Copyright	(C) 2013-16 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	Safe
Language	Haskell98

Control.Lens.Combinators

Description

This lets the subset of users who vociferously disagree about the full scope and set of operators that should be exported from lens to not have to look at any operator with which they disagree.

import Control.Lens.Combinators

Synopsis

class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
class Contravariant (f :: Type -> Type) where
- contramap :: (a -> b) -> f b -> f a
- (>$) :: b -> f b -> f a
class Bifunctor (p :: Type -> Type -> Type) where
- bimap :: (a -> b) -> (c -> d) -> p a c -> p b d
newtype Identity a = Identity {
- runIdentity :: a
}
newtype Const a (b :: k) :: forall k. Type -> k -> Type = Const {
- getConst :: a
}
class Profunctor (p :: Type -> Type -> Type) where
- dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
- lmap :: (a -> b) -> p b c -> p a c
- rmap :: (b -> c) -> p a b -> p a c
class Profunctor p => Choice (p :: Type -> Type -> Type) where
- left' :: p a b -> p (Either a c) (Either b c)
- right' :: p a b -> p (Either c a) (Either c b)
sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a)
traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b)
foldMapBy :: Foldable t => (r -> r -> r) -> r -> (a -> r) -> t a -> r
foldBy :: Foldable t => (a -> a -> a) -> a -> t a -> a
class (Foldable1 t, Traversable t) => Traversable1 (t :: Type -> Type) where
- traverse1 :: Apply f => (a -> f b) -> t a -> f (t b)
data Rightmost a
data Leftmost a
data Sequenced a m
data Traversed a f
newtype Indexed i a b = Indexed {
- runIndexed :: i -> a -> b
}
class Conjoined p => Indexable i p where
- indexed :: p a b -> i -> a -> b
class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p, Closed p) => Conjoined p where
- distrib :: Functor f => p a b -> p (f a) (f b)
- conjoined :: (p ~ (->) => q (a -> b) r) -> q (p a b) r -> q (p a b) r
indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t
indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t
withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t)
asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s)
type Context' a = Context a a
data Context a b t = Context (b -> t) a
type Bazaar1' p a = Bazaar1 p a a
newtype Bazaar1 p a b t = Bazaar1 {
- runBazaar1 :: forall f. Apply f => p a (f b) -> f t
}
type Bazaar' p a = Bazaar p a a
newtype Bazaar p a b t = Bazaar {
- runBazaar :: forall f. Applicative f => p a (f b) -> f t
}
class Reversing t where
- reversing :: t -> t
data Level i a
data Magma i t b a
class (Profunctor p, Bifunctor p) => Reviewable p
retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b
class (Applicative f, Distributive f, Traversable f) => Settable f
type Over' p f s a = Over p f s s a a
type Over p f s t a b = p a (f b) -> s -> f t
type IndexedLensLike' i f s a = IndexedLensLike i f s s a a
type IndexedLensLike i f s t a b = forall p. Indexable i p => p a (f b) -> s -> f t
type LensLike' f s a = LensLike f s s a a
type LensLike f s t a b = (a -> f b) -> s -> f t
type Optical' p q f s a = Optical p q f s s a a
type Optical p q f s t a b = p a (f b) -> q s (f t)
type Optic' p f s a = Optic p f s s a a
type Optic p f s t a b = p a (f b) -> p s (f t)
type Simple f s a = f s s a a
type IndexPreservingFold1 s a = forall p f. (Conjoined p, Contravariant f, Apply f) => p a (f a) -> p s (f s)
type IndexedFold1 i s a = forall p f. (Indexable i p, Contravariant f, Apply f) => p a (f a) -> s -> f s
type Fold1 s a = forall f. (Contravariant f, Apply f) => (a -> f a) -> s -> f s
type IndexPreservingFold s a = forall p f. (Conjoined p, Contravariant f, Applicative f) => p a (f a) -> p s (f s)
type IndexedFold i s a = forall p f. (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> s -> f s
type Fold s a = forall f. (Contravariant f, Applicative f) => (a -> f a) -> s -> f s
type IndexPreservingGetter s a = forall p f. (Conjoined p, Contravariant f, Functor f) => p a (f a) -> p s (f s)
type IndexedGetter i s a = forall p f. (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s
type Getter s a = forall f. (Contravariant f, Functor f) => (a -> f a) -> s -> f s
type As a = Equality' a a
type Equality' s a = Equality s s a a
type Equality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = forall k3 (p :: k1 -> k3 -> Type) (f :: k2 -> k3). p a (f b) -> p s (f t)
type Prism' s a = Prism s s a a
type Prism s t a b = forall p f. (Choice p, Applicative f) => p a (f b) -> p s (f t)
type AReview t b = Optic' Tagged Identity t b
type Review t b = forall p f. (Choice p, Bifunctor p, Settable f) => Optic' p f t b
type Iso' s a = Iso s s a a
type Iso s t a b = forall p f. (Profunctor p, Functor f) => p a (f b) -> p s (f t)
type IndexPreservingSetter' s a = IndexPreservingSetter s s a a
type IndexPreservingSetter s t a b = forall p f. (Conjoined p, Settable f) => p a (f b) -> p s (f t)
type IndexedSetter' i s a = IndexedSetter i s s a a
type IndexedSetter i s t a b = forall f p. (Indexable i p, Settable f) => p a (f b) -> s -> f t
type Setter' s a = Setter s s a a
type Setter s t a b = forall f. Settable f => (a -> f b) -> s -> f t
type IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a
type IndexPreservingTraversal1 s t a b = forall p f. (Conjoined p, Apply f) => p a (f b) -> p s (f t)
type IndexPreservingTraversal' s a = IndexPreservingTraversal s s a a
type IndexPreservingTraversal s t a b = forall p f. (Conjoined p, Applicative f) => p a (f b) -> p s (f t)
type IndexedTraversal1' i s a = IndexedTraversal1 i s s a a
type IndexedTraversal1 i s t a b = forall p f. (Indexable i p, Apply f) => p a (f b) -> s -> f t
type IndexedTraversal' i s a = IndexedTraversal i s s a a
type IndexedTraversal i s t a b = forall p f. (Indexable i p, Applicative f) => p a (f b) -> s -> f t
type Traversal1' s a = Traversal1 s s a a
type Traversal1 s t a b = forall f. Apply f => (a -> f b) -> s -> f t
type Traversal' s a = Traversal s s a a
type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t
type IndexPreservingLens' s a = IndexPreservingLens s s a a
type IndexPreservingLens s t a b = forall p f. (Conjoined p, Functor f) => p a (f b) -> p s (f t)
type IndexedLens' i s a = IndexedLens i s s a a
type IndexedLens i s t a b = forall f p. (Indexable i p, Functor f) => p a (f b) -> s -> f t
type Lens' s a = Lens s s a a
type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t
type Setting' p s a = Setting p s s a a
type Setting p s t a b = p a (Identity b) -> s -> Identity t
type AnIndexedSetter' i s a = AnIndexedSetter i s s a a
type AnIndexedSetter i s t a b = Indexed i a (Identity b) -> s -> Identity t
type ASetter' s a = ASetter s s a a
type ASetter s t a b = (a -> Identity b) -> s -> Identity t
mapped :: Functor f => Setter (f a) (f b) a b
lifted :: Monad m => Setter (m a) (m b) a b
contramapped :: Contravariant f => Setter (f b) (f a) a b
argument :: Profunctor p => Setter (p b r) (p a r) a b
setting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b
sets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> Optical p q f s t a b
cloneSetter :: ASetter s t a b -> Setter s t a b
cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b
cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b
over :: ASetter s t a b -> (a -> b) -> s -> t
set :: ASetter s t a b -> b -> s -> t
set' :: ASetter' s a -> a -> s -> s
assign :: MonadState s m => ASetter s s a b -> b -> m ()
modifying :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m ()
passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a
ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a
censoring :: MonadWriter w m => Setter w w u v -> (u -> v) -> m a -> m a
icensoring :: MonadWriter w m => IndexedSetter i w w u v -> (i -> u -> v) -> m a -> m a
iover :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
iset :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t
isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b
imodifying :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()
assignA :: Arrow p => ASetter s t a b -> p s b -> p s t
mapOf :: ASetter s t a b -> (a -> b) -> s -> t
imapOf :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
type AnIndexedLens' i s a = AnIndexedLens i s s a a
type AnIndexedLens i s t a b = Optical (Indexed i) (->) (Pretext (Indexed i) a b) s t a b
type ALens' s a = ALens s s a a
type ALens s t a b = LensLike (Pretext (->) a b) s t a b
lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b
ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b
inside :: Corepresentable p => ALens s t a b -> Lens (p e s) (p e t) (p e a) (p e b)
choosing :: Functor f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f (Either s s') (Either t t') a b
chosen :: IndexPreservingLens (Either a a) (Either b b) a b
alongside :: LensLike (AlongsideLeft f b') s t a b -> LensLike (AlongsideRight f t) s' t' a' b' -> LensLike f (s, s') (t, t') (a, a') (b, b')
locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) a b
cloneLens :: ALens s t a b -> Lens s t a b
cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b
cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b
overA :: Arrow ar => LensLike (Context a b) s t a b -> ar a b -> ar s t
storing :: ALens s t a b -> b -> s -> t
devoid :: Over p f Void Void a b
united :: Lens' a ()
fusing :: Functor f => LensLike (Yoneda f) s t a b -> LensLike f s t a b
class Field19 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _19 :: Lens s t a b
class Field18 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _18 :: Lens s t a b
class Field17 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _17 :: Lens s t a b
class Field16 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _16 :: Lens s t a b
class Field15 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _15 :: Lens s t a b
class Field14 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _14 :: Lens s t a b
class Field13 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _13 :: Lens s t a b
class Field12 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _12 :: Lens s t a b
class Field11 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _11 :: Lens s t a b
class Field10 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _10 :: Lens s t a b
class Field9 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _9 :: Lens s t a b
class Field8 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _8 :: Lens s t a b
class Field7 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _7 :: Lens s t a b
class Field6 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _6 :: Lens s t a b
class Field5 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _5 :: Lens s t a b
class Field4 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _4 :: Lens s t a b
class Field3 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _3 :: Lens s t a b
class Field2 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _2 :: Lens s t a b
class Field1 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _1 :: Lens s t a b
_1' :: Field1 s t a b => Lens s t a b
_2' :: Field2 s t a b => Lens s t a b
_3' :: Field3 s t a b => Lens s t a b
_4' :: Field4 s t a b => Lens s t a b
_5' :: Field5 s t a b => Lens s t a b
_6' :: Field6 s t a b => Lens s t a b
_7' :: Field7 s t a b => Lens s t a b
_8' :: Field8 s t a b => Lens s t a b
_9' :: Field9 s t a b => Lens s t a b
_10' :: Field10 s t a b => Lens s t a b
_11' :: Field11 s t a b => Lens s t a b
_12' :: Field12 s t a b => Lens s t a b
_13' :: Field13 s t a b => Lens s t a b
_14' :: Field14 s t a b => Lens s t a b
_15' :: Field15 s t a b => Lens s t a b
_16' :: Field16 s t a b => Lens s t a b
_17' :: Field17 s t a b => Lens s t a b
_18' :: Field18 s t a b => Lens s t a b
_19' :: Field19 s t a b => Lens s t a b
type Accessing p m s a = p a (Const m a) -> s -> Const m s
type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s
type Getting r s a = (a -> Const r a) -> s -> Const r s
to :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a
ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a
like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a
ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a
view :: MonadReader s m => Getting a s a -> m a
views :: MonadReader s m => LensLike' (Const r) s a -> (a -> r) -> m r
use :: MonadState s m => Getting a s a -> m a
uses :: MonadState s m => LensLike' (Const r) s a -> (a -> r) -> m r
listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u)
ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u))
listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v)
ilistenings :: MonadWriter w m => IndexedGetting i v w u -> (i -> u -> v) -> m a -> m (a, v)
iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a)
iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a)
iuses :: MonadState s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a
unto :: (Profunctor p, Bifunctor p, Functor f) => (b -> t) -> Optic p f s t a b
un :: (Profunctor p, Bifunctor p, Functor f) => Getting a s a -> Optic' p f a s
re :: AReview t b -> Getter b t
review :: MonadReader b m => AReview t b -> m t
reviews :: MonadReader b m => AReview t b -> (t -> r) -> m r
reuse :: MonadState b m => AReview t b -> m t
reuses :: MonadState b m => AReview t b -> (t -> r) -> m r
type APrism' s a = APrism s s a a
type APrism s t a b = Market a b a (Identity b) -> Market a b s (Identity t)
withPrism :: APrism s t a b -> ((b -> t) -> (s -> Either t a) -> r) -> r
clonePrism :: APrism s t a b -> Prism s t a b
prism :: (b -> t) -> (s -> Either t a) -> Prism s t a b
prism' :: (b -> s) -> (s -> Maybe a) -> Prism s s a b
outside :: Representable p => APrism s t a b -> Lens (p t r) (p s r) (p b r) (p a r)
without :: APrism s t a b -> APrism u v c d -> Prism (Either s u) (Either t v) (Either a c) (Either b d)
aside :: APrism s t a b -> Prism (e, s) (e, t) (e, a) (e, b)
below :: Traversable f => APrism' s a -> Prism' (f s) (f a)
isn't :: APrism s t a b -> s -> Bool
matching :: APrism s t a b -> s -> Either t a
_Left :: Prism (Either a c) (Either b c) a b
_Right :: Prism (Either c a) (Either c b) a b
_Just :: Prism (Maybe a) (Maybe b) a b
_Nothing :: Prism' (Maybe a) ()
_Void :: Prism s s a Void
only :: Eq a => a -> Prism' a ()
nearly :: a -> (a -> Bool) -> Prism' a ()
_Show :: (Read a, Show a) => Prism' String a
folding :: Foldable f => (s -> f a) -> Fold s a
ifolding :: (Foldable f, Indexable i p, Contravariant g, Applicative g) => (s -> f (i, a)) -> Over p g s t a b
foldring :: (Contravariant f, Applicative f) => ((a -> f a -> f a) -> f a -> s -> f a) -> LensLike f s t a b
ifoldring :: (Indexable i p, Contravariant f, Applicative f) => ((i -> a -> f a -> f a) -> f a -> s -> f a) -> Over p f s t a b
folded :: Foldable f => IndexedFold Int (f a) a
folded64 :: Foldable f => IndexedFold Int64 (f a) a
repeated :: Apply f => LensLike' f a a
replicated :: Int -> Fold a a
cycled :: Apply f => LensLike f s t a b -> LensLike f s t a b
unfolded :: (b -> Maybe (a, b)) -> Fold b a
iterated :: Apply f => (a -> a) -> LensLike' f a a
filtered :: (Choice p, Applicative f) => (a -> Bool) -> Optic' p f a a
takingWhile :: (Conjoined p, Applicative f) => (a -> Bool) -> Over p (TakingWhile p f a a) s t a a -> Over p f s t a a
droppingWhile :: (Conjoined p, Profunctor q, Applicative f) => (a -> Bool) -> Optical p q (Compose (State Bool) f) s t a a -> Optical p q f s t a a
worded :: Applicative f => IndexedLensLike' Int f String String
lined :: Applicative f => IndexedLensLike' Int f String String
foldMapOf :: Getting r s a -> (a -> r) -> s -> r
foldOf :: Getting a s a -> s -> a
foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r
foldlOf :: Getting (Dual (Endo r)) s a -> (r -> a -> r) -> r -> s -> r
toListOf :: Getting (Endo [a]) s a -> s -> [a]
toNonEmptyOf :: Getting (NonEmptyDList a) s a -> s -> NonEmpty a
andOf :: Getting All s Bool -> s -> Bool
orOf :: Getting Any s Bool -> s -> Bool
anyOf :: Getting Any s a -> (a -> Bool) -> s -> Bool
allOf :: Getting All s a -> (a -> Bool) -> s -> Bool
noneOf :: Getting Any s a -> (a -> Bool) -> s -> Bool
productOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a
sumOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a
traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f ()
forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f ()
sequenceAOf_ :: Functor f => Getting (Traversed a f) s (f a) -> s -> f ()
traverse1Of_ :: Functor f => Getting (TraversedF r f) s a -> (a -> f r) -> s -> f ()
for1Of_ :: Functor f => Getting (TraversedF r f) s a -> s -> (a -> f r) -> f ()
sequence1Of_ :: Functor f => Getting (TraversedF a f) s (f a) -> s -> f ()
mapMOf_ :: Monad m => Getting (Sequenced r m) s a -> (a -> m r) -> s -> m ()
forMOf_ :: Monad m => Getting (Sequenced r m) s a -> s -> (a -> m r) -> m ()
sequenceOf_ :: Monad m => Getting (Sequenced a m) s (m a) -> s -> m ()
asumOf :: Alternative f => Getting (Endo (f a)) s (f a) -> s -> f a
msumOf :: MonadPlus m => Getting (Endo (m a)) s (m a) -> s -> m a
elemOf :: Eq a => Getting Any s a -> a -> s -> Bool
notElemOf :: Eq a => Getting All s a -> a -> s -> Bool
concatMapOf :: Getting [r] s a -> (a -> [r]) -> s -> [r]
concatOf :: Getting [r] s [r] -> s -> [r]
lengthOf :: Getting (Endo (Endo Int)) s a -> s -> Int
firstOf :: Getting (Leftmost a) s a -> s -> Maybe a
first1Of :: Getting (First a) s a -> s -> a
lastOf :: Getting (Rightmost a) s a -> s -> Maybe a
last1Of :: Getting (Last a) s a -> s -> a
nullOf :: Getting All s a -> s -> Bool
notNullOf :: Getting Any s a -> s -> Bool
maximumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a
maximum1Of :: Ord a => Getting (Max a) s a -> s -> a
minimumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a
minimum1Of :: Ord a => Getting (Min a) s a -> s -> a
maximumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a
findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)
lookupOf :: Eq k => Getting (Endo (Maybe v)) s (k, v) -> k -> s -> Maybe v
foldr1Of :: HasCallStack => Getting (Endo (Maybe a)) s a -> (a -> a -> a) -> s -> a
foldl1Of :: HasCallStack => Getting (Dual (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a
foldrOf' :: Getting (Dual (Endo (Endo r))) s a -> (a -> r -> r) -> r -> s -> r
foldlOf' :: Getting (Endo (Endo r)) s a -> (r -> a -> r) -> r -> s -> r
foldr1Of' :: HasCallStack => Getting (Dual (Endo (Endo (Maybe a)))) s a -> (a -> a -> a) -> s -> a
foldl1Of' :: HasCallStack => Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a
foldrMOf :: Monad m => Getting (Dual (Endo (r -> m r))) s a -> (a -> r -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Getting (Endo (r -> m r)) s a -> (r -> a -> m r) -> r -> s -> m r
has :: Getting Any s a -> s -> Bool
hasn't :: Getting All s a -> s -> Bool
pre :: Getting (First a) s a -> IndexPreservingGetter s (Maybe a)
ipre :: IndexedGetting i (First (i, a)) s a -> IndexPreservingGetter s (Maybe (i, a))
preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a)
ipreview :: MonadReader s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))
previews :: MonadReader s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)
preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a)
ipreuse :: MonadState s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))
preuses :: MonadState s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)
backwards :: (Profunctor p, Profunctor q) => Optical p q (Backwards f) s t a b -> Optical p q f s t a b
ifoldMapOf :: IndexedGetting i m s a -> (i -> a -> m) -> s -> m
ifoldrOf :: IndexedGetting i (Endo r) s a -> (i -> a -> r -> r) -> r -> s -> r
ifoldlOf :: IndexedGetting i (Dual (Endo r)) s a -> (i -> r -> a -> r) -> r -> s -> r
ianyOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedGetting i All s a -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool
itraverseOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> (i -> a -> f r) -> s -> f ()
iforOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> s -> (i -> a -> f r) -> f ()
imapMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> (i -> a -> m r) -> s -> m ()
iforMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> s -> (i -> a -> m r) -> m ()
iconcatMapOf :: IndexedGetting i [r] s a -> (i -> a -> [r]) -> s -> [r]
ifindOf :: IndexedGetting i (Endo (Maybe a)) s a -> (i -> a -> Bool) -> s -> Maybe a
ifindMOf :: Monad m => IndexedGetting i (Endo (m (Maybe a))) s a -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifoldrOf' :: IndexedGetting i (Dual (Endo (r -> r))) s a -> (i -> a -> r -> r) -> r -> s -> r
ifoldlOf' :: IndexedGetting i (Endo (r -> r)) s a -> (i -> r -> a -> r) -> r -> s -> r
ifoldrMOf :: Monad m => IndexedGetting i (Dual (Endo (r -> m r))) s a -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedGetting i (Endo (r -> m r)) s a -> (i -> r -> a -> m r) -> r -> s -> m r
itoListOf :: IndexedGetting i (Endo [(i, a)]) s a -> s -> [(i, a)]
elemIndexOf :: Eq a => IndexedGetting i (First i) s a -> a -> s -> Maybe i
elemIndicesOf :: Eq a => IndexedGetting i (Endo [i]) s a -> a -> s -> [i]
findIndexOf :: IndexedGetting i (First i) s a -> (a -> Bool) -> s -> Maybe i
findIndicesOf :: IndexedGetting i (Endo [i]) s a -> (a -> Bool) -> s -> [i]
ifiltered :: (Indexable i p, Applicative f) => (i -> a -> Bool) -> Optical' p (Indexed i) f a a
itakingWhile :: (Indexable i p, Profunctor q, Contravariant f, Applicative f) => (i -> a -> Bool) -> Optical' (Indexed i) q (Const (Endo (f s))) s a -> Optical' p q f s a
idroppingWhile :: (Indexable i p, Profunctor q, Applicative f) => (i -> a -> Bool) -> Optical (Indexed i) q (Compose (State Bool) f) s t a a -> Optical p q f s t a a
foldByOf :: Fold s a -> (a -> a -> a) -> a -> s -> a
foldMapByOf :: Fold s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r
class Ord k => TraverseMax k m | m -> k where
- traverseMax :: IndexedTraversal' k (m v) v
class Ord k => TraverseMin k m | m -> k where
- traverseMin :: IndexedTraversal' k (m v) v
type Traversing1' p f s a = Traversing1 p f s s a a
type Traversing' p f s a = Traversing p f s s a a
type Traversing1 p f s t a b = Over p (BazaarT1 p f a b) s t a b
type Traversing p f s t a b = Over p (BazaarT p f a b) s t a b
type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a
type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a
type AnIndexedTraversal1 i s t a b = Over (Indexed i) (Bazaar1 (Indexed i) a b) s t a b
type AnIndexedTraversal i s t a b = Over (Indexed i) (Bazaar (Indexed i) a b) s t a b
type ATraversal1' s a = ATraversal1 s s a a
type ATraversal1 s t a b = LensLike (Bazaar1 (->) a b) s t a b
type ATraversal' s a = ATraversal s s a a
type ATraversal s t a b = LensLike (Bazaar (->) a b) s t a b
traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t
forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t
sequenceAOf :: LensLike f s t (f b) b -> s -> f t
mapMOf :: LensLike (WrappedMonad m) s t a b -> (a -> m b) -> s -> m t
forMOf :: LensLike (WrappedMonad m) s t a b -> s -> (a -> m b) -> m t
sequenceOf :: LensLike (WrappedMonad m) s t (m b) b -> s -> m t
transposeOf :: LensLike ZipList s t [a] a -> s -> [t]
mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
scanr1Of :: LensLike (Backwards (State (Maybe a))) s t a a -> (a -> a -> a) -> s -> t
scanl1Of :: LensLike (State (Maybe a)) s t a a -> (a -> a -> a) -> s -> t
loci :: Traversal (Bazaar (->) a c s) (Bazaar (->) b c s) a b
iloci :: IndexedTraversal i (Bazaar (Indexed i) a c s) (Bazaar (Indexed i) b c s) a b
partsOf :: Functor f => Traversing (->) f s t a a -> LensLike f s t [a] [a]
ipartsOf :: forall i p f s t a. (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a a -> Over p f s t [a] [a]
partsOf' :: ATraversal s t a a -> Lens s t [a] [a]
ipartsOf' :: forall i p f s t a. (Indexable [i] p, Functor f) => Over (Indexed i) (Bazaar' (Indexed i) a) s t a a -> Over p f s t [a] [a]
unsafePartsOf :: Functor f => Traversing (->) f s t a b -> LensLike f s t [a] [b]
iunsafePartsOf :: forall i p f s t a b. (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a b -> Over p f s t [a] [b]
unsafePartsOf' :: ATraversal s t a b -> Lens s t [a] [b]
iunsafePartsOf' :: forall i s t a b. Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b]
singular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a a -> Over p f s t a a
unsafeSingular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a b -> Over p f s t a b
holesOf :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
both :: Bitraversable r => Traversal (r a a) (r b b) a b
both1 :: Bitraversable1 r => Traversal1 (r a a) (r b b) a b
beside :: (Representable q, Applicative (Rep q), Applicative f, Bitraversable r) => Optical p q f s t a b -> Optical p q f s' t' a b -> Optical p q f (r s s') (r t t') a b
taking :: (Conjoined p, Applicative f) => Int -> Traversing p f s t a a -> Over p f s t a a
dropping :: (Conjoined p, Applicative f) => Int -> Over p (Indexing f) s t a a -> Over p f s t a a
cloneTraversal :: ATraversal s t a b -> Traversal s t a b
cloneIndexPreservingTraversal :: ATraversal s t a b -> IndexPreservingTraversal s t a b
cloneIndexedTraversal :: AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b
cloneTraversal1 :: ATraversal1 s t a b -> Traversal1 s t a b
cloneIndexPreservingTraversal1 :: ATraversal1 s t a b -> IndexPreservingTraversal1 s t a b
cloneIndexedTraversal1 :: AnIndexedTraversal1 i s t a b -> IndexedTraversal1 i s t a b
itraverseOf :: (Indexed i a (f b) -> s -> f t) -> (i -> a -> f b) -> s -> f t
iforOf :: (Indexed i a (f b) -> s -> f t) -> s -> (i -> a -> f b) -> f t
imapMOf :: Over (Indexed i) (WrappedMonad m) s t a b -> (i -> a -> m b) -> s -> m t
iforMOf :: (Indexed i a (WrappedMonad m b) -> s -> WrappedMonad m t) -> s -> (i -> a -> m b) -> m t
imapAccumROf :: Over (Indexed i) (Backwards (State acc)) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
imapAccumLOf :: Over (Indexed i) (State acc) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
traversed :: Traversable f => IndexedTraversal Int (f a) (f b) a b
traversed1 :: Traversable1 f => IndexedTraversal1 Int (f a) (f b) a b
traversed64 :: Traversable f => IndexedTraversal Int64 (f a) (f b) a b
ignored :: Applicative f => pafb -> s -> f s
elementOf :: Applicative f => LensLike (Indexing f) s t a a -> Int -> IndexedLensLike Int f s t a a
element :: Traversable t => Int -> IndexedTraversal' Int (t a) a
elementsOf :: Applicative f => LensLike (Indexing f) s t a a -> (Int -> Bool) -> IndexedLensLike Int f s t a a
elements :: Traversable t => (Int -> Bool) -> IndexedTraversal' Int (t a) a
failover :: Alternative m => LensLike ((,) Any) s t a b -> (a -> b) -> s -> m t
ifailover :: Alternative m => Over (Indexed i) ((,) Any) s t a b -> (i -> a -> b) -> s -> m t
failing :: (Conjoined p, Applicative f) => Traversing p f s t a b -> Over p f s t a b -> Over p f s t a b
deepOf :: (Conjoined p, Applicative f) => LensLike f s t s t -> Traversing p f s t a b -> Over p f s t a b
confusing :: Applicative f => LensLike (Curried (Yoneda f) (Yoneda f)) s t a b -> LensLike f s t a b
traverseByOf :: Traversal s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> s -> f t
sequenceByOf :: Traversal s t (f b) b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> s -> f t
levels :: Applicative f => Traversing (->) f s t a b -> IndexedLensLike Int f s t (Level () a) (Level () b)
ilevels :: Applicative f => Traversing (Indexed i) f s t a b -> IndexedLensLike Int f s t (Level i a) (Level j b)
type ReifiedPrism' s a = ReifiedPrism s s a a
newtype ReifiedPrism s t a b = Prism {
- runPrism :: Prism s t a b
}
type ReifiedIso' s a = ReifiedIso s s a a
newtype ReifiedIso s t a b = Iso {
- runIso :: Iso s t a b
}
type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a
newtype ReifiedIndexedSetter i s t a b = IndexedSetter {
- runIndexedSetter :: IndexedSetter i s t a b
}
type ReifiedSetter' s a = ReifiedSetter s s a a
newtype ReifiedSetter s t a b = Setter {
- runSetter :: Setter s t a b
}
newtype ReifiedIndexedFold i s a = IndexedFold {
- runIndexedFold :: IndexedFold i s a
}
newtype ReifiedFold s a = Fold {
- runFold :: Fold s a
}
newtype ReifiedIndexedGetter i s a = IndexedGetter {
- runIndexedGetter :: IndexedGetter i s a
}
newtype ReifiedGetter s a = Getter {
- runGetter :: Getter s a
}
type ReifiedTraversal' s a = ReifiedTraversal s s a a
newtype ReifiedTraversal s t a b = Traversal {
- runTraversal :: Traversal s t a b
}
type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a
newtype ReifiedIndexedTraversal i s t a b = IndexedTraversal {
- runIndexedTraversal :: IndexedTraversal i s t a b
}
type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a
newtype ReifiedIndexedLens i s t a b = IndexedLens {
- runIndexedLens :: IndexedLens i s t a b
}
type ReifiedLens' s a = ReifiedLens s s a a
newtype ReifiedLens s t a b = Lens {
- runLens :: Lens s t a b
}
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)
- itraversed :: IndexedTraversal i (t a) (t b) a b
class Foldable f => FoldableWithIndex i f | f -> i where
- ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m
- ifolded :: IndexedFold i (f a) a
- ifoldr :: (i -> a -> b -> b) -> b -> f a -> b
- ifoldl :: (i -> b -> a -> b) -> b -> f a -> b
- ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b
- ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b
class Functor f => FunctorWithIndex i f | f -> i where
- imap :: (i -> a -> b) -> f a -> f b
- imapped :: IndexedSetter i (f a) (f b) a b
selfIndex :: Indexable a p => p a fb -> a -> fb
reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r
icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r
indices :: (Indexable i p, Applicative f) => (i -> Bool) -> Optical' p (Indexed i) f a a
index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a
iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
none :: Foldable f => (a -> Bool) -> f a -> Bool
itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f ()
ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f ()
imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m ()
iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m ()
iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b]
ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a)
ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b
ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b
itoList :: FoldableWithIndex i f => f a -> [(i, a)]
ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b)
imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b)
iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b)
imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r
ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r
itraverseBy :: TraversableWithIndex i t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> t a -> f (t b)
itraverseByOf :: IndexedTraversal i s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> s -> f t
type AnEquality' s a = AnEquality s s a a
type AnEquality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = Identical a (Proxy b) a (Proxy b) -> Identical a (Proxy b) s (Proxy t)
data Identical a b s t where
- Identical :: Identical a b a b
runEq :: AnEquality s t a b -> Identical s t a b
substEq :: AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r
mapEq :: forall (s :: k1) (t :: k2) (a :: k1) (b :: k2) (f :: k1 -> *). AnEquality s t a b -> f s -> f a
fromEq :: AnEquality s t a b -> Equality b a t s
simply :: (Optic' p f s a -> r) -> Optic' p f s a -> r
simple :: Equality' a a
class Strict lazy strict | lazy -> strict, strict -> lazy where
- strict :: Iso' lazy strict
class Bifunctor p => Swapped p where
- swapped :: Iso (p a b) (p c d) (p b a) (p d c)
type AnIso' s a = AnIso s s a a
type AnIso s t a b = Exchange a b a (Identity b) -> Exchange a b s (Identity t)
pattern List :: forall l. IsList l => [Item l] -> l
pattern Reversed :: forall t. Reversing t => t -> t
pattern Swapped :: forall (p :: Type -> Type -> Type) c d. Swapped p => p d c -> p c d
pattern Lazy :: forall t s. Strict t s => t -> s
pattern Strict :: forall s t. Strict s t => t -> s
iso :: (s -> a) -> (b -> t) -> Iso s t a b
from :: AnIso s t a b -> Iso b a t s
withIso :: AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r
cloneIso :: AnIso s t a b -> Iso s t a b
au :: Functor f => AnIso s t a b -> ((b -> t) -> f s) -> f a
auf :: Optic (Costar f) g s t a b -> (f a -> g b) -> f s -> g t
under :: AnIso s t a b -> (t -> s) -> b -> a
enum :: Enum a => Iso' Int a
mapping :: (Functor f, Functor g) => AnIso s t a b -> Iso (f s) (g t) (f a) (g b)
non :: Eq a => a -> Iso' (Maybe a) a
non' :: APrism' a () -> Iso' (Maybe a) a
anon :: a -> (a -> Bool) -> Iso' (Maybe a) a
curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f)
uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f)
flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c')
lazy :: Strict lazy strict => Iso' strict lazy
reversed :: Reversing a => Iso' a a
involuted :: (a -> a) -> Iso' a a
magma :: LensLike (Mafic a b) s t a b -> Iso s u (Magma Int t b a) (Magma j u c c)
imagma :: Over (Indexed i) (Molten i a b) s t a b -> Iso s t' (Magma i t b a) (Magma j t' c c)
contramapping :: Contravariant f => AnIso s t a b -> Iso (f a) (f b) (f s) (f t)
dimapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (p a s') (q b t') (p s a') (q t b')
lmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p a x) (q b y) (p s x) (q t y)
rmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p x s) (q y t) (p x a) (q y b)
bimapping :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (f s s') (g t t') (f a a') (g b b')
firsting :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f s x) (g t y) (f a x) (g b y)
seconding :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f x s) (g y t) (f x a) (g y b)
coerced :: forall s t a b. (Coercible s a, Coercible t b) => Iso s t a b
class AsEmpty a where
- _Empty :: Prism' a ()
pattern Empty :: forall s. AsEmpty s => s
class Snoc s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _Snoc :: Prism s t (s, a) (t, b)
class Cons s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _Cons :: Prism s t (a, s) (b, t)
cons :: Cons s s a a => a -> s -> s
uncons :: Cons s s a a => s -> Maybe (a, s)
_head :: Cons s s a a => Traversal' s a
_tail :: Cons s s a a => Traversal' s s
_init :: Snoc s s a a => Traversal' s s
_last :: Snoc s s a a => Traversal' s a
snoc :: Snoc s s a a => s -> a -> s
unsnoc :: Snoc s s a a => s -> Maybe (s, a)
class (Rewrapped s t, Rewrapped t s) => Rewrapping s t
class Wrapped s => Rewrapped (s :: *) (t :: *)
class Wrapped s where
- type Unwrapped s :: *
- _Wrapped' :: Iso' s (Unwrapped s)
pattern Unwrapped :: forall t. Rewrapped t t => t -> Unwrapped t
pattern Wrapped :: forall s. Rewrapped s s => Unwrapped s -> s
_GWrapped' :: (Generic s, D1 d (C1 c (S1 s' (Rec0 a))) ~ Rep s, Unwrapped s ~ GUnwrapped (Rep s)) => Iso' s (Unwrapped s)
_Unwrapped' :: Wrapped s => Iso' (Unwrapped s) s
_Wrapped :: Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t)
_Unwrapped :: Rewrapping s t => Iso (Unwrapped t) (Unwrapped s) t s
op :: Wrapped s => (Unwrapped s -> s) -> s -> Unwrapped s
_Wrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' s (Unwrapped s)
_Unwrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' (Unwrapped s) s
_Wrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso s t (Unwrapped s) (Unwrapped t)
_Unwrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso (Unwrapped t) (Unwrapped s) t s
ala :: (Functor f, Rewrapping s t) => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> f s) -> f (Unwrapped s)
alaf :: (Functor f, Functor g, Rewrapping s t) => (Unwrapped s -> s) -> (f t -> g s) -> f (Unwrapped t) -> g (Unwrapped s)
class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify m n b a | m -> b, n -> a, m a -> n, n b -> m where
- magnify :: LensLike' (Magnified m c) a b -> m c -> n c
class (MonadState s m, MonadState t n) => Zoom m n s t | m -> s, n -> t, m t -> n, n s -> m where
- zoom :: LensLike' (Zoomed m c) t s -> m c -> n c
type family Magnified (m :: * -> *) :: * -> * -> *
type family Zoomed (m :: * -> *) :: * -> * -> *
class GPlated a g
class Plated a where
- plate :: Traversal' a a
deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b
children :: Plated a => a -> [a]
rewrite :: Plated a => (a -> Maybe a) -> a -> a
rewriteOf :: ASetter a b a b -> (b -> Maybe a) -> a -> b
rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t
rewriteOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> Maybe a) -> s -> t
rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a
rewriteMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> a -> m b
rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t
rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> s -> m t
universe :: Plated a => a -> [a]
universeOf :: Getting [a] a a -> a -> [a]
universeOn :: Plated a => Getting [a] s a -> s -> [a]
universeOnOf :: Getting [a] s a -> Getting [a] a a -> s -> [a]
cosmos :: Plated a => Fold a a
cosmosOf :: (Applicative f, Contravariant f) => LensLike' f a a -> LensLike' f a a
cosmosOn :: (Applicative f, Contravariant f, Plated a) => LensLike' f s a -> LensLike' f s a
cosmosOnOf :: (Applicative f, Contravariant f) => LensLike' f s a -> LensLike' f a a -> LensLike' f s a
transform :: Plated a => (a -> a) -> a -> a
transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t
transformOf :: ASetter a b a b -> (b -> b) -> a -> b
transformOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> b) -> s -> t
transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a
transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t
transformMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m b) -> a -> m b
transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m b) -> s -> m t
contexts :: Plated a => a -> [Context a a a]
contextsOf :: ATraversal' a a -> a -> [Context a a a]
contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t]
contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t]
holes :: Plated a => a -> [Pretext (->) a a a]
holesOn :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Over p (Bazaar p r r) a b r r -> s -> [Pretext p r r t]
paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r
para :: Plated a => (a -> [r] -> r) -> a -> r
composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b
parts :: Plated a => Lens' a [a]
gplate :: (Generic a, GPlated a (Rep a)) => Traversal' a a
class Each s t a b | s -> a, t -> b, s b -> t, t a -> s where
- each :: Traversal s t a b
class Ixed m => At m where
- at :: Index m -> Lens' m (Maybe (IxValue m))
class Ixed m where
- ix :: Index m -> Traversal' m (IxValue m)
type family IxValue (m :: *) :: *
class Contains m where
- contains :: Index m -> Lens' m Bool
type family Index (s :: *) :: *
icontains :: Contains m => Index m -> IndexedLens' (Index m) m Bool
iix :: Ixed m => Index m -> IndexedTraversal' (Index m) m (IxValue m)
ixAt :: At m => Index m -> Traversal' m (IxValue m)
sans :: At m => Index m -> m -> m
iat :: At m => Index m -> IndexedLens' (Index m) m (Maybe (IxValue m))
makePrisms :: Name -> DecsQ
makeClassyPrisms :: Name -> DecsQ
type ClassyNamer = Name -> Maybe (Name, Name)
data DefName
- = TopName Name
- | MethodName Name Name
type FieldNamer = Name -> [Name] -> Name -> [DefName]
data LensRules
simpleLenses :: Lens' LensRules Bool
generateSignatures :: Lens' LensRules Bool
generateUpdateableOptics :: Lens' LensRules Bool
generateLazyPatterns :: Lens' LensRules Bool
createClass :: Lens' LensRules Bool
lensField :: Lens' LensRules FieldNamer
lensClass :: Lens' LensRules ClassyNamer
lensRules :: LensRules
underscoreNoPrefixNamer :: FieldNamer
lensRulesFor :: [(String, String)] -> LensRules
lookingupNamer :: [(String, String)] -> FieldNamer
mappingNamer :: (String -> [String]) -> FieldNamer
classyRules :: LensRules
classyRules_ :: LensRules
makeLenses :: Name -> DecsQ
makeClassy :: Name -> DecsQ
makeClassy_ :: Name -> DecsQ
makeLensesFor :: [(String, String)] -> Name -> DecsQ
makeClassyFor :: String -> String -> [(String, String)] -> Name -> DecsQ
makeLensesWith :: LensRules -> Name -> DecsQ
declareLenses :: DecsQ -> DecsQ
declareLensesFor :: [(String, String)] -> DecsQ -> DecsQ
declareClassy :: DecsQ -> DecsQ
declareClassyFor :: [(String, (String, String))] -> [(String, String)] -> DecsQ -> DecsQ
declarePrisms :: DecsQ -> DecsQ
declareWrapped :: DecsQ -> DecsQ
declareFields :: DecsQ -> DecsQ
declareLensesWith :: LensRules -> DecsQ -> DecsQ
makeWrapped :: Name -> DecsQ
underscoreFields :: LensRules
underscoreNamer :: FieldNamer
camelCaseFields :: LensRules
camelCaseNamer :: FieldNamer
classUnderscoreNoPrefixFields :: LensRules
classUnderscoreNoPrefixNamer :: FieldNamer
abbreviatedFields :: LensRules
abbreviatedNamer :: FieldNamer
makeFields :: Name -> DecsQ
makeFieldsNoPrefix :: Name -> DecsQ
defaultFieldRules :: LensRules

Documentation

class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

naturality: t . traverse f = traverse (t . f) for every applicative transformation t
identity: traverse Identity = Identity
composition: traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality: t . sequenceA = sequenceA . fmap t for every applicative transformation t
identity: sequenceA . fmap Identity = Identity
composition: sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

```
t (pure x) = pure x
```
```
t (x <*> y) = t x <*> t y
```

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative Identity where
    pure x = Identity x
    Identity f <*> Identity x = Identity (f x)

  newtype Compose f g a = Compose (f (g a))

  instance (Functor f, Functor g) => Functor (Compose f g) where
    fmap f (Compose x) = Compose (fmap (fmap f) x)

  instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

Instances are similar to Functor, e.g. given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Traversable Tree where
   traverse f Empty = pure Empty
   traverse f (Leaf x) = Leaf <$> f x
   traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

In the Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).
In the Foldable instance, foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).

Minimal complete definition

traverse | sequenceA

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.

Instances

Traversable []	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> [a] -> f [b] # sequenceA :: Applicative f => [f a] -> f [a] # mapM :: Monad m => (a -> m b) -> [a] -> m [b] # sequence :: Monad m => [m a] -> m [a] #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Traversable Par1	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) # sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) # mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) # sequence :: Monad m => Par1 (m a) -> m (Par1 a) #
Traversable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Traversable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) # sequenceA :: Applicative f => Min (f a) -> f (Min a) # mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) # sequence :: Monad m => Min (m a) -> m (Min a) #
Traversable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) # sequenceA :: Applicative f => Max (f a) -> f (Max a) # mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) # sequence :: Monad m => Max (m a) -> m (Max a) #
Traversable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) # sequenceA :: Applicative f => Option (f a) -> f (Option a) # mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) # sequence :: Monad m => Option (m a) -> m (Option a) #
Traversable ZipList	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) # sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) # mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) # sequence :: Monad m => ZipList (m a) -> m (ZipList a) #
Traversable Identity	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Traversable First	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Traversable Down	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Down a -> f (Down b) # sequenceA :: Applicative f => Down (f a) -> f (Down a) # mapM :: Monad m => (a -> m b) -> Down a -> m (Down b) # sequence :: Monad m => Down (m a) -> m (Down a) #
Traversable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) #
Traversable IntMap
Instance details Defined in Data.IntMap.Internal Methods traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b) # sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a) # mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b) # sequence :: Monad m => IntMap (m a) -> m (IntMap a) #
Traversable Tree
Instance details Defined in Data.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree a -> f (Tree b) # sequenceA :: Applicative f => Tree (f a) -> f (Tree a) # mapM :: Monad m => (a -> m b) -> Tree a -> m (Tree b) # sequence :: Monad m => Tree (m a) -> m (Tree a) #
Traversable Seq
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) # sequenceA :: Applicative f => Seq (f a) -> f (Seq a) # mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) # sequence :: Monad m => Seq (m a) -> m (Seq a) #
Traversable FingerTree
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> FingerTree a -> f (FingerTree b) # sequenceA :: Applicative f => FingerTree (f a) -> f (FingerTree a) # mapM :: Monad m => (a -> m b) -> FingerTree a -> m (FingerTree b) # sequence :: Monad m => FingerTree (m a) -> m (FingerTree a) #
Traversable Digit
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Digit a -> f (Digit b) # sequenceA :: Applicative f => Digit (f a) -> f (Digit a) # mapM :: Monad m => (a -> m b) -> Digit a -> m (Digit b) # sequence :: Monad m => Digit (m a) -> m (Digit a) #
Traversable Node
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Node a -> f (Node b) # sequenceA :: Applicative f => Node (f a) -> f (Node a) # mapM :: Monad m => (a -> m b) -> Node a -> m (Node b) # sequence :: Monad m => Node (m a) -> m (Node a) #
Traversable Elem
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Elem a -> f (Elem b) # sequenceA :: Applicative f => Elem (f a) -> f (Elem a) # mapM :: Monad m => (a -> m b) -> Elem a -> m (Elem b) # sequence :: Monad m => Elem (m a) -> m (Elem a) #
Traversable ViewL
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b) # sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a) # mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b) # sequence :: Monad m => ViewL (m a) -> m (ViewL a) #
Traversable ViewR
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b) # sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a) # mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b) # sequence :: Monad m => ViewR (m a) -> m (ViewR a) #
Traversable SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods traverse :: Applicative f => (a -> f b) -> SmallArray a -> f (SmallArray b) # sequenceA :: Applicative f => SmallArray (f a) -> f (SmallArray a) # mapM :: Monad m => (a -> m b) -> SmallArray a -> m (SmallArray b) # sequence :: Monad m => SmallArray (m a) -> m (SmallArray a) #
Traversable Array
Instance details Defined in Data.Primitive.Array Methods traverse :: Applicative f => (a -> f b) -> Array a -> f (Array b) # sequenceA :: Applicative f => Array (f a) -> f (Array a) # mapM :: Monad m => (a -> m b) -> Array a -> m (Array b) # sequence :: Monad m => Array (m a) -> m (Array a) #
Traversable Vector
Instance details Defined in Data.Vector Methods traverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) # sequenceA :: Applicative f => Vector (f a) -> f (Vector a) # mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) # sequence :: Monad m => Vector (m a) -> m (Vector a) #
Traversable Deque #
Instance details Defined in Control.Lens.Internal.Deque Methods traverse :: Applicative f => (a -> f b) -> Deque a -> f (Deque b) # sequenceA :: Applicative f => Deque (f a) -> f (Deque a) # mapM :: Monad m => (a -> m b) -> Deque a -> m (Deque b) # sequence :: Monad m => Deque (m a) -> m (Deque a) #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Traversable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Traversable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) # sequenceA :: Applicative f => U1 (f a) -> f (U1 a) # mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) # sequence :: Monad m => U1 (m a) -> m (U1 a) #
Traversable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequenceA :: Applicative f => (a, f a0) -> f (a, a0) # mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b) # sequence :: Monad m => (a, m a0) -> m (a, a0) #
Ix i => Traversable (Array i)	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) # sequenceA :: Applicative f => Array i (f a) -> f (Array i a) # mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) # sequence :: Monad m => Array i (m a) -> m (Array i a) #
Traversable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) #
Traversable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
Traversable (Map k)
Instance details Defined in Data.Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) # sequenceA :: Applicative f => Map k (f a) -> f (Map k a) # mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) # sequence :: Monad m => Map k (m a) -> m (Map k a) #
Traversable f => Traversable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods traverse :: Applicative f0 => (a -> f0 b) -> MaybeT f a -> f0 (MaybeT f b) # sequenceA :: Applicative f0 => MaybeT f (f0 a) -> f0 (MaybeT f a) # mapM :: Monad m => (a -> m b) -> MaybeT f a -> m (MaybeT f b) # sequence :: Monad m => MaybeT f (m a) -> m (MaybeT f a) #
(Monad m, Traversable m) => Traversable (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods traverse :: Applicative f => (a -> f b) -> CatchT m a -> f (CatchT m b) # sequenceA :: Applicative f => CatchT m (f a) -> f (CatchT m a) # mapM :: Monad m0 => (a -> m0 b) -> CatchT m a -> m0 (CatchT m b) # sequence :: Monad m0 => CatchT m (m0 a) -> m0 (CatchT m a) #
Traversable f => Traversable (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # sequenceA :: Applicative f0 => Cofree f (f0 a) -> f0 (Cofree f a) # mapM :: Monad m => (a -> m b) -> Cofree f a -> m (Cofree f b) # sequence :: Monad m => Cofree f (m a) -> m (Cofree f a) #
Traversable w => Traversable (CoiterT w)
Instance details Defined in Control.Comonad.Trans.Coiter Methods traverse :: Applicative f => (a -> f b) -> CoiterT w a -> f (CoiterT w b) # sequenceA :: Applicative f => CoiterT w (f a) -> f (CoiterT w a) # mapM :: Monad m => (a -> m b) -> CoiterT w a -> m (CoiterT w b) # sequence :: Monad m => CoiterT w (m a) -> m (CoiterT w a) #
Traversable f => Traversable (F f)
Instance details Defined in Control.Monad.Free.Church Methods traverse :: Applicative f0 => (a -> f0 b) -> F f a -> f0 (F f b) # sequenceA :: Applicative f0 => F f (f0 a) -> f0 (F f a) # mapM :: Monad m => (a -> m b) -> F f a -> m (F f b) # sequence :: Monad m => F f (m a) -> m (F f a) #
Traversable f => Traversable (Free f)
Instance details Defined in Control.Monad.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> Free f a -> f0 (Free f b) # sequenceA :: Applicative f0 => Free f (f0 a) -> f0 (Free f a) # mapM :: Monad m => (a -> m b) -> Free f a -> m (Free f b) # sequence :: Monad m => Free f (m a) -> m (Free f a) #
(Monad m, Traversable m) => Traversable (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods traverse :: Applicative f => (a -> f b) -> IterT m a -> f (IterT m b) # sequenceA :: Applicative f => IterT m (f a) -> f (IterT m a) # mapM :: Monad m0 => (a -> m0 b) -> IterT m a -> m0 (IterT m b) # sequence :: Monad m0 => IterT m (m0 a) -> m0 (IterT m a) #
Traversable f => Traversable (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods traverse :: Applicative f0 => (a -> f0 b) -> Yoneda f a -> f0 (Yoneda f b) # sequenceA :: Applicative f0 => Yoneda f (f0 a) -> f0 (Yoneda f a) # mapM :: Monad m => (a -> m b) -> Yoneda f a -> m (Yoneda f b) # sequence :: Monad m => Yoneda f (m a) -> m (Yoneda f a) #
Traversable f => Traversable (ListT f)
Instance details Defined in Control.Monad.Trans.List Methods traverse :: Applicative f0 => (a -> f0 b) -> ListT f a -> f0 (ListT f b) # sequenceA :: Applicative f0 => ListT f (f0 a) -> f0 (ListT f a) # mapM :: Monad m => (a -> m b) -> ListT f a -> m (ListT f b) # sequence :: Monad m => ListT f (m a) -> m (ListT f a) #
Traversable (HashMap k)
Instance details Defined in Data.HashMap.Base Methods traverse :: Applicative f => (a -> f b) -> HashMap k a -> f (HashMap k b) # sequenceA :: Applicative f => HashMap k (f a) -> f (HashMap k a) # mapM :: Monad m => (a -> m b) -> HashMap k a -> m (HashMap k b) # sequence :: Monad m => HashMap k (m a) -> m (HashMap k a) #
Traversable f => Traversable (Lift f)
Instance details Defined in Control.Applicative.Lift Methods traverse :: Applicative f0 => (a -> f0 b) -> Lift f a -> f0 (Lift f b) # sequenceA :: Applicative f0 => Lift f (f0 a) -> f0 (Lift f a) # mapM :: Monad m => (a -> m b) -> Lift f a -> m (Lift f b) # sequence :: Monad m => Lift f (m a) -> m (Lift f a) #
Traversable (Level i) #
Instance details Defined in Control.Lens.Internal.Level Methods traverse :: Applicative f => (a -> f b) -> Level i a -> f (Level i b) # sequenceA :: Applicative f => Level i (f a) -> f (Level i a) # mapM :: Monad m => (a -> m b) -> Level i a -> m (Level i b) # sequence :: Monad m => Level i (m a) -> m (Level i a) #
Traversable f => Traversable (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a) # mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) # sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) #
Traversable (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) # sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) # mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) # sequence :: Monad m => URec Char (m a) -> m (URec Char a) #
Traversable (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) # sequence :: Monad m => URec Double (m a) -> m (URec Double a) #
Traversable (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) # sequence :: Monad m => URec Float (m a) -> m (URec Float a) #
Traversable (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) # sequence :: Monad m => URec Int (m a) -> m (URec Int a) #
Traversable (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) # sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) # mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) # sequence :: Monad m => URec Word (m a) -> m (URec Word a) #
Traversable (URec (Ptr ()) :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec (Ptr ()) a -> f (URec (Ptr ()) b) # sequenceA :: Applicative f => URec (Ptr ()) (f a) -> f (URec (Ptr ()) a) # mapM :: Monad m => (a -> m b) -> URec (Ptr ()) a -> m (URec (Ptr ()) b) # sequence :: Monad m => URec (Ptr ()) (m a) -> m (URec (Ptr ()) a) #
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Traversable f => Traversable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) # sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) # mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) # sequence :: Monad m => Ap f (m a) -> m (Ap f a) #
Traversable f => Traversable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) # mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) # sequence :: Monad m => Alt f (m a) -> m (Alt f a) #
Bitraversable p => Traversable (Join p)
Instance details Defined in Data.Bifunctor.Join Methods traverse :: Applicative f => (a -> f b) -> Join p a -> f (Join p b) # sequenceA :: Applicative f => Join p (f a) -> f (Join p a) # mapM :: Monad m => (a -> m b) -> Join p a -> m (Join p b) # sequence :: Monad m => Join p (m a) -> m (Join p a) #
Bitraversable p => Traversable (Fix p)
Instance details Defined in Data.Bifunctor.Fix Methods traverse :: Applicative f => (a -> f b) -> Fix p a -> f (Fix p b) # sequenceA :: Applicative f => Fix p (f a) -> f (Fix p a) # mapM :: Monad m => (a -> m b) -> Fix p a -> m (Fix p b) # sequence :: Monad m => Fix p (m a) -> m (Fix p a) #
Traversable w => Traversable (EnvT e w)
Instance details Defined in Control.Comonad.Trans.Env Methods traverse :: Applicative f => (a -> f b) -> EnvT e w a -> f (EnvT e w b) # sequenceA :: Applicative f => EnvT e w (f a) -> f (EnvT e w a) # mapM :: Monad m => (a -> m b) -> EnvT e w a -> m (EnvT e w b) # sequence :: Monad m => EnvT e w (m a) -> m (EnvT e w a) #
Traversable f => Traversable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 (IdentityT f a) # mapM :: Monad m => (a -> m b) -> IdentityT f a -> m (IdentityT f b) # sequence :: Monad m => IdentityT f (m a) -> m (IdentityT f a) #
Traversable f => Traversable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 (ExceptT e f b) # sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 (ExceptT e f a) # mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b) # sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a) #
Traversable f => Traversable (FreeF f a)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a0 -> f0 b) -> FreeF f a a0 -> f0 (FreeF f a b) # sequenceA :: Applicative f0 => FreeF f a (f0 a0) -> f0 (FreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> FreeF f a a0 -> m (FreeF f a b) # sequence :: Monad m => FreeF f a (m a0) -> m (FreeF f a a0) #
(Monad m, Traversable m, Traversable f) => Traversable (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> FreeT f m a -> f0 (FreeT f m b) # sequenceA :: Applicative f0 => FreeT f m (f0 a) -> f0 (FreeT f m a) # mapM :: Monad m0 => (a -> m0 b) -> FreeT f m a -> m0 (FreeT f m b) # sequence :: Monad m0 => FreeT f m (m0 a) -> m0 (FreeT f m a) #
Traversable f => Traversable (CofreeF f a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a0 -> f0 b) -> CofreeF f a a0 -> f0 (CofreeF f a b) # sequenceA :: Applicative f0 => CofreeF f a (f0 a0) -> f0 (CofreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> CofreeF f a a0 -> m (CofreeF f a b) # sequence :: Monad m => CofreeF f a (m a0) -> m (CofreeF f a a0) #
(Traversable f, Traversable w) => Traversable (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> CofreeT f w a -> f0 (CofreeT f w b) # sequenceA :: Applicative f0 => CofreeT f w (f0 a) -> f0 (CofreeT f w a) # mapM :: Monad m => (a -> m b) -> CofreeT f w a -> m (CofreeT f w b) # sequence :: Monad m => CofreeT f w (m a) -> m (CofreeT f w a) #
Traversable f => Traversable (ErrorT e f)
Instance details Defined in Control.Monad.Trans.Error Methods traverse :: Applicative f0 => (a -> f0 b) -> ErrorT e f a -> f0 (ErrorT e f b) # sequenceA :: Applicative f0 => ErrorT e f (f0 a) -> f0 (ErrorT e f a) # mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m (ErrorT e f b) # sequence :: Monad m => ErrorT e f (m a) -> m (ErrorT e f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable (Forget r a)
Instance details Defined in Data.Profunctor.Types Methods traverse :: Applicative f => (a0 -> f b) -> Forget r a a0 -> f (Forget r a b) # sequenceA :: Applicative f => Forget r a (f a0) -> f (Forget r a a0) # mapM :: Monad m => (a0 -> m b) -> Forget r a a0 -> m (Forget r a b) # sequence :: Monad m => Forget r a (m a0) -> m (Forget r a a0) #
Traversable (Tagged s)
Instance details Defined in Data.Tagged Methods traverse :: Applicative f => (a -> f b) -> Tagged s a -> f (Tagged s b) # sequenceA :: Applicative f => Tagged s (f a) -> f (Tagged s a) # mapM :: Monad m => (a -> m b) -> Tagged s a -> m (Tagged s b) # sequence :: Monad m => Tagged s (m a) -> m (Tagged s a) #
Traversable f => Traversable (Reverse f)	Traverse from right to left.
Instance details Defined in Data.Functor.Reverse Methods traverse :: Applicative f0 => (a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # sequenceA :: Applicative f0 => Reverse f (f0 a) -> f0 (Reverse f a) # mapM :: Monad m => (a -> m b) -> Reverse f a -> m (Reverse f b) # sequence :: Monad m => Reverse f (m a) -> m (Reverse f a) #
Traversable (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods traverse :: Applicative f => (a0 -> f b) -> Constant a a0 -> f (Constant a b) # sequenceA :: Applicative f => Constant a (f a0) -> f (Constant a a0) # mapM :: Monad m => (a0 -> m b) -> Constant a a0 -> m (Constant a b) # sequence :: Monad m => Constant a (m a0) -> m (Constant a a0) #
Traversable f => Traversable (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods traverse :: Applicative f0 => (a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # sequenceA :: Applicative f0 => Backwards f (f0 a) -> f0 (Backwards f a) # mapM :: Monad m => (a -> m b) -> Backwards f a -> m (Backwards f b) # sequence :: Monad m => Backwards f (m a) -> m (Backwards f a) #
Traversable f => Traversable (AlongsideRight f a) #
Instance details Defined in Control.Lens.Internal.Getter Methods traverse :: Applicative f0 => (a0 -> f0 b) -> AlongsideRight f a a0 -> f0 (AlongsideRight f a b) # sequenceA :: Applicative f0 => AlongsideRight f a (f0 a0) -> f0 (AlongsideRight f a a0) # mapM :: Monad m => (a0 -> m b) -> AlongsideRight f a a0 -> m (AlongsideRight f a b) # sequence :: Monad m => AlongsideRight f a (m a0) -> m (AlongsideRight f a a0) #
Traversable f => Traversable (AlongsideLeft f b) #
Instance details Defined in Control.Lens.Internal.Getter Methods traverse :: Applicative f0 => (a -> f0 b0) -> AlongsideLeft f b a -> f0 (AlongsideLeft f b b0) # sequenceA :: Applicative f0 => AlongsideLeft f b (f0 a) -> f0 (AlongsideLeft f b a) # mapM :: Monad m => (a -> m b0) -> AlongsideLeft f b a -> m (AlongsideLeft f b b0) # sequence :: Monad m => AlongsideLeft f b (m a) -> m (AlongsideLeft f b a) #
Traversable (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) # sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) # mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) # sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) #
(Traversable f, Traversable g) => Traversable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
(Traversable f, Traversable g) => Traversable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #
(Traversable f, Traversable g) => Traversable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) # sequence :: Monad m => Product f g (m a) -> m (Product f g a) #
(Traversable f, Traversable g) => Traversable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods traverse :: Applicative f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequenceA :: Applicative f0 => Sum f g (f0 a) -> f0 (Sum f g a) # mapM :: Monad m => (a -> m b) -> Sum f g a -> m (Sum f g b) # sequence :: Monad m => Sum f g (m a) -> m (Sum f g a) #
Traversable (Magma i t b) #
Instance details Defined in Control.Lens.Internal.Magma Methods traverse :: Applicative f => (a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # sequenceA :: Applicative f => Magma i t b (f a) -> f (Magma i t b a) # mapM :: Monad m => (a -> m b0) -> Magma i t b a -> m (Magma i t b b0) # sequence :: Monad m => Magma i t b (m a) -> m (Magma i t b a) #
Traversable f => Traversable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) # sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) #
(Traversable f, Traversable g) => Traversable (f :.: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #
(Traversable f, Traversable g) => Traversable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) # mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) # sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) #
Bitraversable p => Traversable (WrappedBifunctor p a)
Instance details Defined in Data.Bifunctor.Wrapped Methods traverse :: Applicative f => (a0 -> f b) -> WrappedBifunctor p a a0 -> f (WrappedBifunctor p a b) # sequenceA :: Applicative f => WrappedBifunctor p a (f a0) -> f (WrappedBifunctor p a a0) # mapM :: Monad m => (a0 -> m b) -> WrappedBifunctor p a a0 -> m (WrappedBifunctor p a b) # sequence :: Monad m => WrappedBifunctor p a (m a0) -> m (WrappedBifunctor p a a0) #
Traversable g => Traversable (Joker g a)
Instance details Defined in Data.Bifunctor.Joker Methods traverse :: Applicative f => (a0 -> f b) -> Joker g a a0 -> f (Joker g a b) # sequenceA :: Applicative f => Joker g a (f a0) -> f (Joker g a a0) # mapM :: Monad m => (a0 -> m b) -> Joker g a a0 -> m (Joker g a b) # sequence :: Monad m => Joker g a (m a0) -> m (Joker g a a0) #
Bitraversable p => Traversable (Flip p a)
Instance details Defined in Data.Bifunctor.Flip Methods traverse :: Applicative f => (a0 -> f b) -> Flip p a a0 -> f (Flip p a b) # sequenceA :: Applicative f => Flip p a (f a0) -> f (Flip p a a0) # mapM :: Monad m => (a0 -> m b) -> Flip p a a0 -> m (Flip p a b) # sequence :: Monad m => Flip p a (m a0) -> m (Flip p a a0) #
Traversable (Clown f a :: Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Clown f a a0 -> f0 (Clown f a b) # sequenceA :: Applicative f0 => Clown f a (f0 a0) -> f0 (Clown f a a0) # mapM :: Monad m => (a0 -> m b) -> Clown f a a0 -> m (Clown f a b) # sequence :: Monad m => Clown f a (m a0) -> m (Clown f a a0) #
(Traversable f, Bitraversable p) => Traversable (Tannen f p a)
Instance details Defined in Data.Bifunctor.Tannen Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Tannen f p a a0 -> f0 (Tannen f p a b) # sequenceA :: Applicative f0 => Tannen f p a (f0 a0) -> f0 (Tannen f p a a0) # mapM :: Monad m => (a0 -> m b) -> Tannen f p a a0 -> m (Tannen f p a b) # sequence :: Monad m => Tannen f p a (m a0) -> m (Tannen f p a a0) #
(Bitraversable p, Traversable g) => Traversable (Biff p f g a)
Instance details Defined in Data.Bifunctor.Biff Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Biff p f g a a0 -> f0 (Biff p f g a b) # sequenceA :: Applicative f0 => Biff p f g a (f0 a0) -> f0 (Biff p f g a a0) # mapM :: Monad m => (a0 -> m b) -> Biff p f g a a0 -> m (Biff p f g a b) # sequence :: Monad m => Biff p f g a (m a0) -> m (Biff p f g a a0) #

class Contravariant (f :: Type -> Type) where #

The class of contravariant functors.

Whereas in Haskell, one can think of a Functor as containing or producing values, a contravariant functor is a functor that can be thought of as consuming values.

As an example, consider the type of predicate functions a -> Bool. One such predicate might be negative x = x < 0, which classifies integers as to whether they are negative. However, given this predicate, we can re-use it in other situations, providing we have a way to map values to integers. For instance, we can use the negative predicate on a person's bank balance to work out if they are currently overdrawn:

newtype Predicate a = Predicate { getPredicate :: a -> Bool }

instance Contravariant Predicate where
  contramap f (Predicate p) = Predicate (p . f)
                                         |   `- First, map the input...
                                         `----- then apply the predicate.

overdrawn :: Predicate Person
overdrawn = contramap personBankBalance negative

Any instance should be subject to the following laws:

contramap id = id
contramap f . contramap g = contramap (g . f)

Note, that the second law follows from the free theorem of the type of contramap and the first law, so you need only check that the former condition holds.

Minimal complete definition

contramap

Methods

contramap :: (a -> b) -> f b -> f a #

(>$) :: b -> f b -> f a infixl 4 #

Replace all locations in the output with the same value. The default definition is contramap . const, but this may be overridden with a more efficient version.

Instances

Contravariant Predicate	A `Predicate` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to the input of the predicate.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Predicate b -> Predicate a # (>$) :: b -> Predicate b -> Predicate a #
Contravariant Comparison	A `Comparison` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to each input of the comparison function.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Comparison b -> Comparison a # (>$) :: b -> Comparison b -> Comparison a #
Contravariant Equivalence	Equivalence relations are `Contravariant`, because you can apply the contramapped function to each input to the equivalence relation.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Equivalence b -> Equivalence a # (>$) :: b -> Equivalence b -> Equivalence a #
Contravariant (V1 :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> V1 b -> V1 a # (>$) :: b -> V1 b -> V1 a #
Contravariant (U1 :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> U1 b -> U1 a # (>$) :: b -> U1 b -> U1 a #
Contravariant (Op a)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a0 -> b) -> Op a b -> Op a a0 # (>$) :: b -> Op a b -> Op a a0 #
Contravariant (Proxy :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Proxy b -> Proxy a # (>$) :: b -> Proxy b -> Proxy a #
Contravariant m => Contravariant (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods contramap :: (a -> b) -> MaybeT m b -> MaybeT m a # (>$) :: b -> MaybeT m b -> MaybeT m a #
Contravariant m => Contravariant (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods contramap :: (a -> b) -> ListT m b -> ListT m a # (>$) :: b -> ListT m b -> ListT m a #
Contravariant f => Contravariant (Indexing64 f) #
Instance details Defined in Control.Lens.Internal.Indexed Methods contramap :: (a -> b) -> Indexing64 f b -> Indexing64 f a # (>$) :: b -> Indexing64 f b -> Indexing64 f a #
Contravariant f => Contravariant (Indexing f) #
Instance details Defined in Control.Lens.Internal.Indexed Methods contramap :: (a -> b) -> Indexing f b -> Indexing f a # (>$) :: b -> Indexing f b -> Indexing f a #
Contravariant f => Contravariant (Rec1 f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Rec1 f b -> Rec1 f a # (>$) :: b -> Rec1 f b -> Rec1 f a #
Contravariant (Const a :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a0 -> b) -> Const a b -> Const a a0 # (>$) :: b -> Const a b -> Const a a0 #
Contravariant f => Contravariant (Alt f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Alt f b -> Alt f a # (>$) :: b -> Alt f b -> Alt f a #
Contravariant f => Contravariant (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods contramap :: (a -> b) -> IdentityT f b -> IdentityT f a # (>$) :: b -> IdentityT f b -> IdentityT f a #
(Functor f, Contravariant g) => Contravariant (ComposeFC f g)
Instance details Defined in Data.Functor.Contravariant.Compose Methods contramap :: (a -> b) -> ComposeFC f g b -> ComposeFC f g a # (>$) :: b -> ComposeFC f g b -> ComposeFC f g a #
(Contravariant f, Functor g) => Contravariant (ComposeCF f g)
Instance details Defined in Data.Functor.Contravariant.Compose Methods contramap :: (a -> b) -> ComposeCF f g b -> ComposeCF f g a # (>$) :: b -> ComposeCF f g b -> ComposeCF f g a #
Contravariant m => Contravariant (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods contramap :: (a -> b) -> ExceptT e m b -> ExceptT e m a # (>$) :: b -> ExceptT e m b -> ExceptT e m a #
Contravariant m => Contravariant (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods contramap :: (a -> b) -> ErrorT e m b -> ErrorT e m a # (>$) :: b -> ErrorT e m b -> ErrorT e m a #
Contravariant m => Contravariant (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods contramap :: (a -> b) -> ReaderT r m b -> ReaderT r m a # (>$) :: b -> ReaderT r m b -> ReaderT r m a #
Contravariant m => Contravariant (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods contramap :: (a -> b) -> StateT s m b -> StateT s m a # (>$) :: b -> StateT s m b -> StateT s m a #
Contravariant m => Contravariant (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods contramap :: (a -> b) -> StateT s m b -> StateT s m a # (>$) :: b -> StateT s m b -> StateT s m a #
Contravariant m => Contravariant (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods contramap :: (a -> b) -> WriterT w m b -> WriterT w m a # (>$) :: b -> WriterT w m b -> WriterT w m a #
Contravariant m => Contravariant (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods contramap :: (a -> b) -> WriterT w m b -> WriterT w m a # (>$) :: b -> WriterT w m b -> WriterT w m a #
Contravariant f => Contravariant (Reverse f)	Derived instance.
Instance details Defined in Data.Functor.Reverse Methods contramap :: (a -> b) -> Reverse f b -> Reverse f a # (>$) :: b -> Reverse f b -> Reverse f a #
Contravariant (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods contramap :: (a0 -> b) -> Constant a b -> Constant a a0 # (>$) :: b -> Constant a b -> Constant a a0 #
Contravariant f => Contravariant (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods contramap :: (a -> b) -> Backwards f b -> Backwards f a # (>$) :: b -> Backwards f b -> Backwards f a #
Contravariant f => Contravariant (AlongsideRight f a) #
Instance details Defined in Control.Lens.Internal.Getter Methods contramap :: (a0 -> b) -> AlongsideRight f a b -> AlongsideRight f a a0 # (>$) :: b -> AlongsideRight f a b -> AlongsideRight f a a0 #
Contravariant f => Contravariant (AlongsideLeft f b) #
Instance details Defined in Control.Lens.Internal.Getter Methods contramap :: (a -> b0) -> AlongsideLeft f b b0 -> AlongsideLeft f b a # (>$) :: b0 -> AlongsideLeft f b b0 -> AlongsideLeft f b a #
Contravariant (Effect m r) #
Instance details Defined in Control.Lens.Internal.Zoom Methods contramap :: (a -> b) -> Effect m r b -> Effect m r a # (>$) :: b -> Effect m r b -> Effect m r a #
Contravariant (K1 i c :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> K1 i c b -> K1 i c a # (>$) :: b -> K1 i c b -> K1 i c a #
(Contravariant f, Contravariant g) => Contravariant (f :+: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> (f :+: g) b -> (f :+: g) a # (>$) :: b -> (f :+: g) b -> (f :+: g) a #
(Contravariant f, Contravariant g) => Contravariant (f :*: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> (f :: g) b -> (f :: g) a # (>$) :: b -> (f :: g) b -> (f :: g) a #
(Contravariant f, Contravariant g) => Contravariant (Product f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Product f g b -> Product f g a # (>$) :: b -> Product f g b -> Product f g a #
(Contravariant f, Contravariant g) => Contravariant (Sum f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Sum f g b -> Sum f g a # (>$) :: b -> Sum f g b -> Sum f g a #
Contravariant f => Contravariant (M1 i c f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> M1 i c f b -> M1 i c f a # (>$) :: b ->