lens-4.17: Lenses, Folds and Traversals

Copyright(C) 2013-16 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityexperimental
Portabilitynon-portable
Safe HaskellSafe
LanguageHaskell98

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

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.

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:

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 ->