    {-# LANGUAGE CPP #-}
    {-# LANGUAGE DeriveDataTypeable #-}
    {-# LANGUAGE FlexibleContexts #-}
    {-# LANGUAGE StandaloneDeriving #-}
    {-# LANGUAGE UndecidableInstances #-}

    #if __GLASGOW_HASKELL__ >= 702
    {-# LANGUAGE DeriveGeneric #-}
    #endif

    #if __GLASGOW_HASKELL__ >= 704
    {-# LANGUAGE Safe #-}
    #elif __GLASGOW_HASKELL__ >= 702
    {-# LANGUAGE Trustworthy #-}
    #endif

    #if __GLASGOW_HASKELL__ >= 706
    {-# LANGUAGE PolyKinds #-}
    #endif
    #include "bifunctors-common.h"

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Bifunctor.Fix
    -- Copyright   :  (C) 2008-2016 Edward Kmett
    -- License     :  BSD-style (see the file LICENSE)
    --
    -- Maintainer  :  Edward Kmett <ekmett@gmail.com>
    -- Stability   :  provisional
    -- Portability :  non-portable
    --
    -----------------------------------------------------------------------------
    module Data.Bifunctor.Fix
      ( Fix(..)
      ) where

    #if __GLASGOW_HASKELL__ < 710
    import Control.Applicative
    #endif

    import Data.Biapplicative
    import Data.Bifoldable
    import Data.Bitraversable

    #if __GLASGOW_HASKELL__ < 710
    import Data.Foldable
    import Data.Traversable
    #endif

    #if __GLASGOW_HASKELL__ >= 708
    import Data.Typeable
    #endif

    #if __GLASGOW_HASKELL__ >= 702
    import GHC.Generics
    #endif

    #if LIFTED_FUNCTOR_CLASSES
    import Data.Functor.Classes
    #endif

    -- | Greatest fixpoint of a 'Bifunctor' (a 'Functor' over the first argument with zipping).
    newtype Fix p a = In { Fix p a -> p (Fix p a) a
    out :: p (Fix p a) a }
      deriving
        (
    #if __GLASGOW_HASKELL__ >= 702
          (forall x. Fix p a -> Rep (Fix p a) x)
    -> (forall x. Rep (Fix p a) x -> Fix p a) -> Generic (Fix p a)
    forall x. Rep (Fix p a) x -> Fix p a
    forall x. Fix p a -> Rep (Fix p a) x
    forall a.
    (forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
    forall k (p :: * -> k -> *) (a :: k) x. Rep (Fix p a) x -> Fix p a
    forall k (p :: * -> k -> *) (a :: k) x. Fix p a -> Rep (Fix p a) x
    $cto :: forall k (p :: * -> k -> *) (a :: k) x. Rep (Fix p a) x -> Fix p a
    $cfrom :: forall k (p :: * -> k -> *) (a :: k) x. Fix p a -> Rep (Fix p a) x
    Generic
    #endif
    #if __GLASGOW_HASKELL__ >= 708
        , Typeable
    #endif
        )

    deriving instance Eq   (p (Fix p a) a) => Eq   (Fix p a)
    deriving instance Ord  (p (Fix p a) a) => Ord  (Fix p a)
    deriving instance Show (p (Fix p a) a) => Show (Fix p a)
    deriving instance Read (p (Fix p a) a) => Read (Fix p a)

    #if LIFTED_FUNCTOR_CLASSES
    instance Eq2 p => Eq1 (Fix p) where
      liftEq :: (a -> b -> Bool) -> Fix p a -> Fix p b -> Bool
    liftEq f :: a -> b -> Bool
    f (In x :: p (Fix p a) a
    x) (In y :: p (Fix p b) b
    y) = (Fix p a -> Fix p b -> Bool)
    -> (a -> b -> Bool) -> p (Fix p a) a -> p (Fix p b) b -> Bool
    forall (f :: * -> * -> *) a b c d.
    Eq2 f =>
    (a -> b -> Bool) -> (c -> d -> Bool) -> f a c -> f b d -> Bool
    liftEq2 ((a -> b -> Bool) -> Fix p a -> Fix p b -> Bool
    forall (f :: * -> *) a b.
    Eq1 f =>
    (a -> b -> Bool) -> f a -> f b -> Bool
    liftEq a -> b -> Bool
    f) a -> b -> Bool
    f p (Fix p a) a
    x p (Fix p b) b
    y

    instance Ord2 p => Ord1 (Fix p) where
      liftCompare :: (a -> b -> Ordering) -> Fix p a -> Fix p b -> Ordering
    liftCompare f :: a -> b -> Ordering
    f (In x :: p (Fix p a) a
    x) (In y :: p (Fix p b) b
    y) = (Fix p a -> Fix p b -> Ordering)
    -> (a -> b -> Ordering)
    -> p (Fix p a) a
    -> p (Fix p b) b
    -> Ordering
    forall (f :: * -> * -> *) a b c d.
    Ord2 f =>
    (a -> b -> Ordering)
    -> (c -> d -> Ordering) -> f a c -> f b d -> Ordering
    liftCompare2 ((a -> b -> Ordering) -> Fix p a -> Fix p b -> Ordering
    forall (f :: * -> *) a b.
    Ord1 f =>
    (a -> b -> Ordering) -> f a -> f b -> Ordering
    liftCompare a -> b -> Ordering
    f) a -> b -> Ordering
    f p (Fix p a) a
    x p (Fix p b) b
    y

    instance Read2 p => Read1 (Fix p) where
      liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Fix p a)
    liftReadsPrec rp1 :: Int -> ReadS a
    rp1 rl1 :: ReadS [a]
    rl1 p :: Int
    p = Bool -> ReadS (Fix p a) -> ReadS (Fix p a)
    forall a. Bool -> ReadS a -> ReadS a
    readParen (Int
    p Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > 10) (ReadS (Fix p a) -> ReadS (Fix p a))
    -> ReadS (Fix p a) -> ReadS (Fix p a)
    forall a b. (a -> b) -> a -> b
    $ \s0 :: String
    s0 -> do
        ("In",  s1 :: String
    s1) <- ReadS String
    lex String
    s0
        ("{",   s2 :: String
    s2) <- ReadS String
    lex String
    s1
        ("out", s3 :: String
    s3) <- ReadS String
    lex String
    s2
        (x :: p (Fix p a) a
    x,     s4 :: String
    s4) <- (Int -> ReadS (Fix p a))
    -> ReadS [Fix p a]
    -> (Int -> ReadS a)
    -> ReadS [a]
    -> Int
    -> ReadS (p (Fix p a) a)
    forall (f :: * -> * -> *) a b.
    Read2 f =>
    (Int -> ReadS a)
    -> ReadS [a]
    -> (Int -> ReadS b)
    -> ReadS [b]
    -> Int
    -> ReadS (f a b)
    liftReadsPrec2 ((Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Fix p a)
    forall (f :: * -> *) a.
    Read1 f =>
    (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)
    liftReadsPrec Int -> ReadS a
    rp1 ReadS [a]
    rl1) ((Int -> ReadS a) -> ReadS [a] -> ReadS [Fix p a]
    forall (f :: * -> *) a.
    Read1 f =>
    (Int -> ReadS a) -> ReadS [a] -> ReadS [f a]
    liftReadList Int -> ReadS a
    rp1 ReadS [a]
    rl1)
                                      Int -> ReadS a
    rp1 ReadS [a]
    rl1 0 String
    s3
        ("}",   s5 :: String
    s5) <- ReadS String
    lex String
    s4
        (Fix p a, String) -> [(Fix p a, String)]
    forall (m :: * -> *) a. Monad m => a -> m a
    return (p (Fix p a) a -> Fix p a
    forall k (p :: * -> k -> *) (a :: k). p (Fix p a) a -> Fix p a
    In p (Fix p a) a
    x, String
    s5)

    instance Show2 p => Show1 (Fix p) where
      liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Fix p a -> ShowS
    liftShowsPrec sp1 :: Int -> a -> ShowS
    sp1 sl1 :: [a] -> ShowS
    sl1 p :: Int
    p (In x :: p (Fix p a) a
    x) = Bool -> ShowS -> ShowS
    showParen (Int
    p Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > 10) (ShowS -> ShowS) -> ShowS -> ShowS
    forall a b. (a -> b) -> a -> b
    $
          String -> ShowS
    showString "In {out = "
        ShowS -> ShowS -> ShowS
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (Int -> Fix p a -> ShowS)
    -> ([Fix p a] -> ShowS)
    -> (Int -> a -> ShowS)
    -> ([a] -> ShowS)
    -> Int
    -> p (Fix p a) a
    -> ShowS
    forall (f :: * -> * -> *) a b.
    Show2 f =>
    (Int -> a -> ShowS)
    -> ([a] -> ShowS)
    -> (Int -> b -> ShowS)
    -> ([b] -> ShowS)
    -> Int
    -> f a b
    -> ShowS
    liftShowsPrec2 ((Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Fix p a -> ShowS
    forall (f :: * -> *) a.
    Show1 f =>
    (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS
    liftShowsPrec Int -> a -> ShowS
    sp1 [a] -> ShowS
    sl1) ((Int -> a -> ShowS) -> ([a] -> ShowS) -> [Fix p a] -> ShowS
    forall (f :: * -> *) a.
    Show1 f =>
    (Int -> a -> ShowS) -> ([a] -> ShowS) -> [f a] -> ShowS
    liftShowList Int -> a -> ShowS
    sp1 [a] -> ShowS
    sl1)
                         Int -> a -> ShowS
    sp1 [a] -> ShowS
    sl1 0 p (Fix p a) a
    x
        ShowS -> ShowS -> ShowS
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Char -> ShowS
    showChar '}'
    #endif

    instance Bifunctor p => Functor (Fix p) where
      fmap :: (a -> b) -> Fix p a -> Fix p b
    fmap f :: a -> b
    f (In p :: p (Fix p a) a
    p) = p (Fix p b) b -> Fix p b
    forall k (p :: * -> k -> *) (a :: k). p (Fix p a) a -> Fix p a
    In ((Fix p a -> Fix p b) -> (a -> b) -> p (Fix p a) a -> p (Fix p b) b
    forall (p :: * -> * -> *) a b c d.
    Bifunctor p =>
    (a -> b) -> (c -> d) -> p a c -> p b d
    bimap ((a -> b) -> Fix p a -> Fix p b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap a -> b
    f) a -> b
    f p (Fix p a) a
    p)
      {-# INLINE fmap #-}

    instance Biapplicative p => Applicative (Fix p) where
      pure :: a -> Fix p a
    pure a :: a
    a = p (Fix p a) a -> Fix p a
    forall k (p :: * -> k -> *) (a :: k). p (Fix p a) a -> Fix p a
    In (Fix p a -> a -> p (Fix p a) a
    forall (p :: * -> * -> *) a b. Biapplicative p => a -> b -> p a b
    bipure (a -> Fix p a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure a
    a) a
    a)
      {-# INLINE pure #-}
      In p :: p (Fix p (a -> b)) (a -> b)
    p <*> :: Fix p (a -> b) -> Fix p a -> Fix p b
    <*> In q :: p (Fix p a) a
    q = p (Fix p b) b -> Fix p b
    forall k (p :: * -> k -> *) (a :: k). p (Fix p a) a -> Fix p a
    In ((Fix p (a -> b) -> Fix p a -> Fix p b)
    -> ((a -> b) -> a -> b)
    -> p (Fix p (a -> b)) (a -> b)
    -> p (Fix p a) a
    -> p (Fix p b) b
    forall (p :: * -> * -> *) a b c d e f.
    Biapplicative p =>
    (a -> b -> c) -> (d -> e -> f) -> p a d -> p b e -> p c f
    biliftA2 Fix p (a -> b) -> Fix p a -> Fix p b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    (<*>) (a -> b) -> a -> b
    forall a b. (a -> b) -> a -> b
    ($) p (Fix p (a -> b)) (a -> b)
    p p (Fix p a) a
    q)
      {-# INLINE (<*>) #-}

    instance Bifoldable p => Foldable (Fix p) where
      foldMap :: (a -> m) -> Fix p a -> m
    foldMap f :: a -> m
    f (In p :: p (Fix p a) a
    p) = (Fix p a -> m) -> (a -> m) -> p (Fix p a) a -> m
    forall (p :: * -> * -> *) m a b.
    (Bifoldable p, Monoid m) =>
    (a -> m) -> (b -> m) -> p a b -> m
    bifoldMap ((a -> m) -> Fix p a -> m
    forall (t :: * -> *) m a.
    (Foldable t, Monoid m) =>
    (a -> m) -> t a -> m
    foldMap a -> m
    f) a -> m
    f p (Fix p a) a
    p
      {-# INLINE foldMap #-}

    instance Bitraversable p => Traversable (Fix p) where
      traverse :: (a -> f b) -> Fix p a -> f (Fix p b)
    traverse f :: a -> f b
    f (In p :: p (Fix p a) a
    p) = p (Fix p b) b -> Fix p b
    forall k (p :: * -> k -> *) (a :: k). p (Fix p a) a -> Fix p a
    In (p (Fix p b) b -> Fix p b) -> f (p (Fix p b) b) -> f (Fix p b)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> (Fix p a -> f (Fix p b))
    -> (a -> f b) -> p (Fix p a) a -> f (p (Fix p b) b)
    forall (t :: * -> * -> *) (f :: * -> *) a c b d.
    (Bitraversable t, Applicative f) =>
    (a -> f c) -> (b -> f d) -> t a b -> f (t c d)
    bitraverse ((a -> f b) -> Fix p a -> f (Fix p b)
    forall (t :: * -> *) (f :: * -> *) a b.
    (Traversable t, Applicative f) =>
    (a -> f b) -> t a -> f (t b)
    traverse a -> f b
    f) a -> f b
    f p (Fix p a) a
    p
      {-# INLINE traverse #-}