{-# LANGUAGE CPP #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
#if __GLASGOW_HASKELL__ >= 702
{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE DefaultSignatures #-}
#endif
#if __GLASGOW_HASKELL__ >= 706
{-# LANGUAGE PolyKinds #-}
#endif
module WithIndex where
import Prelude
(Either (..), Functor (..), Int, Maybe (..), Monad (..), Num (..), error,
flip, id, seq, snd, ($!), ($), (.), zip)
import Control.Applicative
(Applicative (..), Const (..), ZipList (..), (<$>))
import Control.Applicative.Backwards (Backwards (..))
import Control.Monad.Trans.Identity (IdentityT (..))
import Control.Monad.Trans.Reader (ReaderT (..))
import Data.Array (Array)
import Data.Foldable (Foldable (..))
import Data.Functor.Compose (Compose (..))
import Data.Functor.Constant (Constant (..))
import Data.Functor.Identity (Identity (..))
import Data.Functor.Product (Product (..))
import Data.Functor.Reverse (Reverse (..))
import Data.Functor.Sum (Sum (..))
import Data.IntMap (IntMap)
import Data.Ix (Ix (..))
import Data.List.NonEmpty (NonEmpty (..))
import Data.Map (Map)
import Data.Monoid (Dual (..), Endo (..), Monoid (..))
import Data.Proxy (Proxy (..))
import Data.Semigroup (Semigroup (..))
import Data.Sequence (Seq)
import Data.Traversable (Traversable (..))
import Data.Tree (Tree (..))
import Data.Void (Void)
#if __GLASGOW_HASKELL__ >= 702
import GHC.Generics
(K1 (..), Par1 (..), Rec1 (..), U1 (..), V1, (:*:) (..), (:+:) (..),
(:.:) (..))
#else
import Generics.Deriving
(K1 (..), Par1 (..), Rec1 (..), U1 (..), V1, (:*:) (..), (:+:) (..),
(:.:) (..))
#endif
import qualified Data.Array as Array
import qualified Data.IntMap as IntMap
import qualified Data.Map as Map
import qualified Data.Sequence as Seq
#ifdef MIN_VERSION_base_orphans
import Data.Orphans ()
#endif
#if __GLASGOW_HASKELL__ >=708
import Data.Coerce (Coercible, coerce)
#else
import Unsafe.Coerce (unsafeCoerce)
#endif
class Functor f => FunctorWithIndex i f | f -> i where
imap :: (i -> a -> b) -> f a -> f b
#if __GLASGOW_HASKELL__ >= 704
default imap :: TraversableWithIndex i f => (i -> a -> b) -> f a -> f b
imap = (i -> a -> b) -> f a -> f b
forall i (f :: * -> *) a b.
TraversableWithIndex i f =>
(i -> a -> b) -> f a -> f b
imapDefault
{-# INLINE imap #-}
#endif
imapDefault :: TraversableWithIndex i f => (i -> a -> b) -> f a -> f b
imapDefault :: (i -> a -> b) -> f a -> f b
imapDefault i -> a -> b
f = Identity (f b) -> f b
forall a. Identity a -> a
runIdentity (Identity (f b) -> f b) -> (f a -> Identity (f b)) -> f a -> f b
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (i -> a -> Identity b) -> f a -> Identity (f b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (\i
i a
a -> b -> Identity b
forall a. a -> Identity a
Identity (i -> a -> b
f i
i a
a))
{-# INLINE imapDefault #-}
class Foldable f => FoldableWithIndex i f | f -> i where
ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m
#if __GLASGOW_HASKELL__ >= 704
default ifoldMap :: (TraversableWithIndex i f, Monoid m) => (i -> a -> m) -> f a -> m
ifoldMap = (i -> a -> m) -> f a -> m
forall i (f :: * -> *) m a.
(TraversableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMapDefault
{-# INLINE ifoldMap #-}
#endif
ifoldMap' :: Monoid m => (i -> a -> m) -> f a -> m
ifoldMap' i -> a -> m
f = (i -> m -> a -> m) -> m -> f a -> m
forall i (f :: * -> *) b a.
FoldableWithIndex i f =>
(i -> b -> a -> b) -> b -> f a -> b
ifoldl' (\i
i m
acc a
a -> m -> m -> m
forall a. Monoid a => a -> a -> a
mappend m
acc (i -> a -> m
f i
i a
a)) m
forall a. Monoid a => a
mempty
{-# INLINE ifoldMap' #-}
ifoldr :: (i -> a -> b -> b) -> b -> f a -> b
ifoldr i -> a -> b -> b
f b
z f a
t = Endo b -> b -> b
forall a. Endo a -> a -> a
appEndo ((i -> a -> Endo b) -> f a -> Endo b
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (\i
i -> (b -> b) -> Endo b
forall a. (a -> a) -> Endo a
Endo ((b -> b) -> Endo b) -> (a -> b -> b) -> a -> Endo b
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. i -> a -> b -> b
f i
i) f a
t) b
z
{-# INLINE ifoldr #-}
ifoldl :: (i -> b -> a -> b) -> b -> f a -> b
ifoldl i -> b -> a -> b
f b
z f a
t = Endo b -> b -> b
forall a. Endo a -> a -> a
appEndo (Dual (Endo b) -> Endo b
forall a. Dual a -> a
getDual ((i -> a -> Dual (Endo b)) -> f a -> Dual (Endo b)
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (\i
i -> Endo b -> Dual (Endo b)
forall a. a -> Dual a
Dual (Endo b -> Dual (Endo b)) -> (a -> Endo b) -> a -> Dual (Endo b)
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (b -> b) -> Endo b
forall a. (a -> a) -> Endo a
Endo ((b -> b) -> Endo b) -> (a -> b -> b) -> a -> Endo b
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (b -> a -> b) -> a -> b -> b
forall a b c. (a -> b -> c) -> b -> a -> c
flip (i -> b -> a -> b
f i
i)) f a
t)) b
z
{-# INLINE ifoldl #-}
ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b
ifoldr' i -> a -> b -> b
f b
z0 f a
xs = (i -> (b -> b) -> a -> b -> b) -> (b -> b) -> f a -> b -> b
forall i (f :: * -> *) b a.
FoldableWithIndex i f =>
(i -> b -> a -> b) -> b -> f a -> b
ifoldl i -> (b -> b) -> a -> b -> b
f' b -> b
forall a. a -> a
id f a
xs b
z0
where f' :: i -> (b -> b) -> a -> b -> b
f' i
i b -> b
k a
x b
z = b -> b
k (b -> b) -> b -> b
forall a b. (a -> b) -> a -> b
$! i -> a -> b -> b
f i
i a
x b
z
{-# INLINE ifoldr' #-}
ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b
ifoldl' i -> b -> a -> b
f b
z0 f a
xs = (i -> a -> (b -> b) -> b -> b) -> (b -> b) -> f a -> b -> b
forall i (f :: * -> *) a b.
FoldableWithIndex i f =>
(i -> a -> b -> b) -> b -> f a -> b
ifoldr i -> a -> (b -> b) -> b -> b
f' b -> b
forall a. a -> a
id f a
xs b
z0
where f' :: i -> a -> (b -> b) -> b -> b
f' i
i a
x b -> b
k b
z = b -> b
k (b -> b) -> b -> b
forall a b. (a -> b) -> a -> b
$! i -> b -> a -> b
f i
i b
z a
x
{-# INLINE ifoldl' #-}
ifoldMapDefault :: (TraversableWithIndex i f, Monoid m) => (i -> a -> m) -> f a -> m
ifoldMapDefault :: (i -> a -> m) -> f a -> m
ifoldMapDefault i -> a -> m
f = Const m (f Any) -> m
forall a k (b :: k). Const a b -> a
getConst (Const m (f Any) -> m) -> (f a -> Const m (f Any)) -> f a -> m
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. (i -> a -> Const m Any) -> f a -> Const m (f Any)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (\i
i a
a -> m -> Const m Any
forall k a (b :: k). a -> Const a b
Const (i -> a -> m
f i
i a
a))
{-# INLINE ifoldMapDefault #-}
class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i t | t -> i where
itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b)
#if __GLASGOW_HASKELL__ >= 704
default itraverse :: (i ~ Int, Applicative f) => (i -> a -> f b) -> t a -> f (t b)
itraverse i -> a -> f b
f t a
s = (Int, f (t b)) -> f (t b)
forall a b. (a, b) -> b
snd ((Int, f (t b)) -> f (t b)) -> (Int, f (t b)) -> f (t b)
forall a b. (a -> b) -> a -> b
$ Indexing f (t b) -> Int -> (Int, f (t b))
forall k (f :: k -> *) (a :: k). Indexing f a -> Int -> (Int, f a)
runIndexing ((a -> Indexing f b) -> t a -> Indexing f (t b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse (\a
a -> (Int -> (Int, f b)) -> Indexing f b
forall k (f :: k -> *) (a :: k).
(Int -> (Int, f a)) -> Indexing f a
Indexing (\Int
i -> Int
i Int -> (Int, f b) -> (Int, f b)
`seq` (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
1, i -> a -> f b
f i
Int
i a
a))) t a
s) Int
0
{-# INLINE itraverse #-}
#endif
instance FunctorWithIndex r ((->) r) where
imap :: (r -> a -> b) -> (r -> a) -> r -> b
imap r -> a -> b
f r -> a
g r
x = r -> a -> b
f r
x (r -> a
g r
x)
{-# INLINE imap #-}
instance FunctorWithIndex () Maybe where
imap :: (() -> a -> b) -> Maybe a -> Maybe b
imap () -> a -> b
f = (a -> b) -> Maybe a -> Maybe b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (() -> a -> b
f ())
{-# INLINE imap #-}
instance FoldableWithIndex () Maybe where
ifoldMap :: (() -> a -> m) -> Maybe a -> m
ifoldMap () -> a -> m
f = (a -> m) -> Maybe a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap (() -> a -> m
f ())
{-# INLINE ifoldMap #-}
instance TraversableWithIndex () Maybe where
itraverse :: (() -> a -> f b) -> Maybe a -> f (Maybe b)
itraverse () -> a -> f b
f = (a -> f b) -> Maybe a -> f (Maybe b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse (() -> a -> f b
f ())
{-# INLINE itraverse #-}
instance FunctorWithIndex Void Proxy where
imap :: (Void -> a -> b) -> Proxy a -> Proxy b
imap Void -> a -> b
_ Proxy a
Proxy = Proxy b
forall k (t :: k). Proxy t
Proxy
{-# INLINE imap #-}
instance FoldableWithIndex Void Proxy where
ifoldMap :: (Void -> a -> m) -> Proxy a -> m
ifoldMap Void -> a -> m
_ Proxy a
_ = m
forall a. Monoid a => a
mempty
{-# INLINE ifoldMap #-}
instance TraversableWithIndex Void Proxy where
itraverse :: (Void -> a -> f b) -> Proxy a -> f (Proxy b)
itraverse Void -> a -> f b
_ Proxy a
_ = Proxy b -> f (Proxy b)
forall (f :: * -> *) a. Applicative f => a -> f a
pure Proxy b
forall k (t :: k). Proxy t
Proxy
{-# INLINE itraverse #-}
instance FunctorWithIndex k ((,) k) where
imap :: (k -> a -> b) -> (k, a) -> (k, b)
imap k -> a -> b
f (k
k,a
a) = (k
k, k -> a -> b
f k
k a
a)
{-# INLINE imap #-}
instance FoldableWithIndex k ((,) k) where
ifoldMap :: (k -> a -> m) -> (k, a) -> m
ifoldMap = (k -> a -> m) -> (k, a) -> m
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry'
{-# INLINE ifoldMap #-}
instance TraversableWithIndex k ((,) k) where
itraverse :: (k -> a -> f b) -> (k, a) -> f (k, b)
itraverse k -> a -> f b
f (k
k, a
a) = (,) k
k (b -> (k, b)) -> f b -> f (k, b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> k -> a -> f b
f k
k a
a
{-# INLINE itraverse #-}
instance FunctorWithIndex Int [] where
imap :: (Int -> a -> b) -> [a] -> [b]
imap Int -> a -> b
f = Int -> [a] -> [b]
go Int
0 where
go :: Int -> [a] -> [b]
go !Int
_ [] = []
go !Int
n (a
x:[a]
xs) = Int -> a -> b
f Int
n a
x b -> [b] -> [b]
forall a. a -> [a] -> [a]
: Int -> [a] -> [b]
go (Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
1) [a]
xs
{-# INLINE imap #-}
instance FoldableWithIndex Int [] where
ifoldMap :: (Int -> a -> m) -> [a] -> m
ifoldMap = (Int -> a -> m) -> [a] -> m
forall i (f :: * -> *) m a.
(TraversableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMapDefault
{-# INLINE ifoldMap #-}
ifoldr :: (Int -> a -> b -> b) -> b -> [a] -> b
ifoldr Int -> a -> b -> b
f b
z = Int -> [a] -> b
go Int
0 where
go :: Int -> [a] -> b
go !Int
_ [] = b
z
go !Int
n (a
x:[a]
xs) = Int -> a -> b -> b
f Int
n a
x (Int -> [a] -> b
go (Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
1) [a]
xs)
{-# INLINE ifoldr #-}
instance TraversableWithIndex Int [] where
itraverse :: (Int -> a -> f b) -> [a] -> f [b]
itraverse Int -> a -> f b
f = ((Int, a) -> f b) -> [(Int, a)] -> f [b]
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse ((Int -> a -> f b) -> (Int, a) -> f b
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry' Int -> a -> f b
f) ([(Int, a)] -> f [b]) -> ([a] -> [(Int, a)]) -> [a] -> f [b]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Int] -> [a] -> [(Int, a)]
forall a b. [a] -> [b] -> [(a, b)]
zip [Int
0..]
{-# INLINE itraverse #-}
instance FunctorWithIndex Int ZipList where
imap :: (Int -> a -> b) -> ZipList a -> ZipList b
imap Int -> a -> b
f (ZipList [a]
xs) = [b] -> ZipList b
forall a. [a] -> ZipList a
ZipList ((Int -> a -> b) -> [a] -> [b]
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap Int -> a -> b
f [a]
xs)
{-# INLINE imap #-}
instance FoldableWithIndex Int ZipList where
ifoldMap :: (Int -> a -> m) -> ZipList a -> m
ifoldMap Int -> a -> m
f (ZipList [a]
xs) = (Int -> a -> m) -> [a] -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap Int -> a -> m
f [a]
xs
{-# INLINE ifoldMap #-}
instance TraversableWithIndex Int ZipList where
itraverse :: (Int -> a -> f b) -> ZipList a -> f (ZipList b)
itraverse Int -> a -> f b
f (ZipList [a]
xs) = [b] -> ZipList b
forall a. [a] -> ZipList a
ZipList ([b] -> ZipList b) -> f [b] -> f (ZipList b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (Int -> a -> f b) -> [a] -> f [b]
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse Int -> a -> f b
f [a]
xs
{-# INLINE itraverse #-}
instance FunctorWithIndex Int NonEmpty where
imap :: (Int -> a -> b) -> NonEmpty a -> NonEmpty b
imap = (Int -> a -> b) -> NonEmpty a -> NonEmpty b
forall i (f :: * -> *) a b.
TraversableWithIndex i f =>
(i -> a -> b) -> f a -> f b
imapDefault
{-# INLINE imap #-}
instance FoldableWithIndex Int NonEmpty where
ifoldMap :: (Int -> a -> m) -> NonEmpty a -> m
ifoldMap = (Int -> a -> m) -> NonEmpty a -> m
forall i (f :: * -> *) m a.
(TraversableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMapDefault
{-# INLINE ifoldMap #-}
instance TraversableWithIndex Int NonEmpty where
itraverse :: (Int -> a -> f b) -> NonEmpty a -> f (NonEmpty b)
itraverse Int -> a -> f b
f ~(a
a :| [a]
as) =
b -> [b] -> NonEmpty b
forall a. a -> [a] -> NonEmpty a
(:|) (b -> [b] -> NonEmpty b) -> f b -> f ([b] -> NonEmpty b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Int -> a -> f b
f Int
0 a
a f ([b] -> NonEmpty b) -> f [b] -> f (NonEmpty b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> ((Int, a) -> f b) -> [(Int, a)] -> f [b]
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse ((Int -> a -> f b) -> (Int, a) -> f b
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry' Int -> a -> f b
f) ([Int] -> [a] -> [(Int, a)]
forall a b. [a] -> [b] -> [(a, b)]
zip [Int
1..] [a]
as)
{-# INLINE itraverse #-}
instance FunctorWithIndex () Identity where
imap :: (() -> a -> b) -> Identity a -> Identity b
imap () -> a -> b
f (Identity a
a) = b -> Identity b
forall a. a -> Identity a
Identity (() -> a -> b
f () a
a)
{-# INLINE imap #-}
instance FoldableWithIndex () Identity where
ifoldMap :: (() -> a -> m) -> Identity a -> m
ifoldMap () -> a -> m
f (Identity a
a) = () -> a -> m
f () a
a
{-# INLINE ifoldMap #-}
instance TraversableWithIndex () Identity where
itraverse :: (() -> a -> f b) -> Identity a -> f (Identity b)
itraverse () -> a -> f b
f (Identity a
a) = b -> Identity b
forall a. a -> Identity a
Identity (b -> Identity b) -> f b -> f (Identity b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> () -> a -> f b
f () a
a
{-# INLINE itraverse #-}
instance FunctorWithIndex Void (Const e) where
imap :: (Void -> a -> b) -> Const e a -> Const e b
imap Void -> a -> b
_ (Const e
a) = e -> Const e b
forall k a (b :: k). a -> Const a b
Const e
a
{-# INLINE imap #-}
instance FoldableWithIndex Void (Const e) where
ifoldMap :: (Void -> a -> m) -> Const e a -> m
ifoldMap Void -> a -> m
_ Const e a
_ = m
forall a. Monoid a => a
mempty
{-# INLINE ifoldMap #-}
instance TraversableWithIndex Void (Const e) where
itraverse :: (Void -> a -> f b) -> Const e a -> f (Const e b)
itraverse Void -> a -> f b
_ (Const e
a) = Const e b -> f (Const e b)
forall (f :: * -> *) a. Applicative f => a -> f a
pure (e -> Const e b
forall k a (b :: k). a -> Const a b
Const e
a)
{-# INLINE itraverse #-}
instance FunctorWithIndex Void (Constant e) where
imap :: (Void -> a -> b) -> Constant e a -> Constant e b
imap Void -> a -> b
_ (Constant e
a) = e -> Constant e b
forall k a (b :: k). a -> Constant a b
Constant e
a
{-# INLINE imap #-}
instance FoldableWithIndex Void (Constant e) where
ifoldMap :: (Void -> a -> m) -> Constant e a -> m
ifoldMap Void -> a -> m
_ Constant e a
_ = m
forall a. Monoid a => a
mempty
{-# INLINE ifoldMap #-}
instance TraversableWithIndex Void (Constant e) where
itraverse :: (Void -> a -> f b) -> Constant e a -> f (Constant e b)
itraverse Void -> a -> f b
_ (Constant e
a) = Constant e b -> f (Constant e b)
forall (f :: * -> *) a. Applicative f => a -> f a
pure (e -> Constant e b
forall k a (b :: k). a -> Constant a b
Constant e
a)
{-# INLINE itraverse #-}
instance (FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (Compose f g) where
imap :: ((i, j) -> a -> b) -> Compose f g a -> Compose f g b
imap (i, j) -> a -> b
f (Compose f (g a)
fg) = 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 (g b) -> Compose f g b) -> f (g b) -> Compose f g b
forall a b. (a -> b) -> a -> b
$ (i -> g a -> g b) -> f (g a) -> f (g b)
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (\i
k -> (j -> a -> b) -> g a -> g b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap ((i, j) -> a -> b
f ((i, j) -> a -> b) -> (j -> (i, j)) -> j -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (,) i
k)) f (g a)
fg
{-# INLINE imap #-}
instance (FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (Compose f g) where
ifoldMap :: ((i, j) -> a -> m) -> Compose f g a -> m
ifoldMap (i, j) -> a -> m
f (Compose f (g a)
fg) = (i -> g a -> m) -> f (g a) -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (\i
k -> (j -> a -> m) -> g a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap ((i, j) -> a -> m
f ((i, j) -> a -> m) -> (j -> (i, j)) -> j -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (,) i
k)) f (g a)
fg
{-# INLINE ifoldMap #-}
instance (TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (Compose f g) where
itraverse :: ((i, j) -> a -> f b) -> Compose f g a -> f (Compose f g b)
itraverse (i, j) -> a -> f b
f (Compose f (g a)
fg) = 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 (g b) -> Compose f g b) -> f (f (g b)) -> f (Compose f g b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (i -> g a -> f (g b)) -> f (g a) -> f (f (g b))
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (\i
k -> (j -> a -> f b) -> g a -> f (g b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse ((i, j) -> a -> f b
f ((i, j) -> a -> f b) -> (j -> (i, j)) -> j -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (,) i
k)) f (g a)
fg
{-# INLINE itraverse #-}
instance (FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Sum f g) where
imap :: (Either i j -> a -> b) -> Sum f g a -> Sum f g b
imap Either i j -> a -> b
q (InL f a
fa) = f b -> Sum f g b
forall k (f :: k -> *) (g :: k -> *) (a :: k). f a -> Sum f g a
InL ((i -> a -> b) -> f a -> f b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (Either i j -> a -> b
q (Either i j -> a -> b) -> (i -> Either i j) -> i -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
fa)
imap Either i j -> a -> b
q (InR g a
ga) = g b -> Sum f g b
forall k (f :: k -> *) (g :: k -> *) (a :: k). g a -> Sum f g a
InR ((j -> a -> b) -> g a -> g b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (Either i j -> a -> b
q (Either i j -> a -> b) -> (j -> Either i j) -> j -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
ga)
{-# INLINE imap #-}
instance (FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Sum f g) where
ifoldMap :: (Either i j -> a -> m) -> Sum f g a -> m
ifoldMap Either i j -> a -> m
q (InL f a
fa) = (i -> a -> m) -> f a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (Either i j -> a -> m
q (Either i j -> a -> m) -> (i -> Either i j) -> i -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
fa
ifoldMap Either i j -> a -> m
q (InR g a
ga) = (j -> a -> m) -> g a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (Either i j -> a -> m
q (Either i j -> a -> m) -> (j -> Either i j) -> j -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
ga
{-# INLINE ifoldMap #-}
instance (TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Sum f g) where
itraverse :: (Either i j -> a -> f b) -> Sum f g a -> f (Sum f g b)
itraverse Either i j -> a -> f b
q (InL f a
fa) = f b -> Sum f g b
forall k (f :: k -> *) (g :: k -> *) (a :: k). f a -> Sum f g a
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
<$> (i -> a -> f b) -> f a -> f (f b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (Either i j -> a -> f b
q (Either i j -> a -> f b) -> (i -> Either i j) -> i -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
fa
itraverse Either i j -> a -> f b
q (InR g a
ga) = g b -> Sum f g b
forall k (f :: k -> *) (g :: k -> *) (a :: k). g a -> Sum f g a
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
<$> (j -> a -> f b) -> g a -> f (g b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (Either i j -> a -> f b
q (Either i j -> a -> f b) -> (j -> Either i j) -> j -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
ga
{-# INLINE itraverse #-}
instance (FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Product f g) where
imap :: (Either i j -> a -> b) -> Product f g a -> Product f g b
imap Either i j -> a -> b
f (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
Pair ((i -> a -> b) -> f a -> f b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (Either i j -> a -> b
f (Either i j -> a -> b) -> (i -> Either i j) -> i -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
a) ((j -> a -> b) -> g a -> g b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (Either i j -> a -> b
f (Either i j -> a -> b) -> (j -> Either i j) -> j -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
b)
{-# INLINE imap #-}
instance (FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Product f g) where
ifoldMap :: (Either i j -> a -> m) -> Product f g a -> m
ifoldMap Either i j -> a -> m
f (Pair f a
a g a
b) = (i -> a -> m) -> f a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (Either i j -> a -> m
f (Either i j -> a -> m) -> (i -> Either i j) -> i -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` (j -> a -> m) -> g a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (Either i j -> a -> m
f (Either i j -> a -> m) -> (j -> Either i j) -> j -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
b
{-# INLINE ifoldMap #-}
instance (TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Product f g) where
itraverse :: (Either i j -> a -> f b) -> Product f g a -> f (Product f g b)
itraverse Either i j -> a -> f b
f (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
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
<$> (i -> a -> f b) -> f a -> f (f b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (Either i j -> a -> f b
f (Either i j -> a -> f b) -> (i -> Either i j) -> i -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
a f (g b -> Product f g b) -> f (g b) -> f (Product f g b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (j -> a -> f b) -> g a -> f (g b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (Either i j -> a -> f b
f (Either i j -> a -> f b) -> (j -> Either i j) -> j -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
b
{-# INLINE itraverse #-}
instance FunctorWithIndex i m => FunctorWithIndex i (IdentityT m) where
imap :: (i -> a -> b) -> IdentityT m a -> IdentityT m b
imap i -> a -> b
f (IdentityT m a
m) = m b -> IdentityT m b
forall k (f :: k -> *) (a :: k). f a -> IdentityT f a
IdentityT (m b -> IdentityT m b) -> m b -> IdentityT m b
forall a b. (a -> b) -> a -> b
$ (i -> a -> b) -> m a -> m b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap i -> a -> b
f m a
m
{-# INLINE imap #-}
instance FoldableWithIndex i m => FoldableWithIndex i (IdentityT m) where
ifoldMap :: (i -> a -> m) -> IdentityT m a -> m
ifoldMap i -> a -> m
f (IdentityT m a
m) = (i -> a -> m) -> m a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap i -> a -> m
f m a
m
{-# INLINE ifoldMap #-}
instance TraversableWithIndex i m => TraversableWithIndex i (IdentityT m) where
itraverse :: (i -> a -> f b) -> IdentityT m a -> f (IdentityT m b)
itraverse i -> a -> f b
f (IdentityT m a
m) = m b -> IdentityT m b
forall k (f :: k -> *) (a :: k). f a -> IdentityT f a
IdentityT (m b -> IdentityT m b) -> f (m b) -> f (IdentityT m b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (i -> a -> f b) -> m a -> f (m b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse i -> a -> f b
f m a
m
{-# INLINE itraverse #-}
instance FunctorWithIndex i m => FunctorWithIndex (e, i) (ReaderT e m) where
imap :: ((e, i) -> a -> b) -> ReaderT e m a -> ReaderT e m b
imap (e, i) -> a -> b
f (ReaderT e -> m a
m) = (e -> m b) -> ReaderT e m b
forall r (m :: * -> *) a. (r -> m a) -> ReaderT r m a
ReaderT ((e -> m b) -> ReaderT e m b) -> (e -> m b) -> ReaderT e m b
forall a b. (a -> b) -> a -> b
$ \e
k -> (i -> a -> b) -> m a -> m b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap ((e, i) -> a -> b
f ((e, i) -> a -> b) -> (i -> (e, i)) -> i -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (,) e
k) (e -> m a
m e
k)
{-# INLINE imap #-}
instance FunctorWithIndex i f => FunctorWithIndex i (Backwards f) where
imap :: (i -> a -> b) -> Backwards f a -> Backwards f b
imap i -> a -> b
f = f b -> Backwards f b
forall k (f :: k -> *) (a :: k). f a -> Backwards f a
Backwards (f b -> Backwards f b)
-> (Backwards f a -> f b) -> Backwards f a -> Backwards f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (i -> a -> b) -> f a -> f b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap i -> a -> b
f (f a -> f b) -> (Backwards f a -> f a) -> Backwards f a -> 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
{-# INLINE imap #-}
instance FoldableWithIndex i f => FoldableWithIndex i (Backwards f) where
ifoldMap :: (i -> a -> m) -> Backwards f a -> m
ifoldMap i -> a -> m
f = (i -> a -> m) -> f a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap i -> a -> m
f (f a -> m) -> (Backwards f a -> f a) -> Backwards f a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Backwards f a -> f a
forall k (f :: k -> *) (a :: k). Backwards f a -> f a
forwards
{-# INLINE ifoldMap #-}
instance TraversableWithIndex i f => TraversableWithIndex i (Backwards f) where
itraverse :: (i -> a -> f b) -> Backwards f a -> f (Backwards f b)
itraverse i -> a -> f b
f = (f b -> Backwards f b) -> f (f b) -> f (Backwards 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
. (i -> a -> f b) -> f a -> f (f b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse i -> 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
{-# INLINE itraverse #-}
instance FunctorWithIndex i f => FunctorWithIndex i (Reverse f) where
imap :: (i -> a -> b) -> Reverse f a -> Reverse f b
imap i -> a -> b
f = f b -> Reverse f b
forall k (f :: k -> *) (a :: k). f a -> Reverse f a
Reverse (f b -> Reverse f b)
-> (Reverse f a -> f b) -> Reverse f a -> Reverse f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (i -> a -> b) -> f a -> f b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap i -> a -> b
f (f a -> f b) -> (Reverse f a -> f a) -> Reverse f a -> 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
{-# INLINE imap #-}
instance FoldableWithIndex i f => FoldableWithIndex i (Reverse f) where
ifoldMap :: (i -> a -> m) -> Reverse f a -> m
ifoldMap i -> a -> m
f = Dual m -> m
forall a. Dual a -> a
getDual (Dual m -> m) -> (Reverse f a -> Dual m) -> Reverse f a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (i -> a -> Dual m) -> f a -> Dual m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (\i
i -> m -> Dual m
forall a. a -> Dual a
Dual (m -> Dual m) -> (a -> m) -> a -> Dual m
forall b c a. Coercible b c => (b -> c) -> (a -> b) -> a -> c
#. i -> a -> m
f i
i) (f a -> Dual m) -> (Reverse f a -> f a) -> Reverse f a -> Dual m
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
{-# INLINE ifoldMap #-}
instance TraversableWithIndex i f => TraversableWithIndex i (Reverse f) where
itraverse :: (i -> a -> f b) -> Reverse f a -> f (Reverse f b)
itraverse i -> a -> f b
f = (f b -> Reverse f b) -> f (f b) -> f (Reverse 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
. (i -> a -> Backwards f b) -> f a -> Backwards f (f b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (\i
i -> 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
. i -> a -> f b
f i
i) (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
{-# INLINE itraverse #-}
instance Ix i => FunctorWithIndex i (Array i) where
imap :: (i -> a -> b) -> Array i a -> Array i b
imap i -> a -> b
f Array i a
arr = (i, i) -> [b] -> Array i b
forall i e. Ix i => (i, i) -> [e] -> Array i e
Array.listArray (Array i a -> (i, i)
forall i e. Array i e -> (i, i)
Array.bounds Array i a
arr) ([b] -> Array i b) -> ([(i, a)] -> [b]) -> [(i, a)] -> Array i b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. ((i, a) -> b) -> [(i, a)] -> [b]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((i -> a -> b) -> (i, a) -> b
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry' i -> a -> b
f) ([(i, a)] -> Array i b) -> [(i, a)] -> Array i b
forall a b. (a -> b) -> a -> b
$ Array i a -> [(i, a)]
forall i e. Ix i => Array i e -> [(i, e)]
Array.assocs Array i a
arr
{-# INLINE imap #-}
instance Ix i => FoldableWithIndex i (Array i) where
ifoldMap :: (i -> a -> m) -> Array i a -> m
ifoldMap i -> a -> m
f = ((i, a) -> m) -> [(i, a)] -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap ((i -> a -> m) -> (i, a) -> m
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry' i -> a -> m
f) ([(i, a)] -> m) -> (Array i a -> [(i, a)]) -> Array i a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Array i a -> [(i, a)]
forall i e. Ix i => Array i e -> [(i, e)]
Array.assocs
{-# INLINE ifoldMap #-}
instance Ix i => TraversableWithIndex i (Array i) where
itraverse :: (i -> a -> f b) -> Array i a -> f (Array i b)
itraverse i -> a -> f b
f Array i a
arr = (i, i) -> [b] -> Array i b
forall i e. Ix i => (i, i) -> [e] -> Array i e
Array.listArray (Array i a -> (i, i)
forall i e. Array i e -> (i, i)
Array.bounds Array i a
arr) ([b] -> Array i b) -> f [b] -> f (Array i b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> ((i, a) -> f b) -> [(i, a)] -> f [b]
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse ((i -> a -> f b) -> (i, a) -> f b
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry' i -> a -> f b
f) (Array i a -> [(i, a)]
forall i e. Ix i => Array i e -> [(i, e)]
Array.assocs Array i a
arr)
{-# INLINE itraverse #-}
instance FunctorWithIndex [Int] Tree where
imap :: ([Int] -> a -> b) -> Tree a -> Tree b
imap [Int] -> a -> b
f (Node a
a Forest a
as) = b -> Forest b -> Tree b
forall a. a -> Forest a -> Tree a
Node ([Int] -> a -> b
f [] a
a) (Forest b -> Tree b) -> Forest b -> Tree b
forall a b. (a -> b) -> a -> b
$ (Int -> Tree a -> Tree b) -> Forest a -> Forest b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (\Int
i -> ([Int] -> a -> b) -> Tree a -> Tree b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap ([Int] -> a -> b
f ([Int] -> a -> b) -> ([Int] -> [Int]) -> [Int] -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (:) Int
i)) Forest a
as
{-# INLINE imap #-}
instance FoldableWithIndex [Int] Tree where
ifoldMap :: ([Int] -> a -> m) -> Tree a -> m
ifoldMap [Int] -> a -> m
f (Node a
a Forest a
as) = [Int] -> a -> m
f [] a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` (Int -> Tree a -> m) -> Forest a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (\Int
i -> ([Int] -> a -> m) -> Tree a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap ([Int] -> a -> m
f ([Int] -> a -> m) -> ([Int] -> [Int]) -> [Int] -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (:) Int
i)) Forest a
as
{-# INLINE ifoldMap #-}
instance TraversableWithIndex [Int] Tree where
itraverse :: ([Int] -> a -> f b) -> Tree a -> f (Tree b)
itraverse [Int] -> a -> f b
f (Node a
a Forest a
as) = b -> Forest b -> Tree b
forall a. a -> Forest a -> Tree a
Node (b -> Forest b -> Tree b) -> f b -> f (Forest b -> Tree b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> [Int] -> a -> f b
f [] a
a f (Forest b -> Tree b) -> f (Forest b) -> f (Tree b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (Int -> Tree a -> f (Tree b)) -> Forest a -> f (Forest b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (\Int
i -> ([Int] -> a -> f b) -> Tree a -> f (Tree b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse ([Int] -> a -> f b
f ([Int] -> a -> f b) -> ([Int] -> [Int]) -> [Int] -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (:) Int
i)) Forest a
as
{-# INLINE itraverse #-}
instance FunctorWithIndex Int Seq where
imap :: (Int -> a -> b) -> Seq a -> Seq b
imap = (Int -> a -> b) -> Seq a -> Seq b
forall a b. (Int -> a -> b) -> Seq a -> Seq b
Seq.mapWithIndex
{-# INLINE imap #-}
instance FoldableWithIndex Int Seq where
#if MIN_VERSION_containers(0,5,8)
ifoldMap :: (Int -> a -> m) -> Seq a -> m
ifoldMap = (Int -> a -> m) -> Seq a -> m
forall m a. Monoid m => (Int -> a -> m) -> Seq a -> m
Seq.foldMapWithIndex
#else
ifoldMap f = Data.Foldable.fold . Seq.mapWithIndex f
#endif
{-# INLINE ifoldMap #-}
ifoldr :: (Int -> a -> b -> b) -> b -> Seq a -> b
ifoldr = (Int -> a -> b -> b) -> b -> Seq a -> b
forall a b. (Int -> a -> b -> b) -> b -> Seq a -> b
Seq.foldrWithIndex
{-# INLINE ifoldr #-}
ifoldl :: (Int -> b -> a -> b) -> b -> Seq a -> b
ifoldl Int -> b -> a -> b
f = (b -> Int -> a -> b) -> b -> Seq a -> b
forall b a. (b -> Int -> a -> b) -> b -> Seq a -> b
Seq.foldlWithIndex ((Int -> b -> a -> b) -> b -> Int -> a -> b
forall a b c. (a -> b -> c) -> b -> a -> c
flip Int -> b -> a -> b
f)
{-# INLINE ifoldl #-}
instance TraversableWithIndex Int Seq where
#if MIN_VERSION_containers(0,6,0)
itraverse :: (Int -> a -> f b) -> Seq a -> f (Seq b)
itraverse = (Int -> a -> f b) -> Seq a -> f (Seq b)
forall (f :: * -> *) a b.
Applicative f =>
(Int -> a -> f b) -> Seq a -> f (Seq b)
Seq.traverseWithIndex
#else
itraverse f = sequenceA . Seq.mapWithIndex f
#endif
{-# INLINE itraverse #-}
instance FunctorWithIndex Int IntMap where
imap :: (Int -> a -> b) -> IntMap a -> IntMap b
imap = (Int -> a -> b) -> IntMap a -> IntMap b
forall a b. (Int -> a -> b) -> IntMap a -> IntMap b
IntMap.mapWithKey
{-# INLINE imap #-}
instance FoldableWithIndex Int IntMap where
#if MIN_VERSION_containers(0,5,4)
ifoldMap :: (Int -> a -> m) -> IntMap a -> m
ifoldMap = (Int -> a -> m) -> IntMap a -> m
forall m a. Monoid m => (Int -> a -> m) -> IntMap a -> m
IntMap.foldMapWithKey
#else
ifoldMap = ifoldMapDefault
#endif
{-# INLINE ifoldMap #-}
#if MIN_VERSION_containers(0,5,0)
ifoldr :: (Int -> a -> b -> b) -> b -> IntMap a -> b
ifoldr = (Int -> a -> b -> b) -> b -> IntMap a -> b
forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
IntMap.foldrWithKey
ifoldl' :: (Int -> b -> a -> b) -> b -> IntMap a -> b
ifoldl' = (b -> Int -> a -> b) -> b -> IntMap a -> b
forall a b. (a -> Int -> b -> a) -> a -> IntMap b -> a
IntMap.foldlWithKey' ((b -> Int -> a -> b) -> b -> IntMap a -> b)
-> ((Int -> b -> a -> b) -> b -> Int -> a -> b)
-> (Int -> b -> a -> b)
-> b
-> IntMap a
-> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Int -> b -> a -> b) -> b -> Int -> a -> b
forall a b c. (a -> b -> c) -> b -> a -> c
flip
{-# INLINE ifoldr #-}
{-# INLINE ifoldl' #-}
#endif
instance TraversableWithIndex Int IntMap where
#if MIN_VERSION_containers(0,5,0)
itraverse :: (Int -> a -> f b) -> IntMap a -> f (IntMap b)
itraverse = (Int -> a -> f b) -> IntMap a -> f (IntMap b)
forall (f :: * -> *) a b.
Applicative f =>
(Int -> a -> f b) -> IntMap a -> f (IntMap b)
IntMap.traverseWithKey
#else
itraverse f = sequenceA . IntMap.mapWithKey f
#endif
{-# INLINE itraverse #-}
instance FunctorWithIndex k (Map k) where
imap :: (k -> a -> b) -> Map k a -> Map k b
imap = (k -> a -> b) -> Map k a -> Map k b
forall k a b. (k -> a -> b) -> Map k a -> Map k b
Map.mapWithKey
{-# INLINE imap #-}
instance FoldableWithIndex k (Map k) where
#if MIN_VERSION_containers(0,5,4)
ifoldMap :: (k -> a -> m) -> Map k a -> m
ifoldMap = (k -> a -> m) -> Map k a -> m
forall m k a. Monoid m => (k -> a -> m) -> Map k a -> m
Map.foldMapWithKey
#else
ifoldMap = ifoldMapDefault
#endif
{-# INLINE ifoldMap #-}
#if MIN_VERSION_containers(0,5,0)
ifoldr :: (k -> a -> b -> b) -> b -> Map k a -> b
ifoldr = (k -> a -> b -> b) -> b -> Map k a -> b
forall k a b. (k -> a -> b -> b) -> b -> Map k a -> b
Map.foldrWithKey
ifoldl' :: (k -> b -> a -> b) -> b -> Map k a -> b
ifoldl' = (b -> k -> a -> b) -> b -> Map k a -> b
forall a k b. (a -> k -> b -> a) -> a -> Map k b -> a
Map.foldlWithKey' ((b -> k -> a -> b) -> b -> Map k a -> b)
-> ((k -> b -> a -> b) -> b -> k -> a -> b)
-> (k -> b -> a -> b)
-> b
-> Map k a
-> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (k -> b -> a -> b) -> b -> k -> a -> b
forall a b c. (a -> b -> c) -> b -> a -> c
flip
{-# INLINE ifoldr #-}
{-# INLINE ifoldl' #-}
#endif
instance TraversableWithIndex k (Map k) where
#if MIN_VERSION_containers(0,5,0)
itraverse :: (k -> a -> f b) -> Map k a -> f (Map k b)
itraverse = (k -> a -> f b) -> Map k a -> f (Map k b)
forall (t :: * -> *) k a b.
Applicative t =>
(k -> a -> t b) -> Map k a -> t (Map k b)
Map.traverseWithKey
#else
itraverse f = sequenceA . Map.mapWithKey f
#endif
{-# INLINE itraverse #-}
instance FunctorWithIndex Void V1 where
imap :: (Void -> a -> b) -> V1 a -> V1 b
imap Void -> a -> b
_ V1 a
v = V1 a
v V1 a -> V1 b -> V1 b
`seq` [Char] -> V1 b
forall a. HasCallStack => [Char] -> a
error [Char]
"imap @V1"
{-# INLINE imap #-}
instance FoldableWithIndex Void V1 where
ifoldMap :: (Void -> a -> m) -> V1 a -> m
ifoldMap Void -> a -> m
_ V1 a
v = V1 a
v V1 a -> m -> m
`seq` [Char] -> m
forall a. HasCallStack => [Char] -> a
error [Char]
"ifoldMap @V1"
instance TraversableWithIndex Void V1 where
itraverse :: (Void -> a -> f b) -> V1 a -> f (V1 b)
itraverse Void -> a -> f b
_ V1 a
v = V1 a
v V1 a -> f (V1 b) -> f (V1 b)
`seq` [Char] -> f (V1 b)
forall a. HasCallStack => [Char] -> a
error [Char]
"itraverse @V1"
instance FunctorWithIndex Void U1 where
imap :: (Void -> a -> b) -> U1 a -> U1 b
imap Void -> a -> b
_ U1 a
U1 = U1 b
forall k (p :: k). U1 p
U1
{-# INLINE imap #-}
instance FoldableWithIndex Void U1 where
ifoldMap :: (Void -> a -> m) -> U1 a -> m
ifoldMap Void -> a -> m
_ U1 a
_ = m
forall a. Monoid a => a
mempty
{-# INLINE ifoldMap #-}
instance TraversableWithIndex Void U1 where
itraverse :: (Void -> a -> f b) -> U1 a -> f (U1 b)
itraverse Void -> a -> f b
_ U1 a
U1 = U1 b -> f (U1 b)
forall (f :: * -> *) a. Applicative f => a -> f a
pure U1 b
forall k (p :: k). U1 p
U1
{-# INLINE itraverse #-}
instance FunctorWithIndex () Par1 where
imap :: (() -> a -> b) -> Par1 a -> Par1 b
imap () -> a -> b
f = (a -> b) -> Par1 a -> Par1 b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (() -> a -> b
f ())
{-# INLINE imap #-}
instance FoldableWithIndex () Par1 where
ifoldMap :: (() -> a -> m) -> Par1 a -> m
ifoldMap () -> a -> m
f (Par1 a
a) = () -> a -> m
f () a
a
{-# INLINE ifoldMap #-}
instance TraversableWithIndex () Par1 where
itraverse :: (() -> a -> f b) -> Par1 a -> f (Par1 b)
itraverse () -> 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
{-# INLINE itraverse #-}
instance (FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (f :.: g) where
imap :: ((i, j) -> a -> b) -> (:.:) f g a -> (:.:) f g b
imap (i, j) -> a -> b
q (Comp1 f (g a)
fga) = f (g b) -> (:.:) f g b
forall k2 k1 (f :: k2 -> *) (g :: k1 -> k2) (p :: k1).
f (g p) -> (:.:) f g p
Comp1 ((i -> g a -> g b) -> f (g a) -> f (g b)
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (\i
k -> (j -> a -> b) -> g a -> g b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap ((i, j) -> a -> b
q ((i, j) -> a -> b) -> (j -> (i, j)) -> j -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (,) i
k)) f (g a)
fga)
{-# INLINE imap #-}
instance (FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (f :.: g) where
ifoldMap :: ((i, j) -> a -> m) -> (:.:) f g a -> m
ifoldMap (i, j) -> a -> m
q (Comp1 f (g a)
fga) = (i -> g a -> m) -> f (g a) -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (\i
k -> (j -> a -> m) -> g a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap ((i, j) -> a -> m
q ((i, j) -> a -> m) -> (j -> (i, j)) -> j -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (,) i
k)) f (g a)
fga
{-# INLINE ifoldMap #-}
instance (TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (f :.: g) where
itraverse :: ((i, j) -> a -> f b) -> (:.:) f g a -> f ((:.:) f g b)
itraverse (i, j) -> a -> f b
q (Comp1 f (g a)
fga) = 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
<$> (i -> g a -> f (g b)) -> f (g a) -> f (f (g b))
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (\i
k -> (j -> a -> f b) -> g a -> f (g b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse ((i, j) -> a -> f b
q ((i, j) -> a -> f b) -> (j -> (i, j)) -> j -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (,) i
k)) f (g a)
fga
{-# INLINE itraverse #-}
instance (FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (f :*: g) where
imap :: (Either i j -> a -> b) -> (:*:) f g a -> (:*:) f g b
imap Either i j -> a -> b
q (f a
fa :*: g a
ga) = (i -> a -> b) -> f a -> f b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (Either i j -> a -> b
q (Either i j -> a -> b) -> (i -> Either i j) -> i -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
fa f b -> g b -> (:*:) f g b
forall k (f :: k -> *) (g :: k -> *) (p :: k).
f p -> g p -> (:*:) f g p
:*: (j -> a -> b) -> g a -> g b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (Either i j -> a -> b
q (Either i j -> a -> b) -> (j -> Either i j) -> j -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
ga
{-# INLINE imap #-}
instance (FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (f :*: g) where
ifoldMap :: (Either i j -> a -> m) -> (:*:) f g a -> m
ifoldMap Either i j -> a -> m
q (f a
fa :*: g a
ga) = (i -> a -> m) -> f a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (Either i j -> a -> m
q (Either i j -> a -> m) -> (i -> Either i j) -> i -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
fa m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` (j -> a -> m) -> g a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (Either i j -> a -> m
q (Either i j -> a -> m) -> (j -> Either i j) -> j -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
ga
{-# INLINE ifoldMap #-}
instance (TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :*: g) where
itraverse :: (Either i j -> a -> f b) -> (:*:) f g a -> f ((:*:) f g b)
itraverse Either i j -> a -> f b
q (f a
fa :*: g a
ga) = 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
<$> (i -> a -> f b) -> f a -> f (f b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (Either i j -> a -> f b
q (Either i j -> a -> f b) -> (i -> Either i j) -> i -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
fa f (g b -> (:*:) f g b) -> f (g b) -> f ((:*:) f g b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (j -> a -> f b) -> g a -> f (g b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (Either i j -> a -> f b
q (Either i j -> a -> f b) -> (j -> Either i j) -> j -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
ga
{-# INLINE itraverse #-}
instance (FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (f :+: g) where
imap :: (Either i j -> a -> b) -> (:+:) f g a -> (:+:) f g b
imap Either i j -> a -> b
q (L1 f a
fa) = f b -> (:+:) f g b
forall k (f :: k -> *) (g :: k -> *) (p :: k). f p -> (:+:) f g p
L1 ((i -> a -> b) -> f a -> f b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (Either i j -> a -> b
q (Either i j -> a -> b) -> (i -> Either i j) -> i -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
fa)
imap Either i j -> a -> b
q (R1 g a
ga) = g b -> (:+:) f g b
forall k (f :: k -> *) (g :: k -> *) (p :: k). g p -> (:+:) f g p
R1 ((j -> a -> b) -> g a -> g b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap (Either i j -> a -> b
q (Either i j -> a -> b) -> (j -> Either i j) -> j -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
ga)
{-# INLINE imap #-}
instance (FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (f :+: g) where
ifoldMap :: (Either i j -> a -> m) -> (:+:) f g a -> m
ifoldMap Either i j -> a -> m
q (L1 f a
fa) = (i -> a -> m) -> f a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (Either i j -> a -> m
q (Either i j -> a -> m) -> (i -> Either i j) -> i -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
fa
ifoldMap Either i j -> a -> m
q (R1 g a
ga) = (j -> a -> m) -> g a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap (Either i j -> a -> m
q (Either i j -> a -> m) -> (j -> Either i j) -> j -> a -> m
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
ga
{-# INLINE ifoldMap #-}
instance (TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :+: g) where
itraverse :: (Either i j -> a -> f b) -> (:+:) f g a -> f ((:+:) f g b)
itraverse Either i j -> a -> f b
q (L1 f a
fa) = 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
<$> (i -> a -> f b) -> f a -> f (f b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (Either i j -> a -> f b
q (Either i j -> a -> f b) -> (i -> Either i j) -> i -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> Either i j
forall a b. a -> Either a b
Left) f a
fa
itraverse Either i j -> a -> f b
q (R1 g a
ga) = g b -> (:+:) f g b
forall k (f :: k -> *) (g :: k -> *) (p :: k). g p -> (:+:) f g p
R1 (g b -> (:+:) f g b) -> f (g b) -> f ((:+:) f g b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (j -> a -> f b) -> g a -> f (g b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse (Either i j -> a -> f b
q (Either i j -> a -> f b) -> (j -> Either i j) -> j -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. j -> Either i j
forall a b. b -> Either a b
Right) g a
ga
{-# INLINE itraverse #-}
instance FunctorWithIndex i f => FunctorWithIndex i (Rec1 f) where
imap :: (i -> a -> b) -> Rec1 f a -> Rec1 f b
imap i -> a -> b
q (Rec1 f a
f) = f b -> Rec1 f b
forall k (f :: k -> *) (p :: k). f p -> Rec1 f p
Rec1 ((i -> a -> b) -> f a -> f b
forall i (f :: * -> *) a b.
FunctorWithIndex i f =>
(i -> a -> b) -> f a -> f b
imap i -> a -> b
q f a
f)
{-# INLINE imap #-}
instance FoldableWithIndex i f => FoldableWithIndex i (Rec1 f) where
ifoldMap :: (i -> a -> m) -> Rec1 f a -> m
ifoldMap i -> a -> m
q (Rec1 f a
f) = (i -> a -> m) -> f a -> m
forall i (f :: * -> *) m a.
(FoldableWithIndex i f, Monoid m) =>
(i -> a -> m) -> f a -> m
ifoldMap i -> a -> m
q f a
f
{-# INLINE ifoldMap #-}
instance TraversableWithIndex i f => TraversableWithIndex i (Rec1 f) where
itraverse :: (i -> a -> f b) -> Rec1 f a -> f (Rec1 f b)
itraverse i -> a -> f b
q (Rec1 f a
f) = 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
<$> (i -> a -> f b) -> f a -> f (f b)
forall i (t :: * -> *) (f :: * -> *) a b.
(TraversableWithIndex i t, Applicative f) =>
(i -> a -> f b) -> t a -> f (t b)
itraverse i -> a -> f b
q f a
f
{-# INLINE itraverse #-}
instance FunctorWithIndex Void (K1 i c) where
imap :: (Void -> a -> b) -> K1 i c a -> K1 i c b
imap Void -> a -> b
_ (K1 c
c) = c -> K1 i c b
forall k i c (p :: k). c -> K1 i c p
K1 c
c
{-# INLINE imap #-}
instance FoldableWithIndex Void (K1 i c) where
ifoldMap :: (Void -> a -> m) -> K1 i c a -> m
ifoldMap Void -> a -> m
_ K1 i c a
_ = m
forall a. Monoid a => a
mempty
{-# INLINE ifoldMap #-}
instance TraversableWithIndex Void (K1 i c) where
itraverse :: (Void -> a -> f b) -> K1 i c a -> f (K1 i c b)
itraverse Void -> a -> f b
_ (K1 c
a) = K1 i c b -> f (K1 i c b)
forall (f :: * -> *) a. Applicative f => a -> f a
pure (c -> K1 i c b
forall k i c (p :: k). c -> K1 i c p
K1 c
a)
{-# INLINE itraverse #-}
#if __GLASGOW_HASKELL__ >=708
(#.) :: Coercible b c => (b -> c) -> (a -> b) -> (a -> c)
b -> c
_ #. :: (b -> c) -> (a -> b) -> a -> c
#. a -> b
x = (a -> b) -> a -> c
coerce a -> b
x
#else
(#.) :: (b -> c) -> (a -> b) -> (a -> c)
_ #. x = unsafeCoerce x
#endif
infixr 9 #.
{-# INLINE (#.) #-}
skip :: a -> ()
skip :: a -> ()
skip a
_ = ()
{-# INLINE skip #-}
newtype Traversed a f = Traversed { Traversed a f -> f a
getTraversed :: f a }
instance Applicative f => Semigroup (Traversed a f) where
Traversed f a
ma <> :: Traversed a f -> Traversed a f -> Traversed a f
<> Traversed f a
mb = f a -> Traversed a f
forall k (a :: k) (f :: k -> *). f a -> Traversed a f
Traversed (f a
ma f a -> f a -> f a
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> f a
mb)
{-# INLINE (<>) #-}
instance Applicative f => Monoid (Traversed a f) where
mempty :: Traversed a f
mempty = f a -> Traversed a f
forall k (a :: k) (f :: k -> *). f a -> Traversed a f
Traversed (a -> f a
forall (f :: * -> *) a. Applicative f => a -> f a
pure ([Char] -> a
forall a. HasCallStack => [Char] -> a
error [Char]
"Traversed: value used"))
{-# INLINE mempty #-}
Traversed f a
ma mappend :: Traversed a f -> Traversed a f -> Traversed a f
`mappend` Traversed f a
mb = f a -> Traversed a f
forall k (a :: k) (f :: k -> *). f a -> Traversed a f
Traversed (f a
ma f a -> f a -> f a
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> f a
mb)
{-# INLINE mappend #-}
newtype Sequenced a m = Sequenced { Sequenced a m -> m a
getSequenced :: m a }
instance Monad m => Semigroup (Sequenced a m) where
Sequenced m a
ma <> :: Sequenced a m -> Sequenced a m -> Sequenced a m
<> Sequenced m a
mb = m a -> Sequenced a m
forall k (a :: k) (m :: k -> *). m a -> Sequenced a m
Sequenced (m a
ma m a -> m a -> m a
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> m a
mb)
{-# INLINE (<>) #-}
instance Monad m => Monoid (Sequenced a m) where
mempty :: Sequenced a m
mempty = m a -> Sequenced a m
forall k (a :: k) (m :: k -> *). m a -> Sequenced a m
Sequenced (a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return ([Char] -> a
forall a. HasCallStack => [Char] -> a
error [Char]
"Sequenced: value used"))
{-# INLINE mempty #-}
Sequenced m a
ma mappend :: Sequenced a m -> Sequenced a m -> Sequenced a m
`mappend` Sequenced m a
mb = m a -> Sequenced a m
forall k (a :: k) (m :: k -> *). m a -> Sequenced a m
Sequenced (m a
ma m a -> m a -> m a
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> m a
mb)
{-# INLINE mappend #-}
newtype Indexing f a = Indexing { Indexing f a -> Int -> (Int, f a)
runIndexing :: Int -> (Int, f a) }
instance Functor f => Functor (Indexing f) where
fmap :: (a -> b) -> Indexing f a -> Indexing f b
fmap a -> b
f (Indexing Int -> (Int, f a)
m) = (Int -> (Int, f b)) -> Indexing f b
forall k (f :: k -> *) (a :: k).
(Int -> (Int, f a)) -> Indexing f a
Indexing ((Int -> (Int, f b)) -> Indexing f b)
-> (Int -> (Int, f b)) -> Indexing f b
forall a b. (a -> b) -> a -> b
$ \Int
i -> case Int -> (Int, f a)
m Int
i of
(Int
j, f a
x) -> (Int
j, (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f f a
x)
{-# INLINE fmap #-}
instance Applicative f => Applicative (Indexing f) where
pure :: a -> Indexing f a
pure a
x = (Int -> (Int, f a)) -> Indexing f a
forall k (f :: k -> *) (a :: k).
(Int -> (Int, f a)) -> Indexing f a
Indexing ((Int -> (Int, f a)) -> Indexing f a)
-> (Int -> (Int, f a)) -> Indexing f a
forall a b. (a -> b) -> a -> b
$ \Int
i -> (Int
i, a -> f a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
x)
{-# INLINE pure #-}
Indexing Int -> (Int, f (a -> b))
mf <*> :: Indexing f (a -> b) -> Indexing f a -> Indexing f b
<*> Indexing Int -> (Int, f a)
ma = (Int -> (Int, f b)) -> Indexing f b
forall k (f :: k -> *) (a :: k).
(Int -> (Int, f a)) -> Indexing f a
Indexing ((Int -> (Int, f b)) -> Indexing f b)
-> (Int -> (Int, f b)) -> Indexing f b
forall a b. (a -> b) -> a -> b
$ \Int
i -> case Int -> (Int, f (a -> b))
mf Int
i of
(Int
j, f (a -> b)
ff) -> case Int -> (Int, f a)
ma Int
j of
~(Int
k, f a
fa) -> (Int
k, f (a -> b)
ff f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
fa)
{-# INLINE (<*>) #-}
uncurry' :: (a -> b -> c) -> (a, b) -> c
uncurry' :: (a -> b -> c) -> (a, b) -> c
uncurry' a -> b -> c
f (a
a, b
b) = a -> b -> c
f a
a b
b
{-# INLINE uncurry' #-}