    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE NoImplicitPrelude #-}
    {-# LANGUAGE DeriveFunctor #-}
    {-# LANGUAGE DeriveGeneric #-}
    {-# LANGUAGE StandaloneDeriving #-}
    {-# OPTIONS_GHC -Wno-inline-rule-shadowing #-}
        -- The RULES for the methods of class Arrow may never fire
        -- e.g. compose/arr;  see #10528

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  GHC.Internal.Control.Arrow
    -- Copyright   :  (c) Ross Paterson 2002
    -- License     :  BSD-style (see the LICENSE file in the distribution)
    --
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  provisional
    -- Portability :  portable
    --
    -- Basic arrow definitions, based on
    --
    --  * /Generalising Monads to Arrows/, by John Hughes,
    --    /Science of Computer Programming/ 37, pp67-111, May 2000.
    --
    -- plus a couple of definitions ('returnA' and 'loop') from
    --
    --  * /A New Notation for Arrows/, by Ross Paterson, in /ICFP 2001/,
    --    Firenze, Italy, pp229-240.
    --
    -- These papers and more information on arrows can be found at
    -- <http://www.haskell.org/arrows/>.

    module GHC.Internal.Control.Arrow (
        -- * Arrows
        Arrow(..), Kleisli(..),
        -- ** Derived combinators
        returnA,
        (^>>), (>>^),
        (>>>), (<<<), -- reexported
        -- ** Right-to-left variants
        (<<^), (^<<),
        -- * Monoid operations
        ArrowZero(..), ArrowPlus(..),
        -- * Conditionals
        ArrowChoice(..),
        -- * Arrow application
        ArrowApply(..), ArrowMonad(..), leftApp,
        -- * Feedback
        ArrowLoop(..)
        ) where

    import GHC.Internal.Data.Tuple ( fst, snd, uncurry )
    import GHC.Internal.Data.Either
    import GHC.Internal.Control.Monad.Fix
    import GHC.Internal.Control.Category
    import GHC.Internal.Base hiding ( (.), id )
    import GHC.Internal.Generics (Generic, Generic1)

    infixr 5 <+>
    infixr 3 ***
    infixr 3 &&&
    infixr 2 +++
    infixr 2 |||
    infixr 1 ^>>, >>^
    infixr 1 ^<<, <<^

    -- | The basic arrow class.
    --
    -- Instances should satisfy the following laws:
    --
    --  * @'arr' id = 'id'@
    --
    --  * @'arr' (f >>> g) = 'arr' f >>> 'arr' g@
    --
    --  * @'first' ('arr' f) = 'arr' ('first' f)@
    --
    --  * @'first' (f >>> g) = 'first' f >>> 'first' g@
    --
    --  * @'first' f >>> 'arr' 'fst' = 'arr' 'fst' >>> f@
    --
    --  * @'first' f >>> 'arr' ('id' *** g) = 'arr' ('id' *** g) >>> 'first' f@
    --
    --  * @'first' ('first' f) >>> 'arr' assoc = 'arr' assoc >>> 'first' f@
    --
    -- where
    --
    -- > assoc ((a,b),c) = (a,(b,c))
    --
    -- The other combinators have sensible default definitions,
    -- which may be overridden for efficiency.

    class Category a => Arrow a where
        {-# MINIMAL arr, (first | (***)) #-}

        -- | Lift a function to an arrow.
        --
        -- >   b ╭───╮ c
        -- > >───┤ f ├───>
        -- >     ╰───╯
        arr :: (b -> c) -> a b c

        -- | Send the first component of the input through the argument
        --   arrow, and copy the rest unchanged to the output.
        --
        --   The default definition may be overridden with a more efficient
        --   version if desired.
        --
        -- >   b ╭─────╮ c
        -- > >───┼─ f ─┼───>
        -- > >───┼─────┼───>
        -- >   d ╰─────╯ d
        first :: a b c -> a (b,d) (c,d)
        first = (a b c -> a d d -> a (b, d) (c, d)
    forall b c b' c'. a b c -> a b' c' -> a (b, b') (c, c')
    forall (a :: * -> * -> *) b c b' c'.
    Arrow a =>
    a b c -> a b' c' -> a (b, b') (c, c')
    *** a d d
    forall a. a a a
    forall {k} (cat :: k -> k -> *) (a :: k). Category cat => cat a a
    id)

        -- | Send the second component of the input through the argument
        --   arrow, and copy the rest unchanged to the output.
        --
        --   The default definition may be overridden with a more efficient
        --   version if desired.
        --
        -- >   d ╭─────╮ d
        -- > >───┼─────┼───>
        -- > >───┼─ f ─┼───>
        -- >   b ╰─────╯ c
        second :: a b c -> a (d,b) (d,c)
        second = (a d d
    forall a. a a a
    forall {k} (cat :: k -> k -> *) (a :: k). Category cat => cat a a
    id a d d -> a b c -> a (d, b) (d, c)
    forall b c b' c'. a b c -> a b' c' -> a (b, b') (c, c')
    forall (a :: * -> * -> *) b c b' c'.
    Arrow a =>
    a b c -> a b' c' -> a (b, b') (c, c')
    ***)

        -- | Split the input between the two argument arrows and combine
        --   their output.  Note that this is in general not a functor.
        --
        --   The default definition may be overridden with a more efficient
        --   version if desired.
        --
        -- >   b ╭─────╮ c
        -- > >───┼─ f ─┼───>
        -- > >───┼─ g ─┼───>
        -- >   b'╰─────╯ c'
        (***) :: a b c -> a b' c' -> a (b,b') (c,c')
        a b c
    f *** a b' c'
    g = a b c -> a (b, b') (c, b')
    forall b c d. a b c -> a (b, d) (c, d)
    forall (a :: * -> * -> *) b c d.
    Arrow a =>
    a b c -> a (b, d) (c, d)
    first a b c
    f a (b, b') (c, b') -> a (c, b') (c, c') -> a (b, b') (c, c')
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> ((c, b') -> (b', c)) -> a (c, b') (b', c)
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr (c, b') -> (b', c)
    forall {b} {a}. (b, a) -> (a, b)
    swap a (c, b') (b', c) -> a (b', c) (c, c') -> a (c, b') (c, c')
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> a b' c' -> a (b', c) (c', c)
    forall b c d. a b c -> a (b, d) (c, d)
    forall (a :: * -> * -> *) b c d.
    Arrow a =>
    a b c -> a (b, d) (c, d)
    first a b' c'
    g a (b', c) (c', c) -> a (c', c) (c, c') -> a (b', c) (c, c')
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> ((c', c) -> (c, c')) -> a (c', c) (c, c')
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr (c', c) -> (c, c')
    forall {b} {a}. (b, a) -> (a, b)
    swap
          where swap :: (b, a) -> (a, b)
    swap ~(b
    x,a
    y) = (a
    y,b
    x)

        -- | Fanout: send the input to both argument arrows and combine
        --   their output.
        --
        --   The default definition may be overridden with a more efficient
        --   version if desired.
        --
        -- >     ╭───────╮ c
        -- >   b │ ┌─ f ─┼───>
        -- > >───┼─┤     │
        -- >     │ └─ g ─┼───>
        -- >     ╰───────╯ c'
        (&&&) :: a b c -> a b c' -> a b (c,c')
        a b c
    f &&& a b c'
    g = (b -> (b, b)) -> a b (b, b)
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr (\b
    b -> (b
    b,b
    b)) a b (b, b) -> a (b, b) (c, c') -> a b (c, c')
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> a b c
    f a b c -> a b c' -> a (b, b) (c, c')
    forall b c b' c'. a b c -> a b' c' -> a (b, b') (c, c')
    forall (a :: * -> * -> *) b c b' c'.
    Arrow a =>
    a b c -> a b' c' -> a (b, b') (c, c')
    *** a b c'
    g

    {-# RULES
    "compose/arr"   forall f g .
                    (arr f) . (arr g) = arr (f . g)
    "first/arr"     forall f .
                    first (arr f) = arr (first f)
    "second/arr"    forall f .
                    second (arr f) = arr (second f)
    "product/arr"   forall f g .
                    arr f *** arr g = arr (f *** g)
    "fanout/arr"    forall f g .
                    arr f &&& arr g = arr (f &&& g)
    "compose/first" forall f g .
                    (first f) . (first g) = first (f . g)
    "compose/second" forall f g .
                    (second f) . (second g) = second (f . g)
     #-}

    -- Ordinary functions are arrows.

    -- | @since base-2.01
    instance Arrow (->) where
        arr :: forall b c. (b -> c) -> b -> c
    arr b -> c
    f = b -> c
    f
    --  (f *** g) ~(x,y) = (f x, g y)
    --  sorry, although the above defn is fully H'98, nhc98 can't parse it.
        *** :: forall b c b' c'. (b -> c) -> (b' -> c') -> (b, b') -> (c, c')
    (***) b -> c
    f b' -> c'
    g ~(b
    x,b'
    y) = (b -> c
    f b
    x, b' -> c'
    g b'
    y)

    -- | Kleisli arrows of a monad.
    newtype Kleisli m a b = Kleisli { forall (m :: * -> *) a b. Kleisli m a b -> a -> m b
    runKleisli :: a -> m b }

    -- | @since base-4.14.0.0
    deriving instance Generic (Kleisli m a b)

    -- | @since base-4.14.0.0
    deriving instance Generic1 (Kleisli m a)

    -- | @since base-4.14.0.0
    deriving instance Functor m => Functor (Kleisli m a)

    -- | @since base-4.14.0.0
    instance Applicative m => Applicative (Kleisli m a) where
      pure :: forall a. a -> Kleisli m a a
    pure = (a -> m a) -> Kleisli m a a
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli ((a -> m a) -> Kleisli m a a)
    -> (a -> a -> m a) -> a -> Kleisli m a a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
    Category cat =>
    cat b c -> cat a b -> cat a c
    . m a -> a -> m a
    forall a b. a -> b -> a
    const (m a -> a -> m a) -> (a -> m a) -> a -> a -> m a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
    Category cat =>
    cat b c -> cat a b -> cat a c
    . a -> m a
    forall a. a -> m a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure
      {-# INLINE pure #-}
      Kleisli a -> m (a -> b)
    f <*> :: forall a b. Kleisli m a (a -> b) -> Kleisli m a a -> Kleisli m a b
    <*> Kleisli a -> m a
    g = (a -> m b) -> Kleisli m a b
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli ((a -> m b) -> Kleisli m a b) -> (a -> m b) -> Kleisli m a b
    forall a b. (a -> b) -> a -> b
    $ \a
    x -> a -> m (a -> b)
    f a
    x m (a -> b) -> m a -> m b
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> a -> m a
    g a
    x
      {-# INLINE (<*>) #-}
      Kleisli a -> m a
    f *> :: forall a b. Kleisli m a a -> Kleisli m a b -> Kleisli m a b
    *> Kleisli a -> m b
    g = (a -> m b) -> Kleisli m a b
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli ((a -> m b) -> Kleisli m a b) -> (a -> m b) -> Kleisli m a b
    forall a b. (a -> b) -> a -> b
    $ \a
    x -> a -> m a
    f a
    x m a -> m b -> m b
    forall a b. m a -> m b -> m b
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
    *> a -> m b
    g a
    x
      {-# INLINE (*>) #-}
      Kleisli a -> m a
    f <* :: forall a b. Kleisli m a a -> Kleisli m a b -> Kleisli m a a
    <* Kleisli a -> m b
    g = (a -> m a) -> Kleisli m a a
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli ((a -> m a) -> Kleisli m a a) -> (a -> m a) -> Kleisli m a a
    forall a b. (a -> b) -> a -> b
    $ \a
    x -> a -> m a
    f a
    x m a -> m b -> m a
    forall a b. m a -> m b -> m a
    forall (f :: * -> *) a b. Applicative f => f a -> f b -> f a
    <* a -> m b
    g a
    x
      {-# INLINE (<*) #-}

    -- | @since base-4.14.0.0
    instance Alternative m => Alternative (Kleisli m a) where
      empty :: forall a. Kleisli m a a
    empty = (a -> m a) -> Kleisli m a a
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli ((a -> m a) -> Kleisli m a a) -> (a -> m a) -> Kleisli m a a
    forall a b. (a -> b) -> a -> b
    $ m a -> a -> m a
    forall a b. a -> b -> a
    const m a
    forall a. m a
    forall (f :: * -> *) a. Alternative f => f a
    empty
      {-# INLINE empty #-}
      Kleisli a -> m a
    f <|> :: forall a. Kleisli m a a -> Kleisli m a a -> Kleisli m a a
    <|> Kleisli a -> m a
    g = (a -> m a) -> Kleisli m a a
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli ((a -> m a) -> Kleisli m a a) -> (a -> m a) -> Kleisli m a a
    forall a b. (a -> b) -> a -> b
    $ \a
    x -> a -> m a
    f a
    x m a -> m a -> m a
    forall a. m a -> m a -> m a
    forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
    <|> a -> m a
    g a
    x
      {-# INLINE (<|>) #-}

    -- | @since base-4.14.0.0
    instance Monad m => Monad (Kleisli m a) where
      Kleisli a -> m a
    f >>= :: forall a b. Kleisli m a a -> (a -> Kleisli m a b) -> Kleisli m a b
    >>= a -> Kleisli m a b
    k = (a -> m b) -> Kleisli m a b
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli ((a -> m b) -> Kleisli m a b) -> (a -> m b) -> Kleisli m a b
    forall a b. (a -> b) -> a -> b
    $ \a
    x -> a -> m a
    f a
    x m a -> (a -> m b) -> m b
    forall a b. m a -> (a -> m b) -> m b
    forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
    >>= \a
    a -> Kleisli m a b -> a -> m b
    forall (m :: * -> *) a b. Kleisli m a b -> a -> m b
    runKleisli (a -> Kleisli m a b
    k a
    a) a
    x
      {-# INLINE (>>=) #-}

    -- | @since base-4.14.0.0
    instance MonadPlus m => MonadPlus (Kleisli m a) where
      mzero :: forall a. Kleisli m a a
    mzero = (a -> m a) -> Kleisli m a a
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli ((a -> m a) -> Kleisli m a a) -> (a -> m a) -> Kleisli m a a
    forall a b. (a -> b) -> a -> b
    $ m a -> a -> m a
    forall a b. a -> b -> a
    const m a
    forall a. m a
    forall (m :: * -> *) a. MonadPlus m => m a
    mzero
      {-# INLINE mzero #-}
      Kleisli a -> m a
    f mplus :: forall a. Kleisli m a a -> Kleisli m a a -> Kleisli m a a
    `mplus` Kleisli a -> m a
    g = (a -> m a) -> Kleisli m a a
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli ((a -> m a) -> Kleisli m a a) -> (a -> m a) -> Kleisli m a a
    forall a b. (a -> b) -> a -> b
    $ \a
    x -> a -> m a
    f a
    x m a -> m a -> m a
    forall a. m a -> m a -> m a
    forall (m :: * -> *) a. MonadPlus m => m a -> m a -> m a
    `mplus` a -> m a
    g a
    x
      {-# INLINE mplus #-}

    -- | @since base-3.0
    instance Monad m => Category (Kleisli m) where
        id :: forall a. Kleisli m a a
    id = (a -> m a) -> Kleisli m a a
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli a -> m a
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return
        (Kleisli b -> m c
    f) . :: forall b c a. Kleisli m b c -> Kleisli m a b -> Kleisli m a c
    . (Kleisli a -> m b
    g) = (a -> m c) -> Kleisli m a c
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli (\a
    b -> a -> m b
    g a
    b m b -> (b -> m c) -> m c
    forall a b. m a -> (a -> m b) -> m b
    forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
    >>= b -> m c
    f)

    -- | @since base-2.01
    instance Monad m => Arrow (Kleisli m) where
        arr :: forall b c. (b -> c) -> Kleisli m b c
    arr b -> c
    f = (b -> m c) -> Kleisli m b c
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli (c -> m c
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return (c -> m c) -> (b -> c) -> b -> m c
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
    Category cat =>
    cat b c -> cat a b -> cat a c
    . b -> c
    f)
        first :: forall b c d. Kleisli m b c -> Kleisli m (b, d) (c, d)
    first (Kleisli b -> m c
    f) = ((b, d) -> m (c, d)) -> Kleisli m (b, d) (c, d)
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli (\ ~(b
    b,d
    d) -> b -> m c
    f b
    b m c -> (c -> m (c, d)) -> m (c, d)
    forall a b. m a -> (a -> m b) -> m b
    forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
    >>= \c
    c -> (c, d) -> m (c, d)
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return (c
    c,d
    d))
        second :: forall b c d. Kleisli m b c -> Kleisli m (d, b) (d, c)
    second (Kleisli b -> m c
    f) = ((d, b) -> m (d, c)) -> Kleisli m (d, b) (d, c)
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli (\ ~(d
    d,b
    b) -> b -> m c
    f b
    b m c -> (c -> m (d, c)) -> m (d, c)
    forall a b. m a -> (a -> m b) -> m b
    forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
    >>= \c
    c -> (d, c) -> m (d, c)
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return (d
    d,c
    c))

    -- | The identity arrow, which plays the role of 'return' in arrow notation.
    --
    -- >   b
    -- > >───>
    returnA :: Arrow a => a b b
    returnA :: forall (a :: * -> * -> *) b. Arrow a => a b b
    returnA = a b b
    forall a. a a a
    forall {k} (cat :: k -> k -> *) (a :: k). Category cat => cat a a
    id

    -- | Precomposition with a pure function.
    (^>>) :: Arrow a => (b -> c) -> a c d -> a b d
    b -> c
    f ^>> :: forall (a :: * -> * -> *) b c d.
    Arrow a =>
    (b -> c) -> a c d -> a b d
    ^>> a c d
    a = (b -> c) -> a b c
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr b -> c
    f a b c -> a c d -> a b d
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> a c d
    a

    -- | Postcomposition with a pure function.
    (>>^) :: Arrow a => a b c -> (c -> d) -> a b d
    a b c
    a >>^ :: forall (a :: * -> * -> *) b c d.
    Arrow a =>
    a b c -> (c -> d) -> a b d
    >>^ c -> d
    f = a b c
    a a b c -> a c d -> a b d
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> (c -> d) -> a c d
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr c -> d
    f

    -- | Precomposition with a pure function (right-to-left variant).
    (<<^) :: Arrow a => a c d -> (b -> c) -> a b d
    a c d
    a <<^ :: forall (a :: * -> * -> *) c d b.
    Arrow a =>
    a c d -> (b -> c) -> a b d
    <<^ b -> c
    f = a c d
    a a c d -> a b c -> a b d
    forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
    Category cat =>
    cat b c -> cat a b -> cat a c
    <<< (b -> c) -> a b c
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr b -> c
    f

    -- | Postcomposition with a pure function (right-to-left variant).
    (^<<) :: Arrow a => (c -> d) -> a b c -> a b d
    c -> d
    f ^<< :: forall (a :: * -> * -> *) c d b.
    Arrow a =>
    (c -> d) -> a b c -> a b d
    ^<< a b c
    a = (c -> d) -> a c d
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr c -> d
    f a c d -> a b c -> a b d
    forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
    Category cat =>
    cat b c -> cat a b -> cat a c
    <<< a b c
    a

    class Arrow a => ArrowZero a where
        zeroArrow :: a b c

    -- | @since base-2.01
    instance MonadPlus m => ArrowZero (Kleisli m) where
        zeroArrow :: forall b c. Kleisli m b c
    zeroArrow = (b -> m c) -> Kleisli m b c
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli (\b
    _ -> m c
    forall a. m a
    forall (m :: * -> *) a. MonadPlus m => m a
    mzero)

    -- | A monoid on arrows.
    class ArrowZero a => ArrowPlus a where
        -- | An associative operation with identity 'zeroArrow'.
        (<+>) :: a b c -> a b c -> a b c

    -- | @since base-2.01
    instance MonadPlus m => ArrowPlus (Kleisli m) where
        Kleisli b -> m c
    f <+> :: forall b c. Kleisli m b c -> Kleisli m b c -> Kleisli m b c
    <+> Kleisli b -> m c
    g = (b -> m c) -> Kleisli m b c
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli (\b
    x -> b -> m c
    f b
    x m c -> m c -> m c
    forall a. m a -> m a -> m a
    forall (m :: * -> *) a. MonadPlus m => m a -> m a -> m a
    `mplus` b -> m c
    g b
    x)

    -- | Choice, for arrows that support it.  This class underlies the
    -- @if@ and @case@ constructs in arrow notation.
    --
    -- Instances should satisfy the following laws:
    --
    --  * @'left' ('arr' f) = 'arr' ('left' f)@
    --
    --  * @'left' (f >>> g) = 'left' f >>> 'left' g@
    --
    --  * @f >>> 'arr' 'Left' = 'arr' 'Left' >>> 'left' f@
    --
    --  * @'left' f >>> 'arr' ('id' +++ g) = 'arr' ('id' +++ g) >>> 'left' f@
    --
    --  * @'left' ('left' f) >>> 'arr' assocsum = 'arr' assocsum >>> 'left' f@
    --
    -- where
    --
    -- > assocsum (Left (Left x)) = Left x
    -- > assocsum (Left (Right y)) = Right (Left y)
    -- > assocsum (Right z) = Right (Right z)
    --
    -- The other combinators have sensible default definitions, which may
    -- be overridden for efficiency.

    class Arrow a => ArrowChoice a where
        {-# MINIMAL (left | (+++)) #-}

        -- | Feed marked inputs through the argument arrow, passing the
        --   rest through unchanged to the output.
        left :: a b c -> a (Either b d) (Either c d)
        left = (a b c -> a d d -> a (Either b d) (Either c d)
    forall b c b' c'. a b c -> a b' c' -> a (Either b b') (Either c c')
    forall (a :: * -> * -> *) b c b' c'.
    ArrowChoice a =>
    a b c -> a b' c' -> a (Either b b') (Either c c')
    +++ a d d
    forall a. a a a
    forall {k} (cat :: k -> k -> *) (a :: k). Category cat => cat a a
    id)

        -- | A mirror image of 'left'.
        --
        --   The default definition may be overridden with a more efficient
        --   version if desired.
        right :: a b c -> a (Either d b) (Either d c)
        right = (a d d
    forall a. a a a
    forall {k} (cat :: k -> k -> *) (a :: k). Category cat => cat a a
    id a d d -> a b c -> a (Either d b) (Either d c)
    forall b c b' c'. a b c -> a b' c' -> a (Either b b') (Either c c')
    forall (a :: * -> * -> *) b c b' c'.
    ArrowChoice a =>
    a b c -> a b' c' -> a (Either b b') (Either c c')
    +++)

        -- | Split the input between the two argument arrows, retagging
        --   and merging their outputs.
        --   Note that this is in general not a functor.
        --
        --   The default definition may be overridden with a more efficient
        --   version if desired.
        (+++) :: a b c -> a b' c' -> a (Either b b') (Either c c')
        a b c
    f +++ a b' c'
    g = a b c -> a (Either b b') (Either c b')
    forall b c d. a b c -> a (Either b d) (Either c d)
    forall (a :: * -> * -> *) b c d.
    ArrowChoice a =>
    a b c -> a (Either b d) (Either c d)
    left a b c
    f a (Either b b') (Either c b')
    -> a (Either c b') (Either c c') -> a (Either b b') (Either c c')
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> (Either c b' -> Either b' c) -> a (Either c b') (Either b' c)
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr Either c b' -> Either b' c
    forall x y. Either x y -> Either y x
    mirror a (Either c b') (Either b' c)
    -> a (Either b' c) (Either c c') -> a (Either c b') (Either c c')
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> a b' c' -> a (Either b' c) (Either c' c)
    forall b c d. a b c -> a (Either b d) (Either c d)
    forall (a :: * -> * -> *) b c d.
    ArrowChoice a =>
    a b c -> a (Either b d) (Either c d)
    left a b' c'
    g a (Either b' c) (Either c' c)
    -> a (Either c' c) (Either c c') -> a (Either b' c) (Either c c')
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> (Either c' c -> Either c c') -> a (Either c' c) (Either c c')
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr Either c' c -> Either c c'
    forall x y. Either x y -> Either y x
    mirror
          where
            mirror :: Either x y -> Either y x
            mirror :: forall x y. Either x y -> Either y x
    mirror (Left x
    x) = x -> Either y x
    forall a b. b -> Either a b
    Right x
    x
            mirror (Right y
    y) = y -> Either y x
    forall a b. a -> Either a b
    Left y
    y

        -- | Fanin: Split the input between the two argument arrows and
        --   merge their outputs.
        --
        --   The default definition may be overridden with a more efficient
        --   version if desired.
        (|||) :: a b d -> a c d -> a (Either b c) d
        a b d
    f ||| a c d
    g = a b d
    f a b d -> a c d -> a (Either b c) (Either d d)
    forall b c b' c'. a b c -> a b' c' -> a (Either b b') (Either c c')
    forall (a :: * -> * -> *) b c b' c'.
    ArrowChoice a =>
    a b c -> a b' c' -> a (Either b b') (Either c c')
    +++ a c d
    g a (Either b c) (Either d d) -> a (Either d d) d -> a (Either b c) d
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> (Either d d -> d) -> a (Either d d) d
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr Either d d -> d
    forall {a}. Either a a -> a
    untag
          where
            untag :: Either a a -> a
    untag (Left a
    x) = a
    x
            untag (Right a
    y) = a
    y

    {-# RULES
    "left/arr"      forall f .
                    left (arr f) = arr (left f)
    "right/arr"     forall f .
                    right (arr f) = arr (right f)
    "sum/arr"       forall f g .
                    arr f +++ arr g = arr (f +++ g)
    "fanin/arr"     forall f g .
                    arr f ||| arr g = arr (f ||| g)
    "compose/left"  forall f g .
                    left f . left g = left (f . g)
    "compose/right" forall f g .
                    right f . right g = right (f . g)
     #-}

    -- | @since base-2.01
    instance ArrowChoice (->) where
        left :: forall b c d. (b -> c) -> Either b d -> Either c d
    left b -> c
    f = b -> c
    f (b -> c) -> (d -> d) -> Either b d -> Either c d
    forall b c b' c'.
    (b -> c) -> (b' -> c') -> Either b b' -> Either c c'
    forall (a :: * -> * -> *) b c b' c'.
    ArrowChoice a =>
    a b c -> a b' c' -> a (Either b b') (Either c c')
    +++ d -> d
    forall a. a -> a
    forall {k} (cat :: k -> k -> *) (a :: k). Category cat => cat a a
    id
        right :: forall b c d. (b -> c) -> Either d b -> Either d c
    right b -> c
    f = d -> d
    forall a. a -> a
    forall {k} (cat :: k -> k -> *) (a :: k). Category cat => cat a a
    id (d -> d) -> (b -> c) -> Either d b -> Either d c
    forall b c b' c'.
    (b -> c) -> (b' -> c') -> Either b b' -> Either c c'
    forall (a :: * -> * -> *) b c b' c'.
    ArrowChoice a =>
    a b c -> a b' c' -> a (Either b b') (Either c c')
    +++ b -> c
    f
        b -> c
    f +++ :: forall b c b' c'.
    (b -> c) -> (b' -> c') -> Either b b' -> Either c c'
    +++ b' -> c'
    g = (c -> Either c c'
    forall a b. a -> Either a b
    Left (c -> Either c c') -> (b -> c) -> b -> Either c c'
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
    Category cat =>
    cat b c -> cat a b -> cat a c
    . b -> c
    f) (b -> Either c c')
    -> (b' -> Either c c') -> Either b b' -> Either c c'
    forall b d c. (b -> d) -> (c -> d) -> Either b c -> d
    forall (a :: * -> * -> *) b d c.
    ArrowChoice a =>
    a b d -> a c d -> a (Either b c) d
    ||| (c' -> Either c c'
    forall a b. b -> Either a b
    Right (c' -> Either c c') -> (b' -> c') -> b' -> Either c c'
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
    Category cat =>
    cat b c -> cat a b -> cat a c
    . b' -> c'
    g)
        ||| :: forall b d c. (b -> d) -> (c -> d) -> Either b c -> d
    (|||) = (b -> d) -> (c -> d) -> Either b c -> d
    forall b d c. (b -> d) -> (c -> d) -> Either b c -> d
    either

    -- | @since base-2.01
    instance Monad m => ArrowChoice (Kleisli m) where
        left :: forall b c d. Kleisli m b c -> Kleisli m (Either b d) (Either c d)
    left Kleisli m b c
    f = Kleisli m b c
    f Kleisli m b c
    -> Kleisli m d d -> Kleisli m (Either b d) (Either c d)
    forall b c b' c'.
    Kleisli m b c
    -> Kleisli m b' c' -> Kleisli m (Either b b') (Either c c')
    forall (a :: * -> * -> *) b c b' c'.
    ArrowChoice a =>
    a b c -> a b' c' -> a (Either b b') (Either c c')
    +++ (d -> d) -> Kleisli m d d
    forall b c. (b -> c) -> Kleisli m b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr d -> d
    forall a. a -> a
    forall {k} (cat :: k -> k -> *) (a :: k). Category cat => cat a a
    id
        right :: forall b c d. Kleisli m b c -> Kleisli m (Either d b) (Either d c)
    right Kleisli m b c
    f = (d -> d) -> Kleisli m d d
    forall b c. (b -> c) -> Kleisli m b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr d -> d
    forall a. a -> a
    forall {k} (cat :: k -> k -> *) (a :: k). Category cat => cat a a
    id Kleisli m d d
    -> Kleisli m b c -> Kleisli m (Either d b) (Either d c)
    forall b c b' c'.
    Kleisli m b c
    -> Kleisli m b' c' -> Kleisli m (Either b b') (Either c c')
    forall (a :: * -> * -> *) b c b' c'.
    ArrowChoice a =>
    a b c -> a b' c' -> a (Either b b') (Either c c')
    +++ Kleisli m b c
    f
        Kleisli m b c
    f +++ :: forall b c b' c'.
    Kleisli m b c
    -> Kleisli m b' c' -> Kleisli m (Either b b') (Either c c')
    +++ Kleisli m b' c'
    g = (Kleisli m b c
    f Kleisli m b c
    -> Kleisli m c (Either c c') -> Kleisli m b (Either c c')
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> (c -> Either c c') -> Kleisli m c (Either c c')
    forall b c. (b -> c) -> Kleisli m b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr c -> Either c c'
    forall a b. a -> Either a b
    Left) Kleisli m b (Either c c')
    -> Kleisli m b' (Either c c')
    -> Kleisli m (Either b b') (Either c c')
    forall b d c.
    Kleisli m b d -> Kleisli m c d -> Kleisli m (Either b c) d
    forall (a :: * -> * -> *) b d c.
    ArrowChoice a =>
    a b d -> a c d -> a (Either b c) d
    ||| (Kleisli m b' c'
    g Kleisli m b' c'
    -> Kleisli m c' (Either c c') -> Kleisli m b' (Either c c')
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> (c' -> Either c c') -> Kleisli m c' (Either c c')
    forall b c. (b -> c) -> Kleisli m b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr c' -> Either c c'
    forall a b. b -> Either a b
    Right)
        Kleisli b -> m d
    f ||| :: forall b d c.
    Kleisli m b d -> Kleisli m c d -> Kleisli m (Either b c) d
    ||| Kleisli c -> m d
    g = (Either b c -> m d) -> Kleisli m (Either b c) d
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli ((b -> m d) -> (c -> m d) -> Either b c -> m d
    forall b d c. (b -> d) -> (c -> d) -> Either b c -> d
    either b -> m d
    f c -> m d
    g)

    -- | Some arrows allow application of arrow inputs to other inputs.
    -- Instances should satisfy the following laws:
    --
    --  * @'first' ('arr' (\\x -> 'arr' (\\y -> (x,y)))) >>> 'app' = 'id'@
    --
    --  * @'first' ('arr' (g >>>)) >>> 'app' = 'second' g >>> 'app'@
    --
    --  * @'first' ('arr' (>>> h)) >>> 'app' = 'app' >>> h@
    --
    -- Such arrows are equivalent to monads (see 'ArrowMonad').

    class Arrow a => ArrowApply a where
        app :: a (a b c, b) c

    -- | @since base-2.01
    instance ArrowApply (->) where
        app :: forall b c. (b -> c, b) -> c
    app (b -> c
    f,b
    x) = b -> c
    f b
    x

    -- | @since base-2.01
    instance Monad m => ArrowApply (Kleisli m) where
        app :: forall b c. Kleisli m (Kleisli m b c, b) c
    app = ((Kleisli m b c, b) -> m c) -> Kleisli m (Kleisli m b c, b) c
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli (\(Kleisli b -> m c
    f, b
    x) -> b -> m c
    f b
    x)

    -- | The 'ArrowApply' class is equivalent to 'Monad': any monad gives rise
    --   to a 'Kleisli' arrow, and any instance of 'ArrowApply' defines a monad.

    newtype ArrowMonad a b = ArrowMonad (a () b)

    -- | @since base-4.6.0.0
    instance Arrow a => Functor (ArrowMonad a) where
        fmap :: forall a b. (a -> b) -> ArrowMonad a a -> ArrowMonad a b
    fmap a -> b
    f (ArrowMonad a () a
    m) = a () b -> ArrowMonad a b
    forall (a :: * -> * -> *) b. a () b -> ArrowMonad a b
    ArrowMonad (a () b -> ArrowMonad a b) -> a () b -> ArrowMonad a b
    forall a b. (a -> b) -> a -> b
    $ a () a
    m a () a -> a a b -> a () b
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> (a -> b) -> a a b
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr a -> b
    f

    -- | @since base-4.6.0.0
    instance Arrow a => Applicative (ArrowMonad a) where
       pure :: forall a. a -> ArrowMonad a a
    pure a
    x = a () a -> ArrowMonad a a
    forall (a :: * -> * -> *) b. a () b -> ArrowMonad a b
    ArrowMonad ((() -> a) -> a () a
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr (a -> () -> a
    forall a b. a -> b -> a
    const a
    x))
       ArrowMonad a () (a -> b)
    f <*> :: forall a b.
    ArrowMonad a (a -> b) -> ArrowMonad a a -> ArrowMonad a b
    <*> ArrowMonad a () a
    x = a () b -> ArrowMonad a b
    forall (a :: * -> * -> *) b. a () b -> ArrowMonad a b
    ArrowMonad (a () (a -> b)
    f a () (a -> b) -> a () a -> a () (a -> b, a)
    forall b c c'. a b c -> a b c' -> a b (c, c')
    forall (a :: * -> * -> *) b c c'.
    Arrow a =>
    a b c -> a b c' -> a b (c, c')
    &&& a () a
    x a () (a -> b, a) -> a (a -> b, a) b -> a () b
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> ((a -> b, a) -> b) -> a (a -> b, a) b
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr (((a -> b) -> a -> b) -> (a -> b, a) -> b
    forall a b c. (a -> b -> c) -> (a, b) -> c
    uncurry (a -> b) -> a -> b
    forall a. a -> a
    forall {k} (cat :: k -> k -> *) (a :: k). Category cat => cat a a
    id))

    -- | @since base-2.01
    instance ArrowApply a => Monad (ArrowMonad a) where
        ArrowMonad a () a
    m >>= :: forall a b.
    ArrowMonad a a -> (a -> ArrowMonad a b) -> ArrowMonad a b
    >>= a -> ArrowMonad a b
    f = a () b -> ArrowMonad a b
    forall (a :: * -> * -> *) b. a () b -> ArrowMonad a b
    ArrowMonad (a () b -> ArrowMonad a b) -> a () b -> ArrowMonad a b
    forall a b. (a -> b) -> a -> b
    $
            a () a
    m a () a -> a a b -> a () b
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> (a -> (a () b, ())) -> a a (a () b, ())
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr (\a
    x -> let ArrowMonad a () b
    h = a -> ArrowMonad a b
    f a
    x in (a () b
    h, ())) a a (a () b, ()) -> a (a () b, ()) b -> a a b
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> a (a () b, ()) b
    forall b c. a (a b c, b) c
    forall (a :: * -> * -> *) b c. ArrowApply a => a (a b c, b) c
    app

    -- | @since base-4.6.0.0
    instance ArrowPlus a => Alternative (ArrowMonad a) where
       empty :: forall a. ArrowMonad a a
    empty = a () a -> ArrowMonad a a
    forall (a :: * -> * -> *) b. a () b -> ArrowMonad a b
    ArrowMonad a () a
    forall b c. a b c
    forall (a :: * -> * -> *) b c. ArrowZero a => a b c
    zeroArrow
       ArrowMonad a () a
    x <|> :: forall a. ArrowMonad a a -> ArrowMonad a a -> ArrowMonad a a
    <|> ArrowMonad a () a
    y = a () a -> ArrowMonad a a
    forall (a :: * -> * -> *) b. a () b -> ArrowMonad a b
    ArrowMonad (a () a
    x a () a -> a () a -> a () a
    forall b c. a b c -> a b c -> a b c
    forall (a :: * -> * -> *) b c.
    ArrowPlus a =>
    a b c -> a b c -> a b c
    <+> a () a
    y)

    -- | @since base-4.6.0.0
    instance (ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a)

    -- | Any instance of 'ArrowApply' can be made into an instance of
    --   'ArrowChoice' by defining 'left' = 'leftApp'.

    leftApp :: ArrowApply a => a b c -> a (Either b d) (Either c d)
    leftApp :: forall (a :: * -> * -> *) b c d.
    ArrowApply a =>
    a b c -> a (Either b d) (Either c d)
    leftApp a b c
    f = (Either b d -> (a () (Either c d), ()))
    -> a (Either b d) (a () (Either c d), ())
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr ((\b
    b -> ((() -> b) -> a () b
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr (\() -> b
    b) a () b -> a b (Either c d) -> a () (Either c d)
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> a b c
    f a b c -> a c (Either c d) -> a b (Either c d)
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> (c -> Either c d) -> a c (Either c d)
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr c -> Either c d
    forall a b. a -> Either a b
    Left, ())) (b -> (a () (Either c d), ()))
    -> (d -> (a () (Either c d), ()))
    -> Either b d
    -> (a () (Either c d), ())
    forall b d c. (b -> d) -> (c -> d) -> Either b c -> d
    forall (a :: * -> * -> *) b d c.
    ArrowChoice a =>
    a b d -> a c d -> a (Either b c) d
    |||
                 (\d
    d -> ((() -> d) -> a () d
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr (\() -> d
    d) a () d -> a d (Either c d) -> a () (Either c d)
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> (d -> Either c d) -> a d (Either c d)
    forall b c. (b -> c) -> a b c
    forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
    arr d -> Either c d
    forall a b. b -> Either a b
    Right, ()))) a (Either b d) (a () (Either c d), ())
    -> a (a () (Either c d), ()) (Either c d)
    -> a (Either b d) (Either c d)
    forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
    Category cat =>
    cat a b -> cat b c -> cat a c
    >>> a (a () (Either c d), ()) (Either c d)
    forall b c. a (a b c, b) c
    forall (a :: * -> * -> *) b c. ArrowApply a => a (a b c, b) c
    app

    -- | The 'loop' operator expresses computations in which an output value
    -- is fed back as input, although the computation occurs only once.
    -- It underlies the @rec@ value recursion construct in arrow notation.
    -- 'loop' should satisfy the following laws:
    --
    -- [/extension/]
    --      @'loop' ('arr' f) = 'arr' (\\ b -> 'fst' ('fix' (\\ (c,d) -> f (b,d))))@
    --
    -- [/left tightening/]
    --      @'loop' ('first' h >>> f) = h >>> 'loop' f@
    --
    -- [/right tightening/]
    --      @'loop' (f >>> 'first' h) = 'loop' f >>> h@
    --
    -- [/sliding/]
    --      @'loop' (f >>> 'arr' ('id' *** k)) = 'loop' ('arr' ('id' *** k) >>> f)@
    --
    -- [/vanishing/]
    --      @'loop' ('loop' f) = 'loop' ('arr' unassoc >>> f >>> 'arr' assoc)@
    --
    -- [/superposing/]
    --      @'second' ('loop' f) = 'loop' ('arr' assoc >>> 'second' f >>> 'arr' unassoc)@
    --
    -- where
    --
    -- > assoc ((a,b),c) = (a,(b,c))
    -- > unassoc (a,(b,c)) = ((a,b),c)
    --
    class Arrow a => ArrowLoop a where
        -- |
        --
        -- >     ╭──────────────╮
        -- >   b │     ╭───╮    │ c
        -- > >───┼─────┤   ├────┼───>
        -- >     │   ┌─┤   ├─┐  │
        -- >     │ d │ ╰───╯ │  │
        -- >     │   └───<───┘  │
        -- >     ╰──────────────╯
        loop :: a (b,d) (c,d) -> a b c

    -- | @since base-2.01
    instance ArrowLoop (->) where
        loop :: forall b d c. ((b, d) -> (c, d)) -> b -> c
    loop (b, d) -> (c, d)
    f b
    b = let (c
    c,d
    d) = (b, d) -> (c, d)
    f (b
    b,d
    d) in c
    c

    -- | Beware that for many monads (those for which the '>>=' operation
    -- is strict) this instance will /not/ satisfy the right-tightening law
    -- required by the 'ArrowLoop' class.
    --
    -- @since base-2.01
    instance MonadFix m => ArrowLoop (Kleisli m) where
        loop :: forall b d c. Kleisli m (b, d) (c, d) -> Kleisli m b c
    loop (Kleisli (b, d) -> m (c, d)
    f) = (b -> m c) -> Kleisli m b c
    forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
    Kleisli (((c, d) -> c) -> m (c, d) -> m c
    forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
    liftM (c, d) -> c
    forall a b. (a, b) -> a
    fst (m (c, d) -> m c) -> (b -> m (c, d)) -> b -> m c
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
    Category cat =>
    cat b c -> cat a b -> cat a c
    . ((c, d) -> m (c, d)) -> m (c, d)
    forall a. (a -> m a) -> m a
    forall (m :: * -> *) a. MonadFix m => (a -> m a) -> m a
    mfix (((c, d) -> m (c, d)) -> m (c, d))
    -> (b -> (c, d) -> m (c, d)) -> b -> m (c, d)
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
    Category cat =>
    cat b c -> cat a b -> cat a c
    . b -> (c, d) -> m (c, d)
    forall {a}. b -> (a, d) -> m (c, d)
    f')
          where f' :: b -> (a, d) -> m (c, d)
    f' b
    x (a, d)
    y = (b, d) -> m (c, d)
    f (b
    x, (a, d) -> d
    forall a b. (a, b) -> b
    snd (a, d)
    y)