{-# LANGUAGE CPP #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE TypeOperators #-}

#ifdef TRUSTWORTHY
{-# LANGUAGE Trustworthy #-}
#endif

#include "lens-common.h"

-----------------------------------------------------------------------------

-- |

-- Module      :  Control.Lens.At

-- Copyright   :  (C) 2012-16 Edward Kmett

-- License     :  BSD-style (see the file LICENSE)

-- Maintainer  :  Edward Kmett <ekmett@gmail.com>

-- Stability   :  experimental

-- Portability :  non-portable

--

----------------------------------------------------------------------------

module Control.Lens.At
  (
  -- * At

    At(at)
    , sans
    , iat
  -- * Ixed

  , Index
  , IxValue
  , Ixed(ix)
  , ixAt
  , iix
  -- * Contains

  , Contains(contains)
  , icontains
  ) where

import Prelude ()

import Control.Lens.Each
import Control.Lens.Internal.Prelude
import Control.Lens.Traversal
import Control.Lens.Lens
import Control.Lens.Setter
import Control.Lens.Indexed
import Control.Monad (guard)
import Data.Array.IArray as Array
import Data.Array.Unboxed
import qualified Data.ByteString as StrictB
import qualified Data.ByteString.Lazy as LazyB
import Data.Complex
import Data.Functor (($>))
import Data.Hashable
import qualified Data.HashMap.Lazy as HashMap
import Data.HashMap.Lazy (HashMap)
import qualified Data.HashSet as HashSet
import Data.HashSet (HashSet)
import Data.Int
import qualified Data.IntMap as IntMap
import Data.IntMap (IntMap)
import qualified Data.IntSet as IntSet
import Data.IntSet (IntSet)
import Data.Kind
import qualified Data.Map as Map
import Data.Map (Map)
import Data.Maybe (isJust)
import qualified Data.Set as Set
import Data.Set (Set)
import qualified Data.Sequence as Seq
import Data.Sequence (Seq)
import qualified Data.Text as StrictT
import qualified Data.Text.Lazy as LazyT
import Data.Tree
import qualified Data.Vector as Vector
import qualified Data.Vector.Primitive as Prim
import Data.Vector.Primitive (Prim)
import qualified Data.Vector.Storable as Storable
import qualified Data.Vector.Unboxed as Unboxed
import Data.Vector.Unboxed (Unbox)
import Data.Word
import Foreign.Storable (Storable)

type family Index (s :: Type) :: Type
type instance Index (e -> a) = e
type instance Index IntSet = Int
type instance Index (Set a) = a
type instance Index (HashSet a) = a
type instance Index [a] = Int
type instance Index (NonEmpty a) = Int
type instance Index (Seq a) = Int
type instance Index (a,b) = Int
type instance Index (a,b,c) = Int
type instance Index (a,b,c,d) = Int
type instance Index (a,b,c,d,e) = Int
type instance Index (a,b,c,d,e,f) = Int
type instance Index (a,b,c,d,e,f,g) = Int
type instance Index (a,b,c,d,e,f,g,h) = Int
type instance Index (a,b,c,d,e,f,g,h,i) = Int
type instance Index (IntMap a) = Int
type instance Index (Map k a) = k
type instance Index (HashMap k a) = k
type instance Index (Array.Array i e) = i
type instance Index (UArray i e) = i
type instance Index (Vector.Vector a) = Int
type instance Index (Prim.Vector a) = Int
type instance Index (Storable.Vector a) = Int
type instance Index (Unboxed.Vector a) = Int
type instance Index (Complex a) = Int
type instance Index (Identity a) = ()
type instance Index (Maybe a) = ()
type instance Index (Tree a) = [Int]
type instance Index StrictT.Text = Int
type instance Index LazyT.Text = Int64
type instance Index StrictB.ByteString = Int
type instance Index LazyB.ByteString = Int64

-- $setup

-- >>> :set -XNoOverloadedStrings

-- >>> import Control.Lens

-- >>> import qualified Data.IntSet as IntSet

-- >>> import qualified Data.Sequence as Seq

-- >>> import qualified Data.Map as Map

-- >>> import Debug.SimpleReflect.Expr

-- >>> import Debug.SimpleReflect.Vars as Vars hiding (f,g)

-- >>> let f  :: Expr -> Expr; f = Debug.SimpleReflect.Vars.f

-- >>> let g  :: Expr -> Expr; g = Debug.SimpleReflect.Vars.g

-- >>> let f' :: Int -> Expr -> Expr; f' = Debug.SimpleReflect.Vars.f'

-- >>> let h  :: Int -> Expr; h = Debug.SimpleReflect.Vars.h


-- |

-- This class provides a simple 'Lens' that lets you view (and modify)

-- information about whether or not a container contains a given 'Index'.

class Contains m where
  -- |

  -- >>> IntSet.fromList [1,2,3,4] ^. contains 3

  -- True

  --

  -- >>> IntSet.fromList [1,2,3,4] ^. contains 5

  -- False

  --

  -- >>> IntSet.fromList [1,2,3,4] & contains 3 .~ False

  -- fromList [1,2,4]

  contains :: Index m -> Lens' m Bool

-- | An indexed version of 'contains'.

--

-- >>> IntSet.fromList [1,2,3,4] ^@. icontains 3

-- (3,True)

--

-- >>> IntSet.fromList [1,2,3,4] ^@. icontains 5

-- (5,False)

--

-- >>> IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if odd i then not x else x

-- fromList [1,2,4]

--

-- >>> IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if even i then not x else x

-- fromList [1,2,3,4]

icontains :: Contains m => Index m -> IndexedLens' (Index m) m Bool
icontains :: forall m. Contains m => Index m -> IndexedLens' (Index m) m Bool
icontains Index m
i p Bool (f Bool)
f = forall m. Contains m => Index m -> Lens' m Bool
contains Index m
i (forall i (p :: * -> * -> *) a b.
Indexable i p =>
p a b -> i -> a -> b
indexed p Bool (f Bool)
f Index m
i)
{-# INLINE icontains #-}

instance Contains IntSet where
#if MIN_VERSION_containers(0,6,3)
  contains :: Index IntSet -> Lens' IntSet Bool
contains Index IntSet
k Bool -> f Bool
f = forall (f :: * -> *).
Functor f =>
(Bool -> f Bool) -> Key -> IntSet -> f IntSet
IntSet.alterF Bool -> f Bool
f Index IntSet
k
#else
  -- This is a flipped copy of the implementation of `IntSet.alterF`.  Unlike a

  -- `Set`, we don't have to worry about expensive comparisons from descending

  -- multiple times into an `IntSet`. We are careful to share the results of

  -- insertion or deletion across multiple positions in the `Functor`.

  contains k f s = fmap choose (f member_)
    where
      member_ = IntSet.member k s

      (inserted, deleted)
        | member_   = (s, IntSet.delete k s)
        | otherwise = (IntSet.insert k s, s)

      choose True  = inserted
      choose False = deleted
#endif
  {-# INLINE contains #-}

instance Ord a => Contains (Set a) where
#if MIN_VERSION_containers(0,6,3)
  contains :: Index (Set a) -> Lens' (Set a) Bool
contains Index (Set a)
k Bool -> f Bool
f = forall a (f :: * -> *).
(Ord a, Functor f) =>
(Bool -> f Bool) -> a -> Set a -> f (Set a)
Set.alterF Bool -> f Bool
f Index (Set a)
k
#else
  contains k f s = f (Set.member k s) <&> \b ->
    if b then Set.insert k s else Set.delete k s
#endif
  {-# INLINE contains #-}

instance (Eq a, Hashable a) => Contains (HashSet a) where
  contains :: Index (HashSet a) -> Lens' (HashSet a) Bool
contains Index (HashSet a)
k Bool -> f Bool
f HashSet a
s = forall a. HashMap a () -> HashSet a
HashSet.fromMap forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$>
    forall (f :: * -> *) k v.
(Functor f, Eq k, Hashable k) =>
(Maybe v -> f (Maybe v)) -> k -> HashMap k v -> f (HashMap k v)
HashMap.alterF (forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall (f :: * -> *). Alternative f => Bool -> f ()
guard forall b c a. (b -> c) -> (a -> b) -> a -> c
. Bool -> f Bool
f forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Maybe a -> Bool
isJust) Index (HashSet a)
k (forall a. HashSet a -> HashMap a ()
HashSet.toMap HashSet a
s)
  {-# INLINE contains #-}

-- | This provides a common notion of a value at an index that is shared by both 'Ixed' and 'At'.

type family IxValue (m :: Type) :: Type

-- | Provides a simple 'Traversal' lets you 'traverse' the value at a given

-- key in a 'Map' or element at an ordinal position in a list or 'Seq'.

class Ixed m where
  -- |

  -- /NB:/ Setting the value of this 'Traversal' will only set the value in

  -- 'at' if it is already present.

  --

  -- If you want to be able to insert /missing/ values, you want 'at'.

  --

  -- >>> Seq.fromList [a,b,c,d] & ix 2 %~ f

  -- fromList [a,b,f c,d]

  --

  -- >>> Seq.fromList [a,b,c,d] & ix 2 .~ e

  -- fromList [a,b,e,d]

  --

  -- >>> Seq.fromList [a,b,c,d] ^? ix 2

  -- Just c

  --

  -- >>> Seq.fromList [] ^? ix 2

  -- Nothing

  ix :: Index m -> Traversal' m (IxValue m)
  default ix :: At m => Index m -> Traversal' m (IxValue m)
  ix = forall m. At m => Index m -> Traversal' m (IxValue m)
ixAt
  {-# INLINE ix #-}

-- | An indexed version of 'ix'.

--

-- >>> Seq.fromList [a,b,c,d] & iix 2 %@~ f'

-- fromList [a,b,f' 2 c,d]

--

-- >>> Seq.fromList [a,b,c,d] & iix 2 .@~ h

-- fromList [a,b,h 2,d]

--

-- >>> Seq.fromList [a,b,c,d] ^@? iix 2

-- Just (2,c)

--

-- >>> Seq.fromList [] ^@? iix 2

-- Nothing

iix :: Ixed m => Index m -> IndexedTraversal' (Index m) m (IxValue m)
iix :: forall m.
Ixed m =>
Index m -> IndexedTraversal' (Index m) m (IxValue m)
iix Index m
i p (IxValue m) (f (IxValue m))
f = forall m. Ixed m => Index m -> Traversal' m (IxValue m)
ix Index m
i (forall i (p :: * -> * -> *) a b.
Indexable i p =>
p a b -> i -> a -> b
indexed p (IxValue m) (f (IxValue m))
f Index m
i)
{-# INLINE iix #-}

-- | A definition of 'ix' for types with an 'At' instance. This is the default

-- if you don't specify a definition for 'ix'.

ixAt :: At m => Index m -> Traversal' m (IxValue m)
ixAt :: forall m. At m => Index m -> Traversal' m (IxValue m)
ixAt Index m
i = forall m. At m => Index m -> Lens' m (Maybe (IxValue m))
at Index m
i forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse
{-# INLINE ixAt #-}

type instance IxValue (e -> a) = a
instance Eq e => Ixed (e -> a) where
  ix :: Index (e -> a) -> Traversal' (e -> a) (IxValue (e -> a))
ix Index (e -> a)
e IxValue (e -> a) -> f (IxValue (e -> a))
p e -> a
f = IxValue (e -> a) -> f (IxValue (e -> a))
p (e -> a
f Index (e -> a)
e) forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
a e
e' -> if Index (e -> a)
e forall a. Eq a => a -> a -> Bool
== e
e' then a
a else e -> a
f e
e'
  {-# INLINE ix #-}

type instance IxValue (Maybe a) = a
instance Ixed (Maybe a) where
  ix :: Index (Maybe a) -> Traversal' (Maybe a) (IxValue (Maybe a))
ix ~() IxValue (Maybe a) -> f (IxValue (Maybe a))
f (Just a
a) = forall a. a -> Maybe a
Just forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> IxValue (Maybe a) -> f (IxValue (Maybe a))
f a
a
  ix ~() IxValue (Maybe a) -> f (IxValue (Maybe a))
_ Maybe a
Nothing  = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. Maybe a
Nothing
  {-# INLINE ix #-}

type instance IxValue [a] = a
instance Ixed [a] where
  ix :: Index [a] -> Traversal' [a] (IxValue [a])
ix Index [a]
k IxValue [a] -> f (IxValue [a])
f [a]
xs0 | Index [a]
k forall a. Ord a => a -> a -> Bool
< Key
0     = forall (f :: * -> *) a. Applicative f => a -> f a
pure [a]
xs0
             | Bool
otherwise = [a] -> Key -> f [a]
go [a]
xs0 Index [a]
k where
    go :: [a] -> Key -> f [a]
go [] Key
_ = forall (f :: * -> *) a. Applicative f => a -> f a
pure []
    go (a
a:[a]
as) Key
0 = IxValue [a] -> f (IxValue [a])
f a
a forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> (forall a. a -> [a] -> [a]
:[a]
as)
    go (a
a:[a]
as) Key
i = (a
aforall a. a -> [a] -> [a]
:) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> ([a] -> Key -> f [a]
go [a]
as forall a b. (a -> b) -> a -> b
$! Key
i forall a. Num a => a -> a -> a
- Key
1)
  {-# INLINE ix #-}

type instance IxValue (NonEmpty a) = a
instance Ixed (NonEmpty a) where
  ix :: Index (NonEmpty a)
-> Traversal' (NonEmpty a) (IxValue (NonEmpty a))
ix Index (NonEmpty a)
k IxValue (NonEmpty a) -> f (IxValue (NonEmpty a))
f NonEmpty a
xs0 | Index (NonEmpty a)
k forall a. Ord a => a -> a -> Bool
< Key
0 = forall (f :: * -> *) a. Applicative f => a -> f a
pure NonEmpty a
xs0
             | Bool
otherwise = NonEmpty a -> Key -> f (NonEmpty a)
go NonEmpty a
xs0 Index (NonEmpty a)
k where
    go :: NonEmpty a -> Key -> f (NonEmpty a)
go (a
a:|[a]
as) Key
0 = IxValue (NonEmpty a) -> f (IxValue (NonEmpty a))
f a
a forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> (forall a. a -> [a] -> NonEmpty a
:|[a]
as)
    go (a
a:|[a]
as) Key
i = (a
aforall a. a -> [a] -> NonEmpty a
:|) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall m. Ixed m => Index m -> Traversal' m (IxValue m)
ix (Key
i forall a. Num a => a -> a -> a
- Key
1) IxValue (NonEmpty a) -> f (IxValue (NonEmpty a))
f [a]
as
  {-# INLINE ix #-}

type instance IxValue (Identity a) = a
instance Ixed (Identity a) where
  ix :: Index (Identity a)
-> Traversal' (Identity a) (IxValue (Identity a))
ix ~() IxValue (Identity a) -> f (IxValue (Identity a))
f (Identity a
a) = forall a. a -> Identity a
Identity forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> IxValue (Identity a) -> f (IxValue (Identity a))
f a
a
  {-# INLINE ix #-}

type instance IxValue (Tree a) = a
instance Ixed (Tree a) where
  ix :: Index (Tree a) -> Traversal' (Tree a) (IxValue (Tree a))
ix Index (Tree a)
xs0 IxValue (Tree a) -> f (IxValue (Tree a))
f = [Key] -> Tree a -> f (Tree a)
go Index (Tree a)
xs0 where
    go :: [Key] -> Tree a -> f (Tree a)
go [] (Node a
a [Tree a]
as) = IxValue (Tree a) -> f (IxValue (Tree a))
f a
a forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
a' -> forall a. a -> [Tree a] -> Tree a
Node a
a' [Tree a]
as
    go (Key
i:[Key]
is) t :: Tree a
t@(Node a
a [Tree a]
as)
      | Key
i forall a. Ord a => a -> a -> Bool
< Key
0     = forall (f :: * -> *) a. Applicative f => a -> f a
pure Tree a
t
      | Bool
otherwise = forall a. a -> [Tree a] -> Tree a
Node a
a forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall m. Ixed m => Index m -> Traversal' m (IxValue m)
ix Key
i ([Key] -> Tree a -> f (Tree a)
go [Key]
is) [Tree a]
as
  {-# INLINE ix #-}

type instance IxValue (Seq a) = a
instance Ixed (Seq a) where
  ix :: Index (Seq a) -> Traversal' (Seq a) (IxValue (Seq a))
ix Index (Seq a)
i IxValue (Seq a) -> f (IxValue (Seq a))
f Seq a
m
    | Key
0 forall a. Ord a => a -> a -> Bool
<= Index (Seq a)
i Bool -> Bool -> Bool
&& Index (Seq a)
i forall a. Ord a => a -> a -> Bool
< forall a. Seq a -> Key
Seq.length Seq a
m = IxValue (Seq a) -> f (IxValue (Seq a))
f (forall a. Seq a -> Key -> a
Seq.index Seq a
m Index (Seq a)
i) forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
a -> forall a. Key -> a -> Seq a -> Seq a
Seq.update Index (Seq a)
i a
a Seq a
m
    | Bool
otherwise                  = forall (f :: * -> *) a. Applicative f => a -> f a
pure Seq a
m
  {-# INLINE ix #-}

type instance IxValue (IntMap a) = a
instance Ixed (IntMap a) where
  ix :: Index (IntMap a) -> Traversal' (IntMap a) (IxValue (IntMap a))
ix Index (IntMap a)
k IxValue (IntMap a) -> f (IxValue (IntMap a))
f IntMap a
m = case forall a. Key -> IntMap a -> Maybe a
IntMap.lookup Index (IntMap a)
k IntMap a
m of
     Just a
v -> IxValue (IntMap a) -> f (IxValue (IntMap a))
f a
v forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
v' -> forall a. Key -> a -> IntMap a -> IntMap a
IntMap.insert Index (IntMap a)
k a
v' IntMap a
m
     Maybe a
Nothing -> forall (f :: * -> *) a. Applicative f => a -> f a
pure IntMap a
m
  {-# INLINE ix #-}

type instance IxValue (Map k a) = a
instance Ord k => Ixed (Map k a) where
  ix :: Index (Map k a) -> Traversal' (Map k a) (IxValue (Map k a))
ix Index (Map k a)
k IxValue (Map k a) -> f (IxValue (Map k a))
f Map k a
m = case forall k a. Ord k => k -> Map k a -> Maybe a
Map.lookup Index (Map k a)
k Map k a
m of
     Just a
v  -> IxValue (Map k a) -> f (IxValue (Map k a))
f a
v forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
v' -> forall k a. Ord k => k -> a -> Map k a -> Map k a
Map.insert Index (Map k a)
k a
v' Map k a
m
     Maybe a
Nothing -> forall (f :: * -> *) a. Applicative f => a -> f a
pure Map k a
m
  {-# INLINE ix #-}

type instance IxValue (HashMap k a) = a
instance (Eq k, Hashable k) => Ixed (HashMap k a) where
  ix :: Index (HashMap k a)
-> Traversal' (HashMap k a) (IxValue (HashMap k a))
ix Index (HashMap k a)
k IxValue (HashMap k a) -> f (IxValue (HashMap k a))
f HashMap k a
m = case forall k v. (Eq k, Hashable k) => k -> HashMap k v -> Maybe v
HashMap.lookup Index (HashMap k a)
k HashMap k a
m of
     Just a
v  -> IxValue (HashMap k a) -> f (IxValue (HashMap k a))
f a
v forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
v' -> forall k v.
(Eq k, Hashable k) =>
k -> v -> HashMap k v -> HashMap k v
HashMap.insert Index (HashMap k a)
k a
v' HashMap k a
m
     Maybe a
Nothing -> forall (f :: * -> *) a. Applicative f => a -> f a
pure HashMap k a
m
  {-# INLINE ix #-}

type instance IxValue (Set k) = ()
instance Ord k => Ixed (Set k) where
  ix :: Index (Set k) -> Traversal' (Set k) (IxValue (Set k))
ix Index (Set k)
k IxValue (Set k) -> f (IxValue (Set k))
f Set k
m = if forall a. Ord a => a -> Set a -> Bool
Set.member Index (Set k)
k Set k
m
     then IxValue (Set k) -> f (IxValue (Set k))
f () forall (f :: * -> *) a b. Functor f => f a -> b -> f b
$> Set k
m
     else forall (f :: * -> *) a. Applicative f => a -> f a
pure Set k
m
  {-# INLINE ix #-}

type instance IxValue IntSet = ()
instance Ixed IntSet where
  ix :: Index IntSet -> Traversal' IntSet (IxValue IntSet)
ix Index IntSet
k IxValue IntSet -> f (IxValue IntSet)
f IntSet
m = if Key -> IntSet -> Bool
IntSet.member Index IntSet
k IntSet
m
     then IxValue IntSet -> f (IxValue IntSet)
f () forall (f :: * -> *) a b. Functor f => f a -> b -> f b
$> IntSet
m
     else forall (f :: * -> *) a. Applicative f => a -> f a
pure IntSet
m
  {-# INLINE ix #-}

type instance IxValue (HashSet k) = ()
instance (Eq k, Hashable k) => Ixed (HashSet k) where
  ix :: Index (HashSet k) -> Traversal' (HashSet k) (IxValue (HashSet k))
ix Index (HashSet k)
k IxValue (HashSet k) -> f (IxValue (HashSet k))
f HashSet k
m = if forall a. (Eq a, Hashable a) => a -> HashSet a -> Bool
HashSet.member Index (HashSet k)
k HashSet k
m
     then IxValue (HashSet k) -> f (IxValue (HashSet k))
f () forall (f :: * -> *) a b. Functor f => f a -> b -> f b
$> HashSet k
m
     else forall (f :: * -> *) a. Applicative f => a -> f a
pure HashSet k
m
  {-# INLINE ix #-}

type instance IxValue (Array.Array i e) = e
-- |

-- @

-- arr '!' i ≡ arr 'Control.Lens.Getter.^.' 'ix' i

-- arr '//' [(i,e)] ≡ 'ix' i 'Control.Lens.Setter..~' e '$' arr

-- @

instance Ix i => Ixed (Array.Array i e) where
  ix :: Index (Array i e) -> Traversal' (Array i e) (IxValue (Array i e))
ix Index (Array i e)
i IxValue (Array i e) -> f (IxValue (Array i e))
f Array i e
arr
    | forall a. Ix a => (a, a) -> a -> Bool
inRange (forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> (i, i)
bounds Array i e
arr) Index (Array i e)
i = IxValue (Array i e) -> f (IxValue (Array i e))
f (Array i e
arr forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> i -> e
Array.! Index (Array i e)
i) forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \e
e -> Array i e
arr forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> [(i, e)] -> a i e
Array.// [(Index (Array i e)
i,e
e)]
    | Bool
otherwise              = forall (f :: * -> *) a. Applicative f => a -> f a
pure Array i e
arr
  {-# INLINE ix #-}

type instance IxValue (UArray i e) = e
-- |

-- @

-- arr '!' i ≡ arr 'Control.Lens.Getter.^.' 'ix' i

-- arr '//' [(i,e)] ≡ 'ix' i 'Control.Lens.Setter..~' e '$' arr

-- @

instance (IArray UArray e, Ix i) => Ixed (UArray i e) where
  ix :: Index (UArray i e)
-> Traversal' (UArray i e) (IxValue (UArray i e))
ix Index (UArray i e)
i IxValue (UArray i e) -> f (IxValue (UArray i e))
f UArray i e
arr
    | forall a. Ix a => (a, a) -> a -> Bool
inRange (forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> (i, i)
bounds UArray i e
arr) Index (UArray i e)
i = IxValue (UArray i e) -> f (IxValue (UArray i e))
f (UArray i e
arr forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> i -> e
Array.! Index (UArray i e)
i) forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \e
e -> UArray i e
arr forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> [(i, e)] -> a i e
Array.// [(Index (UArray i e)
i,e
e)]
    | Bool
otherwise              = forall (f :: * -> *) a. Applicative f => a -> f a
pure UArray i e
arr
  {-# INLINE ix #-}

type instance IxValue (Vector.Vector a) = a
instance Ixed (Vector.Vector a) where
  ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a))
ix Index (Vector a)
i IxValue (Vector a) -> f (IxValue (Vector a))
f Vector a
v
    | Key
0 forall a. Ord a => a -> a -> Bool
<= Index (Vector a)
i Bool -> Bool -> Bool
&& Index (Vector a)
i forall a. Ord a => a -> a -> Bool
< forall a. Vector a -> Key
Vector.length Vector a
v = IxValue (Vector a) -> f (IxValue (Vector a))
f (Vector a
v forall a. Vector a -> Key -> a
Vector.! Index (Vector a)
i) forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
a -> Vector a
v forall a. Vector a -> [(Key, a)] -> Vector a
Vector.// [(Index (Vector a)
i, a
a)]
    | Bool
otherwise                     = forall (f :: * -> *) a. Applicative f => a -> f a
pure Vector a
v
  {-# INLINE ix #-}

type instance IxValue (Prim.Vector a) = a
instance Prim a => Ixed (Prim.Vector a) where
  ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a))
ix Index (Vector a)
i IxValue (Vector a) -> f (IxValue (Vector a))
f Vector a
v
    | Key
0 forall a. Ord a => a -> a -> Bool
<= Index (Vector a)
i Bool -> Bool -> Bool
&& Index (Vector a)
i forall a. Ord a => a -> a -> Bool
< forall a. Prim a => Vector a -> Key
Prim.length Vector a
v = IxValue (Vector a) -> f (IxValue (Vector a))
f (Vector a
v forall a. Prim a => Vector a -> Key -> a
Prim.! Index (Vector a)
i) forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
a -> Vector a
v forall a. Prim a => Vector a -> [(Key, a)] -> Vector a
Prim.// [(Index (Vector a)
i, a
a)]
    | Bool
otherwise                   = forall (f :: * -> *) a. Applicative f => a -> f a
pure Vector a
v
  {-# INLINE ix #-}

type instance IxValue (Storable.Vector a) = a
instance Storable a => Ixed (Storable.Vector a) where
  ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a))
ix Index (Vector a)
i IxValue (Vector a) -> f (IxValue (Vector a))
f Vector a
v
    | Key
0 forall a. Ord a => a -> a -> Bool
<= Index (Vector a)
i Bool -> Bool -> Bool
&& Index (Vector a)
i forall a. Ord a => a -> a -> Bool
< forall a. Storable a => Vector a -> Key
Storable.length Vector a
v = IxValue (Vector a) -> f (IxValue (Vector a))
f (Vector a
v forall a. Storable a => Vector a -> Key -> a
Storable.! Index (Vector a)
i) forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
a -> Vector a
v forall a. Storable a => Vector a -> [(Key, a)] -> Vector a
Storable.// [(Index (Vector a)
i, a
a)]
    | Bool
otherwise                       = forall (f :: * -> *) a. Applicative f => a -> f a
pure Vector a
v
  {-# INLINE ix #-}

type instance IxValue (Unboxed.Vector a) = a
instance Unbox a => Ixed (Unboxed.Vector a) where
  ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a))
ix Index (Vector a)
i IxValue (Vector a) -> f (IxValue (Vector a))
f Vector a
v
    | Key
0 forall a. Ord a => a -> a -> Bool
<= Index (Vector a)
i Bool -> Bool -> Bool
&& Index (Vector a)
i forall a. Ord a => a -> a -> Bool
< forall a. Unbox a => Vector a -> Key
Unboxed.length Vector a
v = IxValue (Vector a) -> f (IxValue (Vector a))
f (Vector a
v forall a. Unbox a => Vector a -> Key -> a
Unboxed.! Index (Vector a)
i) forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \a
a -> Vector a
v forall a. Unbox a => Vector a -> [(Key, a)] -> Vector a
Unboxed.// [(Index (Vector a)
i, a
a)]
    | Bool
otherwise                      = forall (f :: * -> *) a. Applicative f => a -> f a
pure Vector a
v
  {-# INLINE ix #-}

type instance IxValue StrictT.Text = Char
instance Ixed StrictT.Text where
  ix :: Index Text -> Traversal' Text (IxValue Text)
ix Index Text
e IxValue Text -> f (IxValue Text)
f Text
s 
      | Index Text
e forall a. Ord a => a -> a -> Bool
< Key
0 = forall (f :: * -> *) a. Applicative f => a -> f a
pure Text
s
      | Bool
otherwise = case Key -> Text -> (Text, Text)
StrictT.splitAt Index Text
e Text
s of
            (Text
l, Text
mr) -> case Text -> Maybe (Char, Text)
StrictT.uncons Text
mr of
                Maybe (Char, Text)
Nothing      -> forall (f :: * -> *) a. Applicative f => a -> f a
pure Text
s
                Just (Char
c, Text
xs) -> IxValue Text -> f (IxValue Text)
f Char
c forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \Char
d -> [Text] -> Text
StrictT.concat [Text
l, Char -> Text
StrictT.singleton Char
d, Text
xs]
  {-# INLINE ix #-}

type instance IxValue LazyT.Text = Char
instance Ixed LazyT.Text where
  ix :: Index Text -> Traversal' Text (IxValue Text)
ix Index Text
e IxValue Text -> f (IxValue Text)
f Text
s 
        | Index Text
e forall a. Ord a => a -> a -> Bool
< Int64
0 = forall (f :: * -> *) a. Applicative f => a -> f a
pure Text
s
        | Bool
otherwise = case Int64 -> Text -> (Text, Text)
LazyT.splitAt Index Text
e Text
s of
            (Text
l, Text
mr) -> case Text -> Maybe (Char, Text)
LazyT.uncons Text
mr of
              Maybe (Char, Text)
Nothing      -> forall (f :: * -> *) a. Applicative f => a -> f a
pure Text
s
              Just (Char
c, Text
xs) -> IxValue Text -> f (IxValue Text)
f Char
c forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \Char
d -> Text -> Text -> Text
LazyT.append Text
l (Char -> Text -> Text
LazyT.cons Char
d Text
xs)
  {-# INLINE ix #-}

type instance IxValue StrictB.ByteString = Word8
instance Ixed StrictB.ByteString where
  ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString)
ix Index ByteString
e IxValue ByteString -> f (IxValue ByteString)
f ByteString
s 
        | Index ByteString
e forall a. Ord a => a -> a -> Bool
< Key
0 = forall (f :: * -> *) a. Applicative f => a -> f a
pure ByteString
s
        | Bool
otherwise = case Key -> ByteString -> (ByteString, ByteString)
StrictB.splitAt Index ByteString
e ByteString
s of
          (ByteString
l, ByteString
mr) -> case ByteString -> Maybe (Word8, ByteString)
StrictB.uncons ByteString
mr of
            Maybe (Word8, ByteString)
Nothing      -> forall (f :: * -> *) a. Applicative f => a -> f a
pure ByteString
s
            Just (Word8
c, ByteString
xs) -> IxValue ByteString -> f (IxValue ByteString)
f Word8
c forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \Word8
d -> [ByteString] -> ByteString
StrictB.concat [ByteString
l, Word8 -> ByteString
StrictB.singleton Word8
d, ByteString
xs]
  {-# INLINE ix #-}

type instance IxValue LazyB.ByteString = Word8
instance Ixed LazyB.ByteString where
  -- TODO: we could be lazier, returning each chunk as it is passed

  ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString)
ix Index ByteString
e IxValue ByteString -> f (IxValue ByteString)
f ByteString
s 
        | Index ByteString
e forall a. Ord a => a -> a -> Bool
< Int64
0 = forall (f :: * -> *) a. Applicative f => a -> f a
pure ByteString
s
        | Bool
otherwise =  case Int64 -> ByteString -> (ByteString, ByteString)
LazyB.splitAt Index ByteString
e ByteString
s of
          (ByteString
l, ByteString
mr) -> case ByteString -> Maybe (Word8, ByteString)
LazyB.uncons ByteString
mr of
            Maybe (Word8, ByteString)
Nothing      -> forall (f :: * -> *) a. Applicative f => a -> f a
pure ByteString
s
            Just (Word8
c, ByteString
xs) -> IxValue ByteString -> f (IxValue ByteString)
f Word8
c forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> \Word8
d -> ByteString -> ByteString -> ByteString
LazyB.append ByteString
l (Word8 -> ByteString -> ByteString
LazyB.cons Word8
d ByteString
xs)
  {-# INLINE ix #-}



-- | 'At' provides a 'Lens' that can be used to read,

-- write or delete the value associated with a key in a 'Map'-like

-- container on an ad hoc basis.

--

-- An instance of 'At' should satisfy:

--

-- @

-- 'ix' k ≡ 'at' k '.' 'traverse'

-- @

class Ixed m => At m where
  -- |

  -- >>> Map.fromList [(1,"world")] ^.at 1

  -- Just "world"

  --

  -- >>> at 1 ?~ "hello" $ Map.empty

  -- fromList [(1,"hello")]

  --

  -- /Note:/ 'Map'-like containers form a reasonable instance, but not 'Array'-like ones, where

  -- you cannot satisfy the 'Lens' laws.

  at :: Index m -> Lens' m (Maybe (IxValue m))

-- | Delete the value associated with a key in a 'Map'-like container

--

-- @

-- 'sans' k = 'at' k .~ Nothing

-- @

sans :: At m => Index m -> m -> m
sans :: forall m. At m => Index m -> m -> m
sans Index m
k m
m = m
m forall a b. a -> (a -> b) -> b
& forall m. At m => Index m -> Lens' m (Maybe (IxValue m))
at Index m
k forall s t a b. ASetter s t a b -> b -> s -> t
.~ forall a. Maybe a
Nothing
{-# INLINE sans #-}

-- | An indexed version of 'at'.

--

-- >>> Map.fromList [(1,"world")] ^@. iat 1

-- (1,Just "world")

--

-- >>> iat 1 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.empty

-- fromList [(1,"hello")]

--

-- >>> iat 2 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.empty

-- fromList []

--

iat :: At m => Index m -> IndexedLens' (Index m) m (Maybe (IxValue m))
iat :: forall m.
At m =>
Index m -> IndexedLens' (Index m) m (Maybe (IxValue m))
iat Index m
i p (Maybe (IxValue m)) (f (Maybe (IxValue m)))
f = forall m. At m => Index m -> Lens' m (Maybe (IxValue m))
at Index m
i (forall i (p :: * -> * -> *) a b.
Indexable i p =>
p a b -> i -> a -> b
indexed p (Maybe (IxValue m)) (f (Maybe (IxValue m)))
f Index m
i)
{-# INLINE iat #-}

instance At (Maybe a) where
  at :: Index (Maybe a) -> Lens' (Maybe a) (Maybe (IxValue (Maybe a)))
at ~() Maybe (IxValue (Maybe a)) -> f (Maybe (IxValue (Maybe a)))
f = Maybe (IxValue (Maybe a)) -> f (Maybe (IxValue (Maybe a)))
f
  {-# INLINE at #-}

instance At (IntMap a) where
#if MIN_VERSION_containers(0,5,8)
  at :: Index (IntMap a) -> Lens' (IntMap a) (Maybe (IxValue (IntMap a)))
at Index (IntMap a)
k Maybe (IxValue (IntMap a)) -> f (Maybe (IxValue (IntMap a)))
f = forall (f :: * -> *) a.
Functor f =>
(Maybe a -> f (Maybe a)) -> Key -> IntMap a -> f (IntMap a)
IntMap.alterF Maybe (IxValue (IntMap a)) -> f (Maybe (IxValue (IntMap a)))
f Index (IntMap a)
k
#else
  at k f m = f mv <&> \r -> case r of
    Nothing -> maybe m (const (IntMap.delete k m)) mv
    Just v' -> IntMap.insert k v' m
    where mv = IntMap.lookup k m
#endif
  {-# INLINE at #-}

instance Ord k => At (Map k a) where
#if MIN_VERSION_containers(0,5,8)
  at :: Index (Map k a) -> Lens' (Map k a) (Maybe (IxValue (Map k a)))
at Index (Map k a)
k Maybe (IxValue (Map k a)) -> f (Maybe (IxValue (Map k a)))
f = forall (f :: * -> *) k a.
(Functor f, Ord k) =>
(Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)
Map.alterF Maybe (IxValue (Map k a)) -> f (Maybe (IxValue (Map k a)))
f Index (Map k a)
k
#else
  at k f m = f mv <&> \r -> case r of
    Nothing -> maybe m (const (Map.delete k m)) mv
    Just v' -> Map.insert k v' m
    where mv = Map.lookup k m
#endif
  {-# INLINE at #-}

instance (Eq k, Hashable k) => At (HashMap k a) where
  at :: Index (HashMap k a)
-> Lens' (HashMap k a) (Maybe (IxValue (HashMap k a)))
at Index (HashMap k a)
k Maybe (IxValue (HashMap k a)) -> f (Maybe (IxValue (HashMap k a)))
f = forall (f :: * -> *) k v.
(Functor f, Eq k, Hashable k) =>
(Maybe v -> f (Maybe v)) -> k -> HashMap k v -> f (HashMap k v)
HashMap.alterF Maybe (IxValue (HashMap k a)) -> f (Maybe (IxValue (HashMap k a)))
f Index (HashMap k a)
k
  {-# INLINE at #-}

instance At IntSet where
  -- This is a gently modified copy of the implementation of `IntSet.alterF`.

  -- Unlike a `Set`, we don't have to worry about expensive comparisons from

  -- descending multiple times into an `IntSet`. We are careful to share the

  -- results of insertion or deletion across multiple positions in the

  -- `Functor`.

  at :: Index IntSet -> Lens' IntSet (Maybe (IxValue IntSet))
at Index IntSet
k Maybe (IxValue IntSet) -> f (Maybe (IxValue IntSet))
f IntSet
s = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Maybe () -> IntSet
choose (Maybe (IxValue IntSet) -> f (Maybe (IxValue IntSet))
f (forall (f :: * -> *). Alternative f => Bool -> f ()
guard Bool
member_))
    where
      member_ :: Bool
member_ = Key -> IntSet -> Bool
IntSet.member Index IntSet
k IntSet
s

      (IntSet
inserted, IntSet
deleted)
        | Bool
member_   = (IntSet
s, Key -> IntSet -> IntSet
IntSet.delete Index IntSet
k IntSet
s)
        | Bool
otherwise = (Key -> IntSet -> IntSet
IntSet.insert Index IntSet
k IntSet
s, IntSet
s)

      choose :: Maybe () -> IntSet
choose (Just ~()) = IntSet
inserted
      choose Maybe ()
Nothing = IntSet
deleted
  {-# INLINE at #-}

instance Ord k => At (Set k) where
#if MIN_VERSION_containers(0,6,3)
  at :: Index (Set k) -> Lens' (Set k) (Maybe (IxValue (Set k)))
at Index (Set k)
k Maybe (IxValue (Set k)) -> f (Maybe (IxValue (Set k)))
f = forall a (f :: * -> *).
(Ord a, Functor f) =>
(Bool -> f Bool) -> a -> Set a -> f (Set a)
Set.alterF (forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. Maybe a -> Bool
isJust forall b c a. (b -> c) -> (a -> b) -> a -> c
. Maybe (IxValue (Set k)) -> f (Maybe (IxValue (Set k)))
f forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *). Alternative f => Bool -> f ()
guard) Index (Set k)
k
#else
  at k f m = f mv <&> \r -> case r of
    Nothing -> maybe m (const (Set.delete k m)) mv
    Just ~() -> maybe (Set.insert k m) (const m) mv
    where mv = if Set.member k m then Just () else Nothing
#endif
  {-# INLINE at #-}

instance (Eq k, Hashable k) => At (HashSet k) where
  at :: Index (HashSet k)
-> Lens' (HashSet k) (Maybe (IxValue (HashSet k)))
at Index (HashSet k)
k Maybe (IxValue (HashSet k)) -> f (Maybe (IxValue (HashSet k)))
f HashSet k
s = forall a. HashMap a () -> HashSet a
HashSet.fromMap forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall (f :: * -> *) k v.
(Functor f, Eq k, Hashable k) =>
(Maybe v -> f (Maybe v)) -> k -> HashMap k v -> f (HashMap k v)
HashMap.alterF Maybe (IxValue (HashSet k)) -> f (Maybe (IxValue (HashSet k)))
f Index (HashSet k)
k (forall a. HashSet a -> HashMap a ()
HashSet.toMap HashSet k
s)
  {-# INLINE at #-}


-- | @'ix' :: 'Int' -> 'Traversal'' (a,a) a@

type instance IxValue (a,a2) = a
instance (a~a2) => Ixed (a,a2) where
  ix :: Index (a, a2) -> Traversal' (a, a2) (IxValue (a, a2))
ix Index (a, a2)
p = forall (f :: * -> *) s t a.
Applicative f =>
LensLike (Indexing f) s t a a
-> Key -> IndexedLensLike Key f s t a a
elementOf forall s t a b. Each s t a b => Traversal s t a b
each Index (a, a2)
p

-- | @'ix' :: 'Int' -> 'Traversal'' (a,a,a) a@

type instance IxValue (a,a2,a3) = a
instance (a~a2, a~a3) => Ixed (a,a2,a3) where
  ix :: Index (a, a2, a3) -> Traversal' (a, a2, a3) (IxValue (a, a2, a3))
ix Index (a, a2, a3)
p = forall (f :: * -> *) s t a.
Applicative f =>
LensLike (Indexing f) s t a a
-> Key -> IndexedLensLike Key f s t a a
elementOf forall s t a b. Each s t a b => Traversal s t a b
each Index (a, a2, a3)
p

-- | @'ix' :: 'Int' -> 'Traversal'' (a,a,a,a) a@

type instance IxValue (a,a2,a3,a4) = a
instance (a~a2, a~a3, a~a4) => Ixed (a,a2,a3,a4) where
  ix :: Index (a, a2, a3, a4)
-> Traversal' (a, a2, a3, a4) (IxValue (a, a2, a3, a4))
ix Index (a, a2, a3, a4)
p = forall (f :: * -> *) s t a.
Applicative f =>
LensLike (Indexing f) s t a a
-> Key -> IndexedLensLike Key f s t a a
elementOf forall s t a b. Each s t a b => Traversal s t a b
each Index (a, a2, a3, a4)
p

-- | @'ix' :: 'Int' -> 'Traversal'' (a,a,a,a,a) a@

type instance IxValue (a,a2,a3,a4,a5) = a
instance (a~a2, a~a3, a~a4, a~a5) => Ixed (a,a2,a3,a4,a5) where
  ix :: Index (a, a2, a3, a4, a5)
-> Traversal' (a, a2, a3, a4, a5) (IxValue (a, a2, a3, a4, a5))
ix Index (a, a2, a3, a4, a5)
p = forall (f :: * -> *) s t a.
Applicative f =>
LensLike (Indexing f) s t a a
-> Key -> IndexedLensLike Key f s t a a
elementOf forall s t a b. Each s t a b => Traversal s t a b
each Index (a, a2, a3, a4, a5)
p

-- | @'ix' :: 'Int' -> 'Traversal'' (a,a,a,a,a,a) a@

type instance IxValue (a,a2,a3,a4,a5,a6) = a
instance (a~a2, a~a3, a~a4, a~a5, a~a6) => Ixed (a,a2,a3,a4,a5,a6) where
  ix :: Index (a, a2, a3, a4, a5, a6)
-> Traversal'
     (a, a2, a3, a4, a5, a6) (IxValue (a, a2, a3, a4, a5, a6))
ix Index (a, a2, a3, a4, a5, a6)
p = forall (f :: * -> *) s t a.
Applicative f =>
LensLike (Indexing f) s t a a
-> Key -> IndexedLensLike Key f s t a a
elementOf forall s t a b. Each s t a b => Traversal s t a b
each Index (a, a2, a3, a4, a5, a6)
p

-- | @'ix' :: 'Int' -> 'Traversal'' (a,a,a,a,a,a,a) a@

type instance IxValue (a,a2,a3,a4,a5,a6,a7) = a
instance (a~a2, a~a3, a~a4, a~a5, a~a6, a~a7) => Ixed (a,a2,a3,a4,a5,a6,a7) where
  ix :: Index (a, a2, a3, a4, a5, a6, a7)
-> Traversal'
     (a, a2, a3, a4, a5, a6, a7) (IxValue (a, a2, a3, a4, a5, a6, a7))
ix Index (a, a2, a3, a4, a5, a6, a7)
p = forall (f :: * -> *) s t a.
Applicative f =>
LensLike (Indexing f) s t a a
-> Key -> IndexedLensLike Key f s t a a
elementOf forall s t a b. Each s t a b => Traversal s t a b
each Index (a, a2, a3, a4, a5, a6, a7)
p

-- | @'ix' :: 'Int' -> 'Traversal'' (a,a,a,a,a,a,a,a) a@

type instance IxValue (a,a2,a3,a4,a5,a6,a7,a8) = a
instance (a~a2, a~a3, a~a4, a~a5, a~a6, a~a7, a~a8) => Ixed (a,a2,a3,a4,a5,a6,a7,a8) where
  ix :: Index (a, a2, a3, a4, a5, a6, a7, a8)
-> Traversal'
     (a, a2, a3, a4, a5, a6, a7, a8)
     (IxValue (a, a2, a3, a4, a5, a6, a7, a8))
ix Index (a, a2, a3, a4, a5, a6, a7, a8)
p = forall (f :: * -> *) s t a.
Applicative f =>
LensLike (Indexing f) s t a a
-> Key -> IndexedLensLike Key f s t a a
elementOf forall s t a b. Each s t a b => Traversal s t a b
each Index (a, a2, a3, a4, a5, a6, a7, a8)
p

-- | @'ix' :: 'Int' -> 'Traversal'' (a,a,a,a,a,a,a,a,a) a@

type instance IxValue (a,a2,a3,a4,a5,a6,a7,a8,a9) = a
instance (a~a2, a~a3, a~a4, a~a5, a~a6, a~a7, a~a8, a~a9) => Ixed (a,a2,a3,a4,a5,a6,a7,a8,a9) where
  ix :: Index (a, a2, a3, a4, a5, a6, a7, a8, a9)
-> Traversal'
     (a, a2, a3, a4, a5, a6, a7, a8, a9)
     (IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9))
ix Index (a, a2, a3, a4, a5, a6, a7, a8, a9)
p = forall (f :: * -> *) s t a.
Applicative f =>
LensLike (Indexing f) s t a a
-> Key -> IndexedLensLike Key f s t a a
elementOf forall s t a b. Each s t a b => Traversal s t a b
each Index (a, a2, a3, a4, a5, a6, a7, a8, a9)
p