{-# LANGUAGE CPP, TypeOperators #-}
{-# LANGUAGE Trustworthy #-}


-----------------------------------------------------------------------------
-- |
-- Copyright   :  (C) 2011-2015 Edward Kmett
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  provisional
-- Portability :  portable
--
----------------------------------------------------------------------------
module Data.Semigroup.Traversable.Class
  ( Bitraversable1(..)
  , Traversable1(..)
  ) where

import Control.Applicative
import Data.Bitraversable
import Data.Bifunctor
import Data.Bifunctor.Biff
import Data.Bifunctor.Clown
import Data.Bifunctor.Flip
import Data.Bifunctor.Joker
import Data.Bifunctor.Join
import Data.Bifunctor.Product as Bifunctor
import Data.Bifunctor.Tannen
import Data.Bifunctor.Wrapped
import Data.Functor.Apply
import Data.Functor.Compose

import Data.Complex
import Data.Functor.Identity
import Data.Functor.Product as Functor
import Data.Functor.Sum as Functor
import Data.List.NonEmpty (NonEmpty(..))
import qualified Data.Monoid as Monoid
import Data.Orphans ()
import Data.Semigroup as Semigroup
import Data.Semigroup.Foldable
import Data.Semigroup.Bifoldable
#ifdef MIN_VERSION_tagged
import Data.Tagged
#endif
import Data.Traversable.Instances ()
import GHC.Generics

#ifdef MIN_VERSION_containers
import Data.Tree
#endif

import Control.Applicative.Backwards
import Control.Applicative.Lift
import Control.Monad.Trans.Identity
import Data.Functor.Reverse

class (Bifoldable1 t, Bitraversable t) => Bitraversable1 t where
  bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> t a c -> f (t b d)
  bitraverse1 a -> f b
f c -> f d
g  = t (f b) (f d) -> f (t b d)
forall (f :: * -> *) a b. Apply f => t (f a) (f b) -> f (t a b)
forall (t :: * -> * -> *) (f :: * -> *) a b.
(Bitraversable1 t, Apply f) =>
t (f a) (f b) -> f (t a b)
bisequence1 (t (f b) (f d) -> f (t b d))
-> (t a c -> t (f b) (f d)) -> t a c -> f (t b d)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> f b) -> (c -> f d) -> t a c -> t (f b) (f d)
forall a b c d. (a -> b) -> (c -> d) -> t a c -> t b d
forall (p :: * -> * -> *) a b c d.
Bifunctor p =>
(a -> b) -> (c -> d) -> p a c -> p b d
bimap a -> f b
f c -> f d
g
  {-# INLINE bitraverse1 #-}

  bisequence1 :: Apply f => t (f a) (f b) -> f (t a b)
  bisequence1 = (f a -> f a) -> (f b -> f b) -> t (f a) (f b) -> f (t a b)
forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> t a c -> f (t b d)
forall (t :: * -> * -> *) (f :: * -> *) a b c d.
(Bitraversable1 t, Apply f) =>
(a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bitraverse1 f a -> f a
forall a. a -> a
id f b -> f b
forall a. a -> a
id
  {-# INLINE bisequence1 #-}

  {-# MINIMAL bitraverse1 | bisequence1 #-}

instance Bitraversable1 Arg where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> Arg a c -> f (Arg b d)
bitraverse1 a -> f b
f c -> f d
g (Arg a
a c
b) = b -> d -> Arg b d
forall a b. a -> b -> Arg a b
Arg (b -> d -> Arg b d) -> f b -> f (d -> Arg b d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (d -> Arg b d) -> f d -> f (Arg b d)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> c -> f d
g c
b

instance Bitraversable1 Either where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> Either a c -> f (Either b d)
bitraverse1 a -> f b
f c -> f d
_ (Left a
a) = b -> Either b d
forall a b. a -> Either a b
Left (b -> Either b d) -> f b -> f (Either b d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a
  bitraverse1 a -> f b
_ c -> f d
g (Right c
b) = d -> Either b d
forall a b. b -> Either a b
Right (d -> Either b d) -> f d -> f (Either b d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> c -> f d
g c
b
  {-# INLINE bitraverse1 #-}

instance Bitraversable1 (,) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> (a, c) -> f (b, d)
bitraverse1 a -> f b
f c -> f d
g (a
a, c
b) = (,) (b -> d -> (b, d)) -> f b -> f (d -> (b, d))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (d -> (b, d)) -> f d -> f (b, d)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> c -> f d
g c
b
  {-# INLINE bitraverse1 #-}

instance Bitraversable1 ((,,) x) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> (x, a, c) -> f (x, b, d)
bitraverse1 a -> f b
f c -> f d
g (x
x, a
a, c
b) = (,,) x
x (b -> d -> (x, b, d)) -> f b -> f (d -> (x, b, d))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (d -> (x, b, d)) -> f d -> f (x, b, d)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> c -> f d
g c
b
  {-# INLINE bitraverse1 #-}

instance Bitraversable1 ((,,,) x y) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> (x, y, a, c) -> f (x, y, b, d)
bitraverse1 a -> f b
f c -> f d
g (x
x, y
y, a
a, c
b) = (,,,) x
x y
y (b -> d -> (x, y, b, d)) -> f b -> f (d -> (x, y, b, d))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (d -> (x, y, b, d)) -> f d -> f (x, y, b, d)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> c -> f d
g c
b
  {-# INLINE bitraverse1 #-}

instance Bitraversable1 ((,,,,) x y z) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> (x, y, z, a, c) -> f (x, y, z, b, d)
bitraverse1 a -> f b
f c -> f d
g (x
x, y
y, z
z, a
a, c
b) = (,,,,) x
x y
y z
z (b -> d -> (x, y, z, b, d)) -> f b -> f (d -> (x, y, z, b, d))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (d -> (x, y, z, b, d)) -> f d -> f (x, y, z, b, d)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> c -> f d
g c
b
  {-# INLINE bitraverse1 #-}

instance Bitraversable1 Const where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> Const a c -> f (Const b d)
bitraverse1 a -> f b
f c -> f d
_ (Const a
a) = b -> Const b d
forall {k} a (b :: k). a -> Const a b
Const (b -> Const b d) -> f b -> f (Const b d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a
  {-# INLINE bitraverse1 #-}

#ifdef MIN_VERSION_tagged
instance Bitraversable1 Tagged where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> Tagged a c -> f (Tagged b d)
bitraverse1 a -> f b
_ c -> f d
g (Tagged c
b) = d -> Tagged b d
forall {k} (s :: k) b. b -> Tagged s b
Tagged (d -> Tagged b d) -> f d -> f (Tagged b d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> c -> f d
g c
b
  {-# INLINE bitraverse1 #-}
#endif

instance (Bitraversable1 p, Traversable1 f, Traversable1 g) => Bitraversable1 (Biff p f g) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> Biff p f g a c -> f (Biff p f g b d)
bitraverse1 a -> f b
f c -> f d
g = (p (f b) (g d) -> Biff p f g b d)
-> f (p (f b) (g d)) -> f (Biff p f g b d)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap p (f b) (g d) -> Biff p f g b d
forall {k} {k1} {k2} {k3} (p :: k -> k1 -> *) (f :: k2 -> k)
       (g :: k3 -> k1) (a :: k2) (b :: k3).
p (f a) (g b) -> Biff p f g a b
Biff (f (p (f b) (g d)) -> f (Biff p f g b d))
-> (Biff p f g a c -> f (p (f b) (g d)))
-> Biff p f g a c
-> f (Biff p f g b d)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (f a -> f (f b))
-> (g c -> f (g d)) -> p (f a) (g c) -> f (p (f b) (g d))
forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> p a c -> f (p b d)
forall (t :: * -> * -> *) (f :: * -> *) a b c d.
(Bitraversable1 t, Apply f) =>
(a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bitraverse1 ((a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f) ((c -> f d) -> g c -> f (g d)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> g a -> f (g b)
traverse1 c -> f d
g) (p (f a) (g c) -> f (p (f b) (g d)))
-> (Biff p f g a c -> p (f a) (g c))
-> Biff p f g a c
-> f (p (f b) (g d))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Biff p f g a c -> p (f a) (g c)
forall {k1} {k2} {k3} {k4} (p :: k1 -> k2 -> *) (f :: k3 -> k1)
       (g :: k4 -> k2) (a :: k3) (b :: k4).
Biff p f g a b -> p (f a) (g b)
runBiff
  {-# INLINE bitraverse1 #-}

instance Traversable1 f => Bitraversable1 (Clown f) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> Clown f a c -> f (Clown f b d)
bitraverse1 a -> f b
f c -> f d
_ = (f b -> Clown f b d) -> f (f b) -> f (Clown f b d)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap f b -> Clown f b d
forall {k} {k1} (f :: k -> *) (a :: k) (b :: k1).
f a -> Clown f a b
Clown (f (f b) -> f (Clown f b d))
-> (Clown f a c -> f (f b)) -> Clown f a c -> f (Clown f b d)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f (f a -> f (f b)) -> (Clown f a c -> f a) -> Clown f a c -> f (f b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Clown f a c -> f a
forall {k1} {k2} (f :: k1 -> *) (a :: k1) (b :: k2).
Clown f a b -> f a
runClown
  {-# INLINE bitraverse1 #-}

instance Bitraversable1 p => Bitraversable1 (Flip p) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> Flip p a c -> f (Flip p b d)
bitraverse1 a -> f b
f c -> f d
g = (p d b -> Flip p b d) -> f (p d b) -> f (Flip p b d)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap p d b -> Flip p b d
forall {k} {k1} (p :: k -> k1 -> *) (a :: k1) (b :: k).
p b a -> Flip p a b
Flip (f (p d b) -> f (Flip p b d))
-> (Flip p a c -> f (p d b)) -> Flip p a c -> f (Flip p b d)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (c -> f d) -> (a -> f b) -> p c a -> f (p d b)
forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> p a c -> f (p b d)
forall (t :: * -> * -> *) (f :: * -> *) a b c d.
(Bitraversable1 t, Apply f) =>
(a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bitraverse1 c -> f d
g a -> f b
f (p c a -> f (p d b))
-> (Flip p a c -> p c a) -> Flip p a c -> f (p d b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Flip p a c -> p c a
forall {k1} {k2} (p :: k1 -> k2 -> *) (a :: k2) (b :: k1).
Flip p a b -> p b a
runFlip
  {-# INLINE bitraverse1 #-}

instance Bitraversable1 p => Traversable1 (Join p) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Join p a -> f (Join p b)
traverse1 a -> f b
f (Join p a a
a) = (p b b -> Join p b) -> f (p b b) -> f (Join p b)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap p b b -> Join p b
forall {k} (p :: k -> k -> *) (a :: k). p a a -> Join p a
Join ((a -> f b) -> (a -> f b) -> p a a -> f (p b b)
forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> p a c -> f (p b d)
forall (t :: * -> * -> *) (f :: * -> *) a b c d.
(Bitraversable1 t, Apply f) =>
(a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bitraverse1 a -> f b
f a -> f b
f p a a
a)
  {-# INLINE traverse1 #-}
  sequence1 :: forall (f :: * -> *) b. Apply f => Join p (f b) -> f (Join p b)
sequence1 (Join p (f b) (f b)
a) = (p b b -> Join p b) -> f (p b b) -> f (Join p b)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap p b b -> Join p b
forall {k} (p :: k -> k -> *) (a :: k). p a a -> Join p a
Join (p (f b) (f b) -> f (p b b)
forall (f :: * -> *) a b. Apply f => p (f a) (f b) -> f (p a b)
forall (t :: * -> * -> *) (f :: * -> *) a b.
(Bitraversable1 t, Apply f) =>
t (f a) (f b) -> f (t a b)
bisequence1 p (f b) (f b)
a)
  {-# INLINE sequence1 #-}

instance Traversable1 g => Bitraversable1 (Joker g) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> Joker g a c -> f (Joker g b d)
bitraverse1 a -> f b
_ c -> f d
g = (g d -> Joker g b d) -> f (g d) -> f (Joker g b d)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap g d -> Joker g b d
forall {k} {k1} (g :: k -> *) (a :: k1) (b :: k).
g b -> Joker g a b
Joker (f (g d) -> f (Joker g b d))
-> (Joker g a c -> f (g d)) -> Joker g a c -> f (Joker g b d)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (c -> f d) -> g c -> f (g d)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> g a -> f (g b)
traverse1 c -> f d
g (g c -> f (g d)) -> (Joker g a c -> g c) -> Joker g a c -> f (g d)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Joker g a c -> g c
forall {k1} {k2} (g :: k1 -> *) (a :: k2) (b :: k1).
Joker g a b -> g b
runJoker
  {-# INLINE bitraverse1 #-}

instance (Bitraversable1 f, Bitraversable1 g) => Bitraversable1 (Bifunctor.Product f g) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> Product f g a c -> f (Product f g b d)
bitraverse1 a -> f b
f c -> f d
g (Bifunctor.Pair f a c
x g a c
y) = f b d -> g b d -> Product f g b d
forall {k} {k1} (f :: k -> k1 -> *) (g :: k -> k1 -> *) (a :: k)
       (b :: k1).
f a b -> g a b -> Product f g a b
Bifunctor.Pair (f b d -> g b d -> Product f g b d)
-> f (f b d) -> f (g b d -> Product f g b d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> (c -> f d) -> f a c -> f (f b d)
forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> f a c -> f (f b d)
forall (t :: * -> * -> *) (f :: * -> *) a b c d.
(Bitraversable1 t, Apply f) =>
(a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bitraverse1 a -> f b
f c -> f d
g f a c
x f (g b d -> Product f g b d) -> f (g b d) -> f (Product f g b d)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> (a -> f b) -> (c -> f d) -> g a c -> f (g b d)
forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> g a c -> f (g b d)
forall (t :: * -> * -> *) (f :: * -> *) a b c d.
(Bitraversable1 t, Apply f) =>
(a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bitraverse1 a -> f b
f c -> f d
g g a c
y
  {-# INLINE bitraverse1 #-}

instance (Traversable1 f, Bitraversable1 p) => Bitraversable1 (Tannen f p) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> Tannen f p a c -> f (Tannen f p b d)
bitraverse1 a -> f b
f c -> f d
g = (f (p b d) -> Tannen f p b d)
-> f (f (p b d)) -> f (Tannen f p b d)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap f (p b d) -> Tannen f p b d
forall {k} {k1} {k2} (f :: k -> *) (p :: k1 -> k2 -> k) (a :: k1)
       (b :: k2).
f (p a b) -> Tannen f p a b
Tannen (f (f (p b d)) -> f (Tannen f p b d))
-> (Tannen f p a c -> f (f (p b d)))
-> Tannen f p a c
-> f (Tannen f p b d)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (p a c -> f (p b d)) -> f (p a c) -> f (f (p b d))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 ((a -> f b) -> (c -> f d) -> p a c -> f (p b d)
forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> p a c -> f (p b d)
forall (t :: * -> * -> *) (f :: * -> *) a b c d.
(Bitraversable1 t, Apply f) =>
(a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bitraverse1 a -> f b
f c -> f d
g) (f (p a c) -> f (f (p b d)))
-> (Tannen f p a c -> f (p a c)) -> Tannen f p a c -> f (f (p b d))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Tannen f p a c -> f (p a c)
forall {k1} {k2} {k3} (f :: k1 -> *) (p :: k2 -> k3 -> k1)
       (a :: k2) (b :: k3).
Tannen f p a b -> f (p a b)
runTannen
  {-# INLINE bitraverse1 #-}

instance Bitraversable1 p => Bitraversable1 (WrappedBifunctor p) where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b)
-> (c -> f d)
-> WrappedBifunctor p a c
-> f (WrappedBifunctor p b d)
bitraverse1 a -> f b
f c -> f d
g = (p b d -> WrappedBifunctor p b d)
-> f (p b d) -> f (WrappedBifunctor p b d)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap p b d -> WrappedBifunctor p b d
forall {k} {k1} (p :: k -> k1 -> *) (a :: k) (b :: k1).
p a b -> WrappedBifunctor p a b
WrapBifunctor (f (p b d) -> f (WrappedBifunctor p b d))
-> (WrappedBifunctor p a c -> f (p b d))
-> WrappedBifunctor p a c
-> f (WrappedBifunctor p b d)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> f b) -> (c -> f d) -> p a c -> f (p b d)
forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b) -> (c -> f d) -> p a c -> f (p b d)
forall (t :: * -> * -> *) (f :: * -> *) a b c d.
(Bitraversable1 t, Apply f) =>
(a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bitraverse1 a -> f b
f c -> f d
g (p a c -> f (p b d))
-> (WrappedBifunctor p a c -> p a c)
-> WrappedBifunctor p a c
-> f (p b d)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. WrappedBifunctor p a c -> p a c
forall {k1} {k2} (p :: k1 -> k2 -> *) (a :: k1) (b :: k2).
WrappedBifunctor p a b -> p a b
unwrapBifunctor
  {-# INLINE bitraverse1 #-}


class (Foldable1 t, Traversable t) => Traversable1 t where
  traverse1 :: Apply f => (a -> f b) -> t a -> f (t b)
  sequence1 :: Apply f => t (f b) -> f (t b)

  sequence1 = (f b -> f b) -> t (f b) -> f (t b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> t a -> f (t b)
traverse1 f b -> f b
forall a. a -> a
id
  traverse1 a -> f b
f = t (f b) -> f (t b)
forall (t :: * -> *) (f :: * -> *) b.
(Traversable1 t, Apply f) =>
t (f b) -> f (t b)
forall (f :: * -> *) b. Apply f => t (f b) -> f (t b)
sequence1 (t (f b) -> f (t b)) -> (t a -> t (f b)) -> t a -> f (t b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> f b) -> t a -> t (f b)
forall a b. (a -> b) -> t a -> t b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> f b
f

  {-# MINIMAL traverse1 | sequence1 #-}

instance Traversable1 f => Traversable1 (Rec1 f) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Rec1 f a -> f (Rec1 f b)
traverse1 a -> f b
f (Rec1 f a
as) = f b -> Rec1 f b
forall k (f :: k -> *) (p :: k). f p -> Rec1 f p
Rec1 (f b -> Rec1 f b) -> f (f b) -> f (Rec1 f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f f a
as

instance Traversable1 f => Traversable1 (M1 i c f) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> M1 i c f a -> f (M1 i c f b)
traverse1 a -> f b
f (M1 f a
as) = f b -> M1 i c f b
forall k i (c :: Meta) (f :: k -> *) (p :: k). f p -> M1 i c f p
M1 (f b -> M1 i c f b) -> f (f b) -> f (M1 i c f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f f a
as

instance Traversable1 Par1 where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Par1 a -> f (Par1 b)
traverse1 a -> f b
f (Par1 a
a) = b -> Par1 b
forall p. p -> Par1 p
Par1 (b -> Par1 b) -> f b -> f (Par1 b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a

instance Traversable1 V1 where
  traverse1 :: forall (f :: * -> *) a b. Apply f => (a -> f b) -> V1 a -> f (V1 b)
traverse1 a -> f b
_ V1 a
v = V1 a
v V1 a -> f (V1 b) -> f (V1 b)
forall a b. a -> b -> b
`seq` f (V1 b)
forall a. HasCallStack => a
undefined

instance (Traversable1 f, Traversable1 g) => Traversable1 (f :*: g) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> (:*:) f g a -> f ((:*:) f g b)
traverse1 a -> f b
f (f a
as :*: g a
bs) = f b -> g b -> (:*:) f g b
forall k (f :: k -> *) (g :: k -> *) (p :: k).
f p -> g p -> (:*:) f g p
(:*:) (f b -> g b -> (:*:) f g b) -> f (f b) -> f (g b -> (:*:) f g b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f f a
as f (g b -> (:*:) f g b) -> f (g b) -> f ((:*:) f g b)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> (a -> f b) -> g a -> f (g b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> g a -> f (g b)
traverse1 a -> f b
f g a
bs

instance (Traversable1 f, Traversable1 g) => Traversable1 (f :+: g) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> (:+:) f g a -> f ((:+:) f g b)
traverse1 a -> f b
f (L1 f a
as) = f b -> (:+:) f g b
forall k (f :: k -> *) (g :: k -> *) (p :: k). f p -> (:+:) f g p
L1 (f b -> (:+:) f g b) -> f (f b) -> f ((:+:) f g b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f f a
as
  traverse1 a -> f b
f (R1 g a
bs) = g b -> (:+:) f g b
forall k (f :: k -> *) (g :: k -> *) (p :: k). g p -> (:+:) f g p
R1 (g b -> (:+:) f g b) -> f (g b) -> f ((:+:) f g b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> g a -> f (g b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> g a -> f (g b)
traverse1 a -> f b
f g a
bs

instance (Traversable1 f, Traversable1 g) => Traversable1 (f :.: g) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> (:.:) f g a -> f ((:.:) f g b)
traverse1 a -> f b
f (Comp1 f (g a)
m) = f (g b) -> (:.:) f g b
forall k2 k1 (f :: k2 -> *) (g :: k1 -> k2) (p :: k1).
f (g p) -> (:.:) f g p
Comp1 (f (g b) -> (:.:) f g b) -> f (f (g b)) -> f ((:.:) f g b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (g a -> f (g b)) -> f (g a) -> f (f (g b))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 ((a -> f b) -> g a -> f (g b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> g a -> f (g b)
traverse1 a -> f b
f) f (g a)
m

instance Traversable1 Identity where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Identity a -> f (Identity b)
traverse1 a -> f b
f = (b -> Identity b) -> f b -> f (Identity b)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> Identity b
forall a. a -> Identity a
Identity (f b -> f (Identity b))
-> (Identity a -> f b) -> Identity a -> f (Identity b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> f b
f (a -> f b) -> (Identity a -> a) -> Identity a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Identity a -> a
forall a. Identity a -> a
runIdentity

instance (Traversable1 f, Traversable1 g) => Traversable1 (Functor.Product f g) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Product f g a -> f (Product f g b)
traverse1 a -> f b
f (Functor.Pair f a
a g a
b) = f b -> g b -> Product f g b
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Functor.Pair (f b -> g b -> Product f g b)
-> f (f b) -> f (g b -> Product f g b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f f a
a f (g b -> Product f g b) -> f (g b) -> f (Product f g b)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> (a -> f b) -> g a -> f (g b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> g a -> f (g b)
traverse1 a -> f b
f g a
b

instance (Traversable1 f, Traversable1 g) => Traversable1 (Functor.Sum f g) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Sum f g a -> f (Sum f g b)
traverse1 a -> f b
f (Functor.InL f a
x) = f b -> Sum f g b
forall {k} (f :: k -> *) (g :: k -> *) (a :: k). f a -> Sum f g a
Functor.InL (f b -> Sum f g b) -> f (f b) -> f (Sum f g b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f f a
x
  traverse1 a -> f b
f (Functor.InR g a
y) = g b -> Sum f g b
forall {k} (f :: k -> *) (g :: k -> *) (a :: k). g a -> Sum f g a
Functor.InR (g b -> Sum f g b) -> f (g b) -> f (Sum f g b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> g a -> f (g b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> g a -> f (g b)
traverse1 a -> f b
f g a
y

instance (Traversable1 f, Traversable1 g) => Traversable1 (Compose f g) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Compose f g a -> f (Compose f g b)
traverse1 a -> f b
f = (f (g b) -> Compose f g b) -> f (f (g b)) -> f (Compose f g b)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap f (g b) -> Compose f g b
forall {k} {k1} (f :: k -> *) (g :: k1 -> k) (a :: k1).
f (g a) -> Compose f g a
Compose (f (f (g b)) -> f (Compose f g b))
-> (Compose f g a -> f (f (g b)))
-> Compose f g a
-> f (Compose f g b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (g a -> f (g b)) -> f (g a) -> f (f (g b))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 ((a -> f b) -> g a -> f (g b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> g a -> f (g b)
traverse1 a -> f b
f) (f (g a) -> f (f (g b)))
-> (Compose f g a -> f (g a)) -> Compose f g a -> f (f (g b))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Compose f g a -> f (g a)
forall {k1} {k2} (f :: k1 -> *) (g :: k2 -> k1) (a :: k2).
Compose f g a -> f (g a)
getCompose

instance Traversable1 f => Traversable1 (IdentityT f) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> IdentityT f a -> f (IdentityT f b)
traverse1 a -> f b
f = (f b -> IdentityT f b) -> f (f b) -> f (IdentityT 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 -> IdentityT f b
forall {k} (f :: k -> *) (a :: k). f a -> IdentityT f a
IdentityT (f (f b) -> f (IdentityT f b))
-> (IdentityT f a -> f (f b)) -> IdentityT f a -> f (IdentityT f b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f (f a -> f (f b))
-> (IdentityT f a -> f a) -> IdentityT f a -> f (f b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. IdentityT f a -> f a
forall {k} (f :: k -> *) (a :: k). IdentityT f a -> f a
runIdentityT

instance Traversable1 f => Traversable1 (Backwards f) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Backwards f a -> f (Backwards f b)
traverse1 a -> f b
f = (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 (f (f b) -> f (Backwards f b))
-> (Backwards f a -> f (f b)) -> Backwards f a -> f (Backwards f b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f (f a -> f (f b))
-> (Backwards f a -> f a) -> Backwards f a -> f (f b)
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

instance Traversable1 f => Traversable1 (Lift f) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Lift f a -> f (Lift f b)
traverse1 a -> f b
f (Pure a
x)  = b -> Lift f b
forall (f :: * -> *) a. a -> Lift f a
Pure (b -> Lift f b) -> f b -> f (Lift f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
x
  traverse1 a -> f b
f (Other f a
y) = f b -> Lift f b
forall (f :: * -> *) a. f a -> Lift f a
Other (f b -> Lift f b) -> f (f b) -> f (Lift f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f f a
y

instance Traversable1 f => Traversable1 (Reverse f) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Reverse f a -> f (Reverse f b)
traverse1 a -> f b
f = (f b -> Reverse f b) -> f (f b) -> f (Reverse 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 -> Reverse f b
forall {k} (f :: k -> *) (a :: k). f a -> Reverse f a
Reverse (f (f b) -> f (Reverse f b))
-> (Reverse f a -> f (f b)) -> Reverse f a -> f (Reverse f b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Backwards f (f b) -> f (f b)
forall {k} (f :: k -> *) (a :: k). Backwards f a -> f a
forwards (Backwards f (f b) -> f (f b))
-> (Reverse f a -> Backwards f (f b)) -> Reverse f a -> f (f b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Backwards f b) -> f a -> Backwards f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 (f b -> Backwards f b
forall {k} (f :: k -> *) (a :: k). f a -> Backwards f a
Backwards (f b -> Backwards f b) -> (a -> f b) -> a -> Backwards f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> f b
f) (f a -> Backwards f (f b))
-> (Reverse f a -> f a) -> Reverse f a -> Backwards f (f b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Reverse f a -> f a
forall {k} (f :: k -> *) (a :: k). Reverse f a -> f a
getReverse

instance Traversable1 Complex where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Complex a -> f (Complex b)
traverse1 a -> f b
f (a
a :+ a
b) = b -> b -> Complex b
forall a. a -> a -> Complex a
(:+) (b -> b -> Complex b) -> f b -> f (b -> Complex b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (b -> Complex b) -> f b -> f (Complex b)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> a -> f b
f a
b
  {-# INLINE traverse1 #-}

#ifdef MIN_VERSION_tagged
instance Traversable1 (Tagged a) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Tagged a a -> f (Tagged a b)
traverse1 a -> f b
f (Tagged a
a) = b -> Tagged a b
forall {k} (s :: k) b. b -> Tagged s b
Tagged (b -> Tagged a b) -> f b -> f (Tagged a b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a
#endif

#ifdef MIN_VERSION_containers
instance Traversable1 Tree where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Tree a -> f (Tree b)
traverse1 a -> f b
f (Node a
a []) = (b -> [Tree b] -> Tree b
forall a. a -> [Tree a] -> Tree a
`Node`[]) (b -> Tree b) -> f b -> f (Tree b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a
  traverse1 a -> f b
f (Node a
a (Tree a
x:[Tree a]
xs)) = (\b
b (Tree b
y:|[Tree b]
ys) -> b -> [Tree b] -> Tree b
forall a. a -> [Tree a] -> Tree a
Node b
b (Tree b
yTree b -> [Tree b] -> [Tree b]
forall a. a -> [a] -> [a]
:[Tree b]
ys)) (b -> NonEmpty (Tree b) -> Tree b)
-> f b -> f (NonEmpty (Tree b) -> Tree b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (NonEmpty (Tree b) -> Tree b)
-> f (NonEmpty (Tree b)) -> f (Tree b)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> (Tree a -> f (Tree b))
-> NonEmpty (Tree a) -> f (NonEmpty (Tree b))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> NonEmpty a -> f (NonEmpty b)
traverse1 ((a -> f b) -> Tree a -> f (Tree b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Tree a -> f (Tree b)
traverse1 a -> f b
f) (Tree a
x Tree a -> [Tree a] -> NonEmpty (Tree a)
forall a. a -> [a] -> NonEmpty a
:| [Tree a]
xs)
#endif

instance Traversable1 NonEmpty where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> NonEmpty a -> f (NonEmpty b)
traverse1 a -> f b
f (a
a :| [a]
as) = (a -> (a -> f (NonEmpty b)) -> a -> f (NonEmpty b))
-> (a -> f (NonEmpty b)) -> [a] -> a -> f (NonEmpty b)
forall a b. (a -> b -> b) -> b -> [a] -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr (\a
b a -> f (NonEmpty b)
g a
x -> (\b
a' (b
b':| [b]
bs') -> b
a' b -> [b] -> NonEmpty b
forall a. a -> [a] -> NonEmpty a
:| b
b'b -> [b] -> [b]
forall a. a -> [a] -> [a]
: [b]
bs') (b -> NonEmpty b -> NonEmpty b)
-> f b -> f (NonEmpty b -> NonEmpty b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
x f (NonEmpty b -> NonEmpty b) -> f (NonEmpty b) -> f (NonEmpty b)
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
<.> a -> f (NonEmpty b)
g a
b) ((b -> NonEmpty b) -> f b -> f (NonEmpty b)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (b -> [b] -> NonEmpty b
forall a. a -> [a] -> NonEmpty a
:|[]) (f b -> f (NonEmpty b)) -> (a -> f b) -> a -> f (NonEmpty b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> f b
f) [a]
as a
a

instance Traversable1 ((,) a) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> (a, a) -> f (a, b)
traverse1 a -> f b
f (a
a, a
b) = (,) a
a (b -> (a, b)) -> f b -> f (a, b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
b

instance Traversable1 g => Traversable1 (Joker g a) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Joker g a a -> f (Joker g a b)
traverse1 a -> f b
g = (g b -> Joker g a b) -> f (g b) -> f (Joker g a b)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap g b -> Joker g a b
forall {k} {k1} (g :: k -> *) (a :: k1) (b :: k).
g b -> Joker g a b
Joker (f (g b) -> f (Joker g a b))
-> (Joker g a a -> f (g b)) -> Joker g a a -> f (Joker g a b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> f b) -> g a -> f (g b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> g a -> f (g b)
traverse1 a -> f b
g (g a -> f (g b)) -> (Joker g a a -> g a) -> Joker g a a -> f (g b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Joker g a a -> g a
forall {k1} {k2} (g :: k1 -> *) (a :: k2) (b :: k1).
Joker g a b -> g b
runJoker
  {-# INLINE traverse1 #-}

instance Traversable1 Monoid.Sum where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Sum a -> f (Sum b)
traverse1 a -> f b
g (Monoid.Sum a
a) = b -> Sum b
forall a. a -> Sum a
Monoid.Sum (b -> Sum b) -> f b -> f (Sum b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
g a
a

instance Traversable1 Monoid.Product where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Product a -> f (Product b)
traverse1 a -> f b
g (Monoid.Product a
a) = b -> Product b
forall a. a -> Product a
Monoid.Product (b -> Product b) -> f b -> f (Product b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
g a
a

instance Traversable1 Monoid.Dual where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Dual a -> f (Dual b)
traverse1 a -> f b
g (Monoid.Dual a
a) = b -> Dual b
forall a. a -> Dual a
Monoid.Dual (b -> Dual b) -> f b -> f (Dual b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
g a
a

instance Traversable1 f => Traversable1 (Monoid.Alt f) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Alt f a -> f (Alt f b)
traverse1 a -> f b
g (Monoid.Alt f a
m) = f b -> Alt f b
forall {k} (f :: k -> *) (a :: k). f a -> Alt f a
Monoid.Alt (f b -> Alt f b) -> f (f b) -> f (Alt f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
g f a
m

instance Traversable1 Semigroup.First where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> First a -> f (First b)
traverse1 a -> f b
g (Semigroup.First a
a) = b -> First b
forall a. a -> First a
Semigroup.First (b -> First b) -> f b -> f (First b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
g a
a

instance Traversable1 Semigroup.Last where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Last a -> f (Last b)
traverse1 a -> f b
g (Semigroup.Last a
a) = b -> Last b
forall a. a -> Last a
Semigroup.Last (b -> Last b) -> f b -> f (Last b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
g a
a

instance Traversable1 Semigroup.Min where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Min a -> f (Min b)
traverse1 a -> f b
g (Semigroup.Min a
a) = b -> Min b
forall a. a -> Min a
Semigroup.Min (b -> Min b) -> f b -> f (Min b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
g a
a

instance Traversable1 Semigroup.Max where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> Max a -> f (Max b)
traverse1 a -> f b
g (Semigroup.Max a
a) = b -> Max b
forall a. a -> Max a
Semigroup.Max (b -> Max b) -> f b -> f (Max b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
g a
a