a
    from1 :: forall (a :: k). Backwards f a -> Rep1 (Backwards f) a
    $cto1 :: forall k (f :: k -> *) (a :: k).
    Rep1 (Backwards f) a -> Backwards f a
    to1 :: forall (a :: k). Rep1 (Backwards f) a -> Backwards f a
    Generic1)
    #elif __GLASGOW_HASKELL__ >= 704
        deriving (Generic)
    #endif

    instance (Eq1 f) => Eq1 (Backwards f) where
        liftEq :: forall a b.
    (a -> b -> Bool) -> Backwards f a -> Backwards f b -> Bool
    liftEq a -> b -> Bool
    eq (Backwards f a
    x) (Backwards f b
    y) = (a -> b -> Bool) -> f a -> f b -> Bool
    forall a b. (a -> b -> Bool) -> f a -> f b -> Bool
    forall (f :: * -> *) a b.
    Eq1 f =>
    (a -> b -> Bool) -> f a -> f b -> Bool
    liftEq a -> b -> Bool
    eq f a
    x f b
    y
        {-# INLINE liftEq #-}

    instance (Ord1 f) => Ord1 (Backwards f) where
        liftCompare :: forall a b.
    (a -> b -> Ordering) -> Backwards f a -> Backwards f b -> Ordering
    liftCompare a -> b -> Ordering
    comp (Backwards f a
    x) (Backwards f b
    y) = (a -> b -> Ordering) -> f a -> f b -> Ordering
    forall a b. (a -> b -> Ordering) -> f a -> f b -> Ordering
    forall (f :: * -> *) a b.
    Ord1 f =>
    (a -> b -> Ordering) -> f a -> f b -> Ordering
    liftCompare a -> b -> Ordering
    comp f a
    x f b
    y
        {-# INLINE liftCompare #-}

    instance (Read1 f) => Read1 (Backwards f) where
        liftReadsPrec :: forall a.
    (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Backwards f a)
    liftReadsPrec Int -> ReadS a
    rp ReadS [a]
    rl = (String -> ReadS (Backwards f a)) -> Int -> ReadS (Backwards f a)
    forall a. (String -> ReadS a) -> Int -> ReadS a
    readsData ((String -> ReadS (Backwards f a)) -> Int -> ReadS (Backwards f a))
    -> (String -> ReadS (Backwards f a))
    -> Int
    -> ReadS (Backwards f a)
    forall a b. (a -> b) -> a -> b
    $
            (Int -> ReadS (f a))
    -> String
    -> (f a -> Backwards f a)
    -> String
    -> ReadS (Backwards f a)
    forall a t.
    (Int -> ReadS a) -> String -> (a -> t) -> String -> ReadS t
    readsUnaryWith ((Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)
    forall a. (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)
    forall (f :: * -> *) a.
    Read1 f =>
    (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)
    liftReadsPrec Int -> ReadS a
    rp ReadS [a]
    rl) String
    "Backwards" f a -> Backwards f a
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards

    instance (Show1 f) => Show1 (Backwards f) where
        liftShowsPrec :: forall a.
    (Int -> a -> ShowS)
    -> ([a] -> ShowS) -> Int -> Backwards f a -> ShowS
    liftShowsPrec Int -> a -> ShowS
    sp [a] -> ShowS
    sl Int
    d (Backwards f a
    x) =
            (Int -> f a -> ShowS) -> String -> Int -> f a -> ShowS
    forall a. (Int -> a -> ShowS) -> String -> Int -> a -> ShowS
    showsUnaryWith ((Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS
    forall a.
    (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS
    forall (f :: * -> *) a.
    Show1 f =>
    (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS
    liftShowsPrec Int -> a -> ShowS
    sp [a] -> ShowS
    sl) String
    "Backwards" Int
    d f a
    x

    instance (Eq1 f, Eq a) => Eq (Backwards f a) where == :: Backwards f a -> Backwards f a -> Bool
    (==) = Backwards f a -> Backwards f a -> Bool
    forall (f :: * -> *) a. (Eq1 f, Eq a) => f a -> f a -> Bool
    eq1
    instance (Ord1 f, Ord a) => Ord (Backwards f a) where compare :: Backwards f a -> Backwards f a -> Ordering
    compare = Backwards f a -> Backwards f a -> Ordering
    forall (f :: * -> *) a. (Ord1 f, Ord a) => f a -> f a -> Ordering
    compare1
    instance (Read1 f, Read a) => Read (Backwards f a) where readsPrec :: Int -> ReadS (Backwards f a)
    readsPrec = Int -> ReadS (Backwards f a)
    forall (f :: * -> *) a. (Read1 f, Read a) => Int -> ReadS (f a)
    readsPrec1
    instance (Show1 f, Show a) => Show (Backwards f a) where showsPrec :: Int -> Backwards f a -> ShowS
    showsPrec = Int -> Backwards f a -> ShowS
    forall (f :: * -> *) a. (Show1 f, Show a) => Int -> f a -> ShowS
    showsPrec1

    -- | Derived instance.
    instance (Functor f) => Functor (Backwards f) where
        fmap :: forall a b. (a -> b) -> Backwards f a -> Backwards f b
    fmap a -> b
    f (Backwards f a
    a) = f b -> Backwards f b
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards ((a -> b) -> f a -> f b
    forall a b. (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap a -> b
    f f a
    a)
        {-# INLINE fmap #-}
        a
    x <$ :: forall a b. a -> Backwards f b -> Backwards f a
    <$ Backwards f b
    a = f a -> Backwards f a
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards (a
    x a -> f b -> f a
    forall a b. a -> f b -> f a
    forall (f :: * -> *) a b. Functor f => a -> f b -> f a
    <$ f b
    a)
        {-# INLINE (<$) #-}

    -- | Apply @f@-actions in the reverse order.
    instance (Applicative f) => Applicative (Backwards f) where
        pure :: forall a. a -> Backwards f a
    pure a
    a = f a -> Backwards f a
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards (a -> f a
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure a
    a)
        {-# INLINE pure #-}
        Backwards f (a -> b)
    f <*> :: forall a b. Backwards f (a -> b) -> Backwards f a -> Backwards f b
    <*> Backwards f a
    a = f b -> Backwards f b
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards (f a
    a f a -> f (a -> b) -> f b
    forall (f :: * -> *) a b. Applicative f => f a -> f (a -> b) -> f b
    <**> f (a -> b)
    f)
        {-# INLINE (<*>) #-}
    #if MIN_VERSION_base(4,10,0)
        liftA2 :: forall a b c.
    (a -> b -> c) -> Backwards f a -> Backwards f b -> Backwards f c
    liftA2 a -> b -> c
    f (Backwards f a
    m) (Backwards f b
    n) = f c -> Backwards f c
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards (f c -> Backwards f c) -> f c -> Backwards f c
    forall a b. (a -> b) -> a -> b
    $ (b -> a -> c) -> f b -> f a -> f c
    forall a b c. (a -> b -> c) -> f a -> f b -> f c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 ((a -> b -> c) -> b -> a -> c
    forall a b c. (a -> b -> c) -> b -> a -> c
    flip a -> b -> c
    f) f b
    n f a
    m
        {-# INLINE liftA2 #-}
    #endif
    #if MIN_VERSION_base(4,2,0)
        Backwards f a
    xs *> :: forall a b. Backwards f a -> Backwards f b -> Backwards f b
    *> Backwards f b
    ys = f b -> Backwards f b
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards (f b
    ys f b -> f a -> f b
    forall a b. f a -> f b -> f a
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f a
    <* f a
    xs)
        {-# INLINE (*>) #-}
        Backwards f a
    ys <* :: forall a b. Backwards f a -> Backwards f b -> Backwards f a
    <* Backwards f b
    xs = f a -> Backwards f a
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards (f b
    xs f b -> f a -> f a
    forall a b. f a -> f b -> f b
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
    *> f a
    ys)
        {-# INLINE (<*) #-}
    #endif

    -- | Try alternatives in the same order as @f@.
    instance (Alternative f) => Alternative (Backwards f) where
        empty :: forall a. Backwards f a
    empty = f a -> Backwards f a
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards f a
    forall a. f a
    forall (f :: * -> *) a. Alternative f => f a
    empty
        {-# INLINE empty #-}
        Backwards f a
    x <|> :: forall a. Backwards f a -> Backwards f a -> Backwards f a
    <|> Backwards f a
    y = f a -> Backwards f a
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards (f a
    x f a -> f a -> f a
    forall a. f a -> f a -> f a
    forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
    <|> f a
    y)
        {-# INLINE (<|>) #-}

    -- | Derived instance.
    instance (Foldable f) => Foldable (Backwards f) where
        foldMap :: forall m a. Monoid m => (a -> m) -> Backwards f a -> m
    foldMap a -> m
    f (Backwards f a
    t) = (a -> m) -> f a -> m
    forall m a. Monoid m => (a -> m) -> f a -> m
    forall (t :: * -> *) m a.
    (Foldable t, Monoid m) =>
    (a -> m) -> t a -> m
    foldMap a -> m
    f f a
    t
        {-# INLINE foldMap #-}
        foldr :: forall a b. (a -> b -> b) -> b -> Backwards f a -> b
    foldr a -> b -> b
    f b
    z (Backwards f a
    t) = (a -> b -> b) -> b -> f a -> b
    forall a b. (a -> b -> b) -> b -> f a -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr a -> b -> b
    f b
    z f a
    t
        {-# INLINE foldr #-}
        foldl :: forall b a. (b -> a -> b) -> b -> Backwards f a -> b
    foldl b -> a -> b
    f b
    z (Backwards f a
    t) = (b -> a -> b) -> b -> f a -> b
    forall b a. (b -> a -> b) -> b -> f a -> b
    forall (t :: * -> *) b a.
    Foldable t =>
    (b -> a -> b) -> b -> t a -> b
    foldl b -> a -> b
    f b
    z f a
    t
        {-# INLINE foldl #-}
        foldr1 :: forall a. (a -> a -> a) -> Backwards f a -> a
    foldr1 a -> a -> a
    f (Backwards f a
    t) = (a -> a -> a) -> f a -> a
    forall a. (a -> a -> a) -> f a -> a
    forall (t :: * -> *) a. Foldable t => (a -> a -> a) -> t a -> a
    foldr1 a -> a -> a
    f f a
    t
        {-# INLINE foldr1 #-}
        foldl1 :: forall a. (a -> a -> a) -> Backwards f a -> a
    foldl1 a -> a -> a
    f (Backwards f a
    t) = (a -> a -> a) -> f a -> a
    forall a. (a -> a -> a) -> f a -> a
    forall (t :: * -> *) a. Foldable t => (a -> a -> a) -> t a -> a
    foldl1 a -> a -> a
    f f a
    t
        {-# INLINE foldl1 #-}
    #if MIN_VERSION_base(4,8,0)
        null :: forall a. Backwards f a -> Bool
    null (Backwards f a
    t) = f a -> Bool
    forall a. f a -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null f a
    t
        length :: forall a. Backwards f a -> Int
    length (Backwards f a
    t) = f a -> Int
    forall a. f a -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length f a
    t
    #endif

    #if MIN_VERSION_base(4,18,0)
    -- | Derived instance.
    instance (Foldable1 f) => Foldable1 (Backwards f) where
        foldMap1 :: forall m a. Semigroup m => (a -> m) -> Backwards f a -> m
    foldMap1 a -> m
    f (Backwards f a
    t) = (a -> m) -> f a -> m
    forall m a. Semigroup m => (a -> m) -> f a -> m
    forall (t :: * -> *) m a.
    (Foldable1 t, Semigroup m) =>
    (a -> m) -> t a -> m
    foldMap1 a -> m
    f f a
    t
        {-# INLINE foldMap1 #-}
    #endif

    -- | Derived instance.
    instance (Traversable f) => Traversable (Backwards f) where
        traverse :: forall (f :: * -> *) a b.
    Applicative f =>
    (a -> f b) -> Backwards f a -> f (Backwards f b)
    traverse a -> f b
    f (Backwards f a
    t) = (f b -> Backwards f b) -> f (f b) -> f (Backwards f b)
    forall a b. (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap f b -> Backwards f b
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards ((a -> f b) -> f a -> f (f b)
    forall (t :: * -> *) (f :: * -> *) a b.
    (Traversable t, Applicative f) =>
    (a -> f b) -> t a -> f (t b)
    forall (f :: * -> *) a b.
    Applicative f =>
    (a -> f b) -> f a -> f (f b)
    traverse a -> f b
    f f a
    t)
        {-# INLINE traverse #-}
        sequenceA :: forall (f :: * -> *) a.
    Applicative f =>
    Backwards f (f a) -> f (Backwards f a)
    sequenceA (Backwards f (f a)
    t) = (f a -> Backwards f a) -> f (f a) -> f (Backwards f a)
    forall a b. (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap f a -> Backwards f a
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards (f (f a) -> f (f a)
    forall (t :: * -> *) (f :: * -> *) a.
    (Traversable t, Applicative f) =>
    t (f a) -> f (t a)
    forall (f :: * -> *) a. Applicative f => f (f a) -> f (f a)
    sequenceA f (f a)
    t)
        {-# INLINE sequenceA #-}

    #if MIN_VERSION_base(4,12,0)
    -- | Derived instance.
    instance (Contravariant f) => Contravariant (Backwards f) where
        contramap :: forall a' a. (a' -> a) -> Backwards f a -> Backwards f a'
    contramap a' -> a
    f = f a' -> Backwards f a'
    forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
    Backwards (f a' -> Backwards f a')
    -> (Backwards f a -> f a') -> Backwards f a -> Backwards f a'
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a' -> a) -> f a -> f a'
    forall a' a. (a' -> a) -> f a -> f a'
    forall (f :: * -> *) a' a.
    Contravariant f =>
    (a' -> a) -> f a -> f a'
    contramap a' -> a
    f (f a -> f a') -> (Backwards f a -> f a) -> Backwards f a -> f a'
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Backwards f a -> f a
    forall {k} (f :: k -> *) (a :: k). Backwards f a -> f a
    forwards
        {-# INLINE contramap #-}
    #endif