diagrams-lib-1.4.3: Embedded domain-specific language for declarative graphics

Copyright(c) 2011-2015 diagrams-lib team (see LICENSE)
LicenseBSD-style (see LICENSE)
Maintainerdiagrams-discuss@googlegroups.com
Safe HaskellNone
LanguageHaskell2010

Diagrams.Prelude

Contents

Description

A module to re-export most of the functionality of the diagrams core and standard library.

Synopsis

Diagrams library

Exports from this library for working with diagrams.

module Diagrams

Convenience re-exports from other packages

For working with default values. Diagrams also exports with, an alias for def.

For representing and operating on colors.

alphaChannel :: AlphaColour a -> a #

Returns the opacity of an AlphaColour.

blend :: (Num a, AffineSpace f) => a -> f a -> f a -> f a #

Compute the weighted average of two points. e.g.

blend 0.4 a b = 0.4*a + 0.6*b

The weight can be negative, or greater than 1.0; however, be aware that non-convex combinations may lead to out of gamut colours.

withOpacity :: Num a => Colour a -> a -> AlphaColour a #

Creates an AlphaColour from a Colour with a given opacity.

c `withOpacity` o == dissolve o (opaque c)

dissolve :: Num a => a -> AlphaColour a -> AlphaColour a #

Returns an AlphaColour more transparent by a factor of o.

opaque :: Num a => Colour a -> AlphaColour a #

Creates an opaque AlphaColour from a Colour.

alphaColourConvert :: (Fractional b, Real a) => AlphaColour a -> AlphaColour b #

Change the type used to represent the colour coordinates.

transparent :: Num a => AlphaColour a #

This AlphaColour is entirely transparent and has no associated colour channel.

black :: Num a => Colour a #

colourConvert :: (Fractional b, Real a) => Colour a -> Colour b #

Change the type used to represent the colour coordinates.

data Colour a #

This type represents the human preception of colour. The a parameter is a numeric type used internally for the representation.

The Monoid instance allows one to add colours, but beware that adding colours can take you out of gamut. Consider using blend whenever possible.

Instances
AffineSpace Colour 
Instance details

Defined in Data.Colour.Internal

Methods

affineCombo :: Num a => [(a, Colour a)] -> Colour a -> Colour a #

ColourOps Colour 
Instance details

Defined in Data.Colour.Internal

Methods

over :: Num a => AlphaColour a -> Colour a -> Colour a #

darken :: Num a => a -> Colour a -> Colour a #

Eq a => Eq (Colour a) 
Instance details

Defined in Data.Colour.Internal

Methods

(==) :: Colour a -> Colour a -> Bool #

(/=) :: Colour a -> Colour a -> Bool #

Num a => Semigroup (Colour a) 
Instance details

Defined in Data.Colour.Internal

Methods

(<>) :: Colour a -> Colour a -> Colour a #

sconcat :: NonEmpty (Colour a) -> Colour a #

stimes :: Integral b => b -> Colour a -> Colour a #

Num a => Monoid (Colour a) 
Instance details

Defined in Data.Colour.Internal

Methods

mempty :: Colour a #

mappend :: Colour a -> Colour a -> Colour a #

mconcat :: [Colour a] -> Colour a #

a ~ Double => Color (Colour a) Source # 
Instance details

Defined in Diagrams.Attributes

Parseable (Colour Double) Source #

Parse Colour Double as either a named color from Data.Colour.Names or a hexadecimal color.

Instance details

Defined in Diagrams.Backend.CmdLine

data AlphaColour a #

This type represents a Colour that may be semi-transparent.

The Monoid instance allows you to composite colours.

x `mappend` y == x `over` y

To get the (pre-multiplied) colour channel of an AlphaColour c, simply composite c over black.

c `over` black
Instances
AffineSpace AlphaColour 
Instance details

Defined in Data.Colour.Internal

Methods

affineCombo :: Num a => [(a, AlphaColour a)] -> AlphaColour a -> AlphaColour a #

ColourOps AlphaColour 
Instance details

Defined in Data.Colour.Internal

Methods

over :: Num a => AlphaColour a -> AlphaColour a -> AlphaColour a #

darken :: Num a => a -> AlphaColour a -> AlphaColour a #

Eq a => Eq (AlphaColour a) 
Instance details

Defined in Data.Colour.Internal

Num a => Semigroup (AlphaColour a)

AlphaColour forms a monoid with over and transparent.

Instance details

Defined in Data.Colour.Internal

Num a => Monoid (AlphaColour a) 
Instance details

Defined in Data.Colour.Internal

a ~ Double => Color (AlphaColour a) Source # 
Instance details

Defined in Diagrams.Attributes

Parseable (AlphaColour Double) Source #

Parse AlphaColour Double as either a named color from Data.Colour.Names or a hexadecimal color.

Instance details

Defined in Diagrams.Backend.CmdLine

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

Minimal complete definition

over, darken

Methods

darken :: Num a => a -> f a -> f a #

darken s c blends a colour with black without changing it's opacity.

For Colour, darken s c = blend s c mempty

Instances
ColourOps Colour 
Instance details

Defined in Data.Colour.Internal

Methods

over :: Num a => AlphaColour a -> Colour a -> Colour a #

darken :: Num a => a -> Colour a -> Colour a #

ColourOps AlphaColour 
Instance details

Defined in Data.Colour.Internal

Methods

over :: Num a => AlphaColour a -> AlphaColour a -> AlphaColour a #

darken :: Num a => a -> AlphaColour a -> AlphaColour a #

A large list of color names.

yellow :: (Ord a, Floating a) => Colour a #

whitesmoke :: (Ord a, Floating a) => Colour a #

white :: (Ord a, Floating a) => Colour a #

wheat :: (Ord a, Floating a) => Colour a #

violet :: (Ord a, Floating a) => Colour a #

turquoise :: (Ord a, Floating a) => Colour a #

tomato :: (Ord a, Floating a) => Colour a #

thistle :: (Ord a, Floating a) => Colour a #

teal :: (Ord a, Floating a) => Colour a #

steelblue :: (Ord a, Floating a) => Colour a #

snow :: (Ord a, Floating a) => Colour a #

slategrey :: (Ord a, Floating a) => Colour a #

slategray :: (Ord a, Floating a) => Colour a #

slateblue :: (Ord a, Floating a) => Colour a #

skyblue :: (Ord a, Floating a) => Colour a #

silver :: (Ord a, Floating a) => Colour a #

sienna :: (Ord a, Floating a) => Colour a #

seashell :: (Ord a, Floating a) => Colour a #

seagreen :: (Ord a, Floating a) => Colour a #

sandybrown :: (Ord a, Floating a) => Colour a #

salmon :: (Ord a, Floating a) => Colour a #

royalblue :: (Ord a, Floating a) => Colour a #

rosybrown :: (Ord a, Floating a) => Colour a #

red :: (Ord a, Floating a) => Colour a #

purple :: (Ord a, Floating a) => Colour a #

powderblue :: (Ord a, Floating a) => Colour a #

plum :: (Ord a, Floating a) => Colour a #

pink :: (Ord a, Floating a) => Colour a #

peru :: (Ord a, Floating a) => Colour a #

peachpuff :: (Ord a, Floating a) => Colour a #

papayawhip :: (Ord a, Floating a) => Colour a #

palegreen :: (Ord a, Floating a) => Colour a #

orchid :: (Ord a, Floating a) => Colour a #

orangered :: (Ord a, Floating a) => Colour a #

orange :: (Ord a, Floating a) => Colour a #

olivedrab :: (Ord a, Floating a) => Colour a #

olive :: (Ord a, Floating a) => Colour a #

oldlace :: (Ord a, Floating a) => Colour a #

navy :: (Ord a, Floating a) => Colour a #

moccasin :: (Ord a, Floating a) => Colour a #

mistyrose :: (Ord a, Floating a) => Colour a #

mintcream :: (Ord a, Floating a) => Colour a #

mediumblue :: (Ord a, Floating a) => Colour a #

maroon :: (Ord a, Floating a) => Colour a #

magenta :: (Ord a, Floating a) => Colour a #

linen :: (Ord a, Floating a) => Colour a #

limegreen :: (Ord a, Floating a) => Colour a #

lime :: (Ord a, Floating a) => Colour a #

lightpink :: (Ord a, Floating a) => Colour a #

lightgrey :: (Ord a, Floating a) => Colour a #

lightgreen :: (Ord a, Floating a) => Colour a #

lightgray :: (Ord a, Floating a) => Colour a #

lightcyan :: (Ord a, Floating a) => Colour a #

lightcoral :: (Ord a, Floating a) => Colour a #

lightblue :: (Ord a, Floating a) => Colour a #

lawngreen :: (Ord a, Floating a) => Colour a #

lavender :: (Ord a, Floating a) => Colour a #

khaki :: (Ord a, Floating a) => Colour a #

ivory :: (Ord a, Floating a) => Colour a #

indigo :: (Ord a, Floating a) => Colour a #

indianred :: (Ord a, Floating a) => Colour a #

hotpink :: (Ord a, Floating a) => Colour a #

honeydew :: (Ord a, Floating a) => Colour a #

green :: (Ord a, Floating a) => Colour a #

grey :: (Ord a, Floating a) => Colour a #

gray :: (Ord a, Floating a) => Colour a #

goldenrod :: (Ord a, Floating a) => Colour a #

gold :: (Ord a, Floating a) => Colour a #

ghostwhite :: (Ord a, Floating a) => Colour a #

gainsboro :: (Ord a, Floating a) => Colour a #

fuchsia :: (Ord a, Floating a) => Colour a #

firebrick :: (Ord a, Floating a) => Colour a #

dodgerblue :: (Ord a, Floating a) => Colour a #

dimgrey :: (Ord a, Floating a) => Colour a #

dimgray :: (Ord a, Floating a) => Colour a #

deeppink :: (Ord a, Floating a) => Colour a #

darkviolet :: (Ord a, Floating a) => Colour a #

darksalmon :: (Ord a, Floating a) => Colour a #

darkred :: (Ord a, Floating a) => Colour a #

darkorchid :: (Ord a, Floating a) => Colour a #

darkorange :: (Ord a, Floating a) => Colour a #

darkkhaki :: (Ord a, Floating a) => Colour a #

darkgrey :: (Ord a, Floating a) => Colour a #

darkgreen :: (Ord a, Floating a) => Colour a #

darkgray :: (Ord a, Floating a) => Colour a #

darkcyan :: (Ord a, Floating a) => Colour a #

darkblue :: (Ord a, Floating a) => Colour a #

cyan :: (Ord a, Floating a) => Colour a #

crimson :: (Ord a, Floating a) => Colour a #

cornsilk :: (Ord a, Floating a) => Colour a #

coral :: (Ord a, Floating a) => Colour a #

chocolate :: (Ord a, Floating a) => Colour a #

chartreuse :: (Ord a, Floating a) => Colour a #

cadetblue :: (Ord a, Floating a) => Colour a #

burlywood :: (Ord a, Floating a) => Colour a #

brown :: (Ord a, Floating a) => Colour a #

blueviolet :: (Ord a, Floating a) => Colour a #

blue :: (Ord a, Floating a) => Colour a #

bisque :: (Ord a, Floating a) => Colour a #

beige :: (Ord a, Floating a) => Colour a #

azure :: (Ord a, Floating a) => Colour a #

aquamarine :: (Ord a, Floating a) => Colour a #

aqua :: (Ord a, Floating a) => Colour a #

aliceblue :: (Ord a, Floating a) => Colour a #

readColourName :: (MonadFail m, Monad m, Ord a, Floating a) => String -> m (Colour a) #

black :: Num a => Colour a #

Specify your own colours.

Semigroups and monoids show up all over the place, so things from Data.Semigroup and Data.Monoid often come in handy.

For computing with vectors.

For computing with points and vectors.

For computing with dot products and norm.

For working with Active (i.e. animated) things.

Most of the lens package. The following functions are not exported from lens because they either conflict with diagrams or may conflict with other libraries:

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 Interval 
Instance details

Defined in Numeric.Interval.Kaucher

Methods

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

sequenceA :: Applicative f => Interval (f a) -> f (Interval a) #

mapM :: Monad m => (a -> m b) -> Interval a -> m (Interval b) #

sequence :: Monad m => Interval (m a) -> m (Interval 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 Plucker 
Instance details

Defined in Linear.Plucker

Methods

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

sequenceA :: Applicative f => Plucker (f a) -> f (Plucker a) #

mapM :: Monad m => (a -> m b) -> Plucker a -> m (Plucker b) #

sequence :: Monad m => Plucker (m a) -> m (Plucker a) #

Traversable Quaternion 
Instance details

Defined in Linear.Quaternion

Methods

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

sequenceA :: Applicative f => Quaternion (f a) -> f (Quaternion a) #

mapM :: Monad m => (a -> m b) -> Quaternion a -> m (Quaternion b) #

sequence :: Monad m => Quaternion (m a) -> m (Quaternion a) #

Traversable V0 
Instance details

Defined in Linear.V0

Methods

traverse :: Applicative f => (a -> f b) -> V0 a -> f (V0 b) #

sequenceA :: Applicative f => V0 (f a) -> f (V0 a) #

mapM :: Monad m => (a -> m b) -> V0 a -> m (V0 b) #

sequence :: Monad m => V0 (m a) -> m (V0 a) #

Traversable V4 
Instance details

Defined in Linear.V4

Methods

traverse :: Applicative f => (a -> f b) -> V4 a -> f (V4 b) #

sequenceA :: Applicative f => V4 (f a) -> f (V4 a) #

mapM :: Monad m => (a -> m b) -> V4 a -> m (V4 b) #

sequence :: Monad m => V4 (m a) -> m (V4 a) #

Traversable V3 
Instance details

Defined in Linear.V3

Methods

traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b) #

sequenceA :: Applicative f => V3 (f a) -> f (V3 a) #

mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b) #

sequence :: Monad m => V3 (m a) -> m (V3 a) #

Traversable V2 
Instance details

Defined in Linear.V2

Methods

traverse :: Applicative f => (a -> f b) -> V2 a -> f (V2 b) #

sequenceA :: Applicative f => V2 (f a) -> f (V2 a) #

mapM :: Monad m => (a -> m b) -> V2 a -> m (V2 b) #

sequence :: Monad m => V2 (m a) -> m (V2 a) #

Traversable V1 
Instance details

Defined in Linear.V1

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 Split 
Instance details

Defined in Data.Monoid.Split

Methods

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

sequenceA :: Applicative f => Split (f a) -> f (Split a) #

mapM :: Monad m => (a -> m b) -> Split a -> m (Split b) #

sequence :: Monad m => Split (m a) -> m (Split a) #

Traversable Recommend 
Instance details

Defined in Data.Monoid.Recommend

Methods

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

sequenceA :: Applicative f => Recommend (f a) -> f (Recommend a) #

mapM :: Monad m => (a -> m b) -> Recommend a -> m (Recommend b) #

sequence :: Monad m => Recommend (m a) -> m (Recommend a) #

Traversable Deletable 
Instance details

Defined in Data.Monoid.Deletable

Methods

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

sequenceA :: Applicative f => Deletable (f a) -> f (Deletable a) #

mapM :: Monad m => (a -> m b) -> Deletable a -> m (Deletable b) #

sequence :: Monad m => Deletable (m a) -> m (Deletable 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 (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 (Point f) 
Instance details

Defined in Linear.Affine

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Point f a -> f0 (Point f b) #

sequenceA :: Applicative f0 => Point f (f0 a) -> f0 (Point f a) #

mapM :: Monad m => (a -> m b) -> Point f a -> m (Point f b) #

sequence :: Monad m => Point f (m a) -> m (Point f 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 (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 (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 (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 (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 (Inf p) 
Instance details

Defined in Data.Monoid.Inf

Methods

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

sequenceA :: Applicative f => Inf p (f a) -> f (Inf p a) #

mapM :: Monad m => (a -> m b) -> Inf p a -> m (Inf p b) #

sequence :: Monad m => Inf p (m a) -> m (Inf p 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 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 (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 (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 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 (V n) 
Instance details

Defined in Linear.V

Methods

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

sequenceA :: Applicative f => V n (f a) -> f (V n a) #

mapM :: Monad m => (a -> m b) -> V n a -> m (V n b) #

sequence :: Monad m => V n (m a) -> m (V n 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 (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 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 (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 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 (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 (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 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 (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 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 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 (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 (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 (Star f a) 
Instance details

Defined in Data.Profunctor.Types

Methods

contramap :: (a0 -> b) -> Star f a b -> Star f a a0 #

(>$) :: b -> Star f a b -> Star f a a0 #

Contravariant (Forget r a) 
Instance details

Defined in Data.Profunctor.Types

Methods

contramap :: (a0 -> b) -> Forget r a b -> Forget r a a0 #

(>$) :: b -> Forget r a b -> Forget r a a0 #

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 (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 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 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 -> M1 i c f b -> M1 i c f a #

(Functor 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 #

(Functor f, Contravariant g) => Contravariant (Compose f g) 
Instance details

Defined in Data.Functor.Contravariant

Methods

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

(>$) :: b -> Compose f g b -> Compose f g a #

Contravariant m => Contravariant (RWST r w s m) 
Instance details

Defined in Control.Monad.Trans.RWS.Strict

Methods

contramap :: (a -> b) -> RWST r w s m b -> RWST r w s m a #

(>$) :: b -> RWST r w s m b -> RWST r w s m a #

Contravariant f => Contravariant (TakingWhile p f a b) 
Instance details

Defined in Control.Lens.Internal.Magma

Methods

contramap :: (a0 -> b0) -> TakingWhile p f a b b0 -> TakingWhile p f a b a0 #

(>$) :: b0 -> TakingWhile p f a b b0 -> TakingWhile p f a b a0 #

(Profunctor p, Contravariant g) => Contravariant (BazaarT p g a b) 
Instance details

Defined in Control.Lens.Internal.Bazaar

Methods

contramap :: (a0 -> b0) -> BazaarT p g a b b0 -> BazaarT p g a b a0 #

(>$) :: b0 -> BazaarT p g a b b0 -> BazaarT p g a b a0 #

(Profunctor p, Contravariant g) => Contravariant (BazaarT1 p g a b) 
Instance details

Defined in Control.Lens.Internal.Bazaar

Methods

contramap :: (a0 -> b0) -> BazaarT1 p g a b b0 -> BazaarT1 p g a b a0 #

(>$) :: b0 -> BazaarT1 p g a b b0 -> BazaarT1 p g a b a0 #

(Profunctor p, Contravariant g) => Contravariant (PretextT p g a b) 
Instance details

Defined in Control.Lens.Internal.Context

Methods

contramap :: (a0 -> b0) -> PretextT p g a b b0 -> PretextT p g a b a0 #

(>$) :: b0 -> PretextT p g a b b0 -> PretextT p g a b a0 #

Contravariant m => Contravariant (RWST r w s m) 
Instance details

Defined in Control.Monad.Trans.RWS.Lazy

Methods

contramap :: (a -> b) -> RWST r w s m b -> RWST r w s m a #

(>$) :: b -> RWST r w s m b -> RWST r w s m a #

class Bifunctor (p :: Type -> Type -> Type) where #

A bifunctor is a type constructor that takes two type arguments and is a functor in both arguments. That is, unlike with Functor, a type constructor such as Either does not need to be partially applied for a Bifunctor instance, and the methods in this class permit mapping functions over the Left value or the Right value, or both at the same time.

Formally, the class Bifunctor represents a bifunctor from Hask -> Hask.

Intuitively it is a bifunctor where both the first and second arguments are covariant.

You can define a Bifunctor by either defining bimap or by defining both first and second.

If you supply bimap, you should ensure that:

bimap id idid

If you supply first and second, ensure:

first idid
second idid

If you supply both, you should also ensure:

bimap f g ≡ first f . second g

These ensure by parametricity:

bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
first  (f . g) ≡ first  f . first  g
second (f . g) ≡ second f . second g

Since: base-4.8.0.0

Minimal complete definition

bimap | first, second

Methods

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d #

Map over both arguments at the same time.

bimap f g ≡ first f . second g

Examples

Expand
>>> bimap toUpper (+1) ('j', 3)
('J',4)
>>> bimap toUpper (+1) (Left 'j')
Left 'J'
>>> bimap toUpper (+1) (Right 3)
Right 4
Instances
Bifunctor Either

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d #

first :: (a -> b) -> Either a c -> Either b c #

second :: (b -> c) -> Either a b -> Either a c #

Bifunctor (,)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) #

first :: (a -> b) -> (a, c) -> (b, c) #

second :: (b -> c) -> (a, b) -> (a, c) #

Bifunctor Arg

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d #

first :: (a -> b) -> Arg a c -> Arg b c #

second :: (b -> c) -> Arg a b -> Arg a c #

Bifunctor ((,,) x1)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d) #

first :: (a -> b) -> (x1, a, c) -> (x1, b, c) #

second :: (b -> c) -> (x1, a, b) -> (x1, a, c) #

Bifunctor (Const :: Type -> Type -> Type)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d #

first :: (a -> b) -> Const a c -> Const b c #

second :: (b -> c) -> Const a b -> Const a c #

Functor f => Bifunctor (FreeF f) 
Instance details

Defined in Control.Monad.Trans.Free

Methods

bimap :: (a -> b) -> (c -> d) -> FreeF f a c -> FreeF f b d #

first :: (a -> b) -> FreeF f a c -> FreeF f b c #

second :: (b -> c) -> FreeF f a b -> FreeF f a c #

Functor f => Bifunctor (CofreeF f) 
Instance details

Defined in Control.Comonad.Trans.Cofree

Methods

bimap :: (a -> b) -> (c -> d) -> CofreeF f a c -> CofreeF f b d #

first :: (a -> b) -> CofreeF f a c -> CofreeF f b c #

second :: (b -> c) -> CofreeF f a b -> CofreeF f a c #

Functor f => Bifunctor (AlongsideLeft f) 
Instance details

Defined in Control.Lens.Internal.Getter

Methods

bimap :: (a -> b) -> (c -> d) -> AlongsideLeft f a c -> AlongsideLeft f b d #

first :: (a -> b) -> AlongsideLeft f a c -> AlongsideLeft f b c #

second :: (b -> c) -> AlongsideLeft f a b -> AlongsideLeft f a c #

Functor f => Bifunctor (AlongsideRight f) 
Instance details

Defined in Control.Lens.Internal.Getter

Methods

bimap :: (a -> b) -> (c -> d) -> AlongsideRight f a c -> AlongsideRight f b d #

first :: (a -> b) -> AlongsideRight f a c -> AlongsideRight f b c #

second :: (b -> c) -> AlongsideRight f a b -> AlongsideRight f a c #

Bifunctor (Tagged :: Type -> Type -> Type) 
Instance details

Defined in Data.Tagged

Methods

bimap :: (a -> b) -> (c -> d) -> Tagged a c -> Tagged b d #

first :: (a -> b) -> Tagged a c -> Tagged b c #

second :: (b -> c) -> Tagged a b -> Tagged a c #

Bifunctor (Constant :: Type -> Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

bimap :: (a -> b) -> (c -> d) -> Constant a c -> Constant b d #

first :: (a -> b) -> Constant a c -> Constant b c #

second :: (b -> c) -> Constant a b -> Constant a c #

Bifunctor (K1 i :: Type -> Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> K1 i a c -> K1 i b d #

first :: (a -> b) -> K1 i a c -> K1 i b c #

second :: (b -> c) -> K1 i a b -> K1 i a c #

Bifunctor ((,,,) x1 x2)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d) #

first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c) #

second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c) #

Bifunctor ((,,,,) x1 x2 x3)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d) #

first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c) #

second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c) #

Bifunctor p => Bifunctor (WrappedBifunctor p) 
Instance details

Defined in Data.Bifunctor.Wrapped

Methods

bimap :: (a -> b) -> (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d #

first :: (a -> b) -> WrappedBifunctor p a c -> WrappedBifunctor p b c #

second :: (b -> c) -> WrappedBifunctor p a b -> WrappedBifunctor p a c #

Functor g => Bifunctor (Joker g :: Type -> Type -> Type) 
Instance details

Defined in Data.Bifunctor.Joker

Methods

bimap :: (a -> b) -> (c -> d) -> Joker g a c -> Joker g b d #

first :: (a -> b) -> Joker g a c -> Joker g b c #

second :: (b -> c) -> Joker g a b -> Joker g a c #

Bifunctor p => Bifunctor (Flip p) 
Instance details

Defined in Data.Bifunctor.Flip

Methods

bimap :: (a -> b) -> (c -> d) -> Flip p a c -> Flip p b d #

first :: (a -> b) -> Flip p a c -> Flip p b c #

second :: (b -> c) -> Flip p a b -> Flip p a c #

Functor f => Bifunctor (Clown f :: Type -> Type -> Type) 
Instance details

Defined in Data.Bifunctor.Clown

Methods

bimap :: (a -> b) -> (c -> d) -> Clown f a c -> Clown f b d #

first :: (a -> b) -> Clown f a c -> Clown f b c #

second :: (b -> c) -> Clown f a b -> Clown f a c #

Bifunctor ((,,,,,) x1 x2 x3 x4)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d) #

first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c) #

second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c) #

(Bifunctor p, Bifunctor q) => Bifunctor (Sum p q) 
Instance details

Defined in Data.Bifunctor.Sum

Methods

bimap :: (a -> b) -> (c -> d) -> Sum p q a c -> Sum p q b d #

first :: (a -> b) -> Sum p q a c -> Sum p q b c #

second :: (b -> c) -> Sum p q a b -> Sum p q a c #

(Bifunctor f, Bifunctor g) => Bifunctor (Product f g) 
Instance details

Defined in Data.Bifunctor.Product

Methods

bimap :: (a -> b) -> (c -> d) -> Product f g a c -> Product f g b d #

first :: (a -> b) -> Product f g a c -> Product f g b c #

second :: (b -> c) -> Product f g a b -> Product f g a c #

Bifunctor ((,,,,,,) x1 x2 x3 x4 x5)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d) #

first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c) #

second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c) #

(Functor f, Bifunctor p) => Bifunctor (Tannen f p) 
Instance details

Defined in Data.Bifunctor.Tannen

Methods

bimap :: (a -> b) -> (c -> d) -> Tannen f p a c -> Tannen f p b d #

first :: (a -> b) -> Tannen f p a c -> Tannen f p b c #

second :: (b -> c) -> Tannen f p a b -> Tannen f p a c #

(Bifunctor p, Functor f, Functor g) => Bifunctor (Biff p f g) 
Instance details

Defined in Data.Bifunctor.Biff

Methods

bimap :: (a -> b) -> (c -> d) -> Biff p f g a c -> Biff p f g b d #

first :: (a -> b) -> Biff p f g a c -> Biff p f g b c #

second :: (b -> c) -> Biff p f g a b -> Biff p f g a c #

newtype Identity a #

Identity functor and monad. (a non-strict monad)

Since: base-4.8.0.0

Constructors

Identity 

Fields

Instances
Monad Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

(>>=) :: Identity a -> (a -> Identity b) -> Identity b #

(>>) :: Identity a -> Identity b -> Identity b #

return :: a -> Identity a #

fail :: String -> Identity a #

Functor Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

fmap :: (a -> b) -> Identity a -> Identity b #

(<$) :: a -> Identity b -> Identity a #

MonadFix Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

mfix :: (a -> Identity a) -> Identity a #

Applicative Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

pure :: a -> Identity a #

(<*>) :: Identity (a -> b) -> Identity a -> Identity b #

liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #

(*>) :: Identity a -> Identity b -> Identity b #

(<*) :: Identity a -> Identity b -> Identity a #

Foldable Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

fold :: Monoid m => Identity m -> m #

foldMap :: Monoid m => (a -> m) -> Identity a -> m #

foldr :: (a -> b -> b) -> b -> Identity a -> b #

foldr' :: (a -> b -> b) -> b -> Identity a -> b #

foldl :: (b -> a -> b) -> b -> Identity a -> b #

foldl' :: (b -> a -> b) -> b -> Identity a -> b #

foldr1 :: (a -> a -> a) -> Identity a -> a #

foldl1 :: (a -> a -> a) -> Identity a -> a #

toList :: Identity a -> [a] #

null :: Identity a -> Bool #

length :: Identity a -> Int #

elem :: Eq a => a -> Identity a -> Bool #

maximum :: Ord a => Identity a -> a #

minimum :: Ord a => Identity a -> a #

sum :: Num a => Identity a -> a #

product :: Num a => Identity a -> 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) #

Apply Identity 
Instance details

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Identity (a -> b) -> Identity a -> Identity b #

(.>) :: Identity a -> Identity b -> Identity b #

(<.) :: Identity a -> Identity b -> Identity a #

liftF2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #

Distributive Identity 
Instance details

Defined in Data.Distributive

Methods

distribute :: Functor f => f (Identity a) -> Identity (f a) #

collect :: Functor f => (a -> Identity b) -> f a -> Identity (f b) #

distributeM :: Monad m => m (Identity a) -> Identity (m a) #

collectM :: Monad m => (a -> Identity b) -> m a -> Identity (m b) #

Representable Identity 
Instance details

Defined in Data.Functor.Rep

Associated Types

type Rep Identity :: Type #

Methods

tabulate :: (Rep Identity -> a) -> Identity a #

index :: Identity a -> Rep Identity -> a #

Eq1 Identity

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> Identity a -> Identity b -> Bool #

Ord1 Identity

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> Identity a -> Identity b -> Ordering #

Read1 Identity

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Identity a) #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Identity a] #

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Identity a) #

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Identity a] #

Show1 Identity

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Identity a -> ShowS #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Identity a] -> ShowS #

Additive Identity 
Instance details

Defined in Linear.Vector

Methods

zero :: Num a => Identity a #

(^+^) :: Num a => Identity a -> Identity a -> Identity a #

(^-^) :: Num a => Identity a -> Identity a -> Identity a #

lerp :: Num a => a -> Identity a -> Identity a -> Identity a #

liftU2 :: (a -> a -> a) -> Identity a -> Identity a -> Identity a #

liftI2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #

Hashable1 Identity 
Instance details

Defined in Data.Hashable.Class

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Identity a -> Int #

Settable Identity

So you can pass our Setter into combinators from other lens libraries.

Instance details

Defined in Control.Lens.Internal.Setter

Methods

untainted :: Identity a -> a #

untaintedDot :: Profunctor p => p a (Identity b) -> p a b #

taintedDot :: Profunctor p => p a b -> p a (Identity b) #

Traversable1 Identity 
Instance details

Defined in Data.Semigroup.Traversable.Class

Methods

traverse1 :: Apply f => (a -> f b) -> Identity a -> f (Identity b) #

sequence1 :: Apply f => Identity (f b) -> f (Identity b) #

Affine Identity 
Instance details

Defined in Linear.Affine

Associated Types

type Diff Identity :: Type -> Type #

Methods

(.-.) :: Num a => Identity a -> Identity a -> Diff Identity a #

(.+^) :: Num a => Identity a -> Diff Identity a -> Identity a #

(.-^) :: Num a => Identity a -> Diff Identity a -> Identity a #

R1 Identity 
Instance details

Defined in Linear.V1

Methods

_x :: Lens' (Identity a) a #

Metric Identity 
Instance details

Defined in Linear.Metric

Methods

dot :: Num a => Identity a -> Identity a -> a #

quadrance :: Num a => Identity a -> a #

qd :: Num a => Identity a -> Identity a -> a #

distance :: Floating a => Identity a -> Identity a -> a #

norm :: Floating a => Identity a -> a #

signorm :: Floating a => Identity a -> Identity a #

Bind Identity 
Instance details

Defined in Data.Functor.Bind.Class

Methods

(>>-) :: Identity a -> (a -> Identity b) -> Identity b #

join :: Identity (Identity a) -> Identity a #

FunctorWithIndex () Identity 
Instance details

Defined in Control.Lens.Indexed

Methods

imap :: (() -> a -> b) -> Identity a -> Identity b #

imapped :: IndexedSetter () (Identity a) (Identity b) a b #

FoldableWithIndex () Identity 
Instance details

Defined in Control.Lens.Indexed

Methods

ifoldMap :: Monoid m => (() -> a -> m) -> Identity a -> m #

ifolded :: IndexedFold () (Identity a) a #

ifoldr :: (() -> a -> b -> b) -> b -> Identity a -> b #

ifoldl :: (() -> b -> a -> b) -> b -> Identity a -> b #

ifoldr' :: (() -> a -> b -> b) -> b -> Identity a -> b #

ifoldl' :: (() -> b -> a -> b) -> b -> Identity a -> b #

TraversableWithIndex () Identity 
Instance details

Defined in Control.Lens.Indexed

Methods

itraverse :: Applicative f => (() -> a -> f b) -> Identity a -> f (Identity b) #

itraversed :: IndexedTraversal () (Identity a) (Identity b) a b #

MonadBaseControl Identity Identity 
Instance details

Defined in Control.Monad.Trans.Control

Associated Types

type StM Identity a :: Type #

Sieve ReifiedGetter Identity 
Instance details

Defined in Control.Lens.Reified

Methods

sieve :: ReifiedGetter a b -> a -> Identity b #

Cosieve ReifiedGetter Identity 
Instance details

Defined in Control.Lens.Reified

Methods

cosieve :: ReifiedGetter a b -> Identity a -> b #

Monad m => MonadFree Identity (IterT m) 
Instance details

Defined in Control.Monad.Trans.Iter

Methods

wrap :: Identity (IterT m a) -> IterT m a #

Comonad w => ComonadCofree Identity (CoiterT w) 
Instance details

Defined in Control.Comonad.Trans.Coiter

Methods

unwrap :: CoiterT w a -> Identity (CoiterT w a) #

Bounded a => Bounded (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Enum a => Enum (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Eq a => Eq (Identity a)

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

(==) :: Identity a -> Identity a -> Bool #

(/=) :: Identity a -> Identity a -> Bool #

Floating a => Floating (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Fractional a => Fractional (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Integral a => Integral (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Data a => Data (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Identity a -> c (Identity a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Identity a) #

toConstr :: Identity a -> Constr #

dataTypeOf :: Identity a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Identity a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Identity a)) #

gmapT :: (forall b. Data b => b -> b) -> Identity a -> Identity a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Identity a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Identity a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Identity a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Identity a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a) #

Num a => Num (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Ord a => Ord (Identity a)

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

compare :: Identity a -> Identity a -> Ordering #

(<) :: Identity a -> Identity a -> Bool #

(<=) :: Identity a -> Identity a -> Bool #

(>) :: Identity a -> Identity a -> Bool #

(>=) :: Identity a -> Identity a -> Bool #

max :: Identity a -> Identity a -> Identity a #

min :: Identity a -> Identity a -> Identity a #

Read a => Read (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Real a => Real (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

toRational :: Identity a -> Rational #

RealFloat a => RealFloat (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

RealFrac a => RealFrac (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

properFraction :: Integral b => Identity a -> (b, Identity a) #

truncate :: Integral b => Identity a -> b #

round :: Integral b => Identity a -> b #

ceiling :: Integral b => Identity a -> b #

floor :: Integral b => Identity a -> b #

Show a => Show (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

showsPrec :: Int -> Identity a -> ShowS #

show :: Identity a -> String #

showList :: [Identity a] -> ShowS #

Ix a => Ix (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

IsString a => IsString (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.String

Methods

fromString :: String -> Identity a #

Generic (Identity a) 
Instance details

Defined in Data.Functor.Identity

Associated Types

type Rep (Identity a) :: Type -> Type #

Methods

from :: Identity a -> Rep (Identity a) x #

to :: Rep (Identity a) x -> Identity a #

Semigroup a => Semigroup (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

(<>) :: Identity a -> Identity a -> Identity a #

sconcat :: NonEmpty (Identity a) -> Identity a #

stimes :: Integral b => b -> Identity a -> Identity a #

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

mempty :: Identity a #

mappend :: Identity a -> Identity a -> Identity a #

mconcat :: [Identity a] -> Identity a #

Storable a => Storable (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

sizeOf :: Identity a -> Int #

alignment :: Identity a -> Int #

peekElemOff :: Ptr (Identity a) -> Int -> IO (Identity a) #

pokeElemOff :: Ptr (Identity a) -> Int -> Identity a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (Identity a) #

pokeByteOff :: Ptr b -> Int -> Identity a -> IO () #

peek :: Ptr (Identity a) -> IO (Identity a) #

poke :: Ptr (Identity a) -> Identity a -> IO () #

Bits a => Bits (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

FiniteBits a => FiniteBits (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Hashable a => Hashable (Identity a) 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Identity a -> Int #

hash :: Identity a -> Int #

Prim a => Prim (Identity a)

Since: primitive-0.6.5.0

Instance details

Defined in Data.Primitive.Types

Ixed (Identity a) 
Instance details

Defined in Control.Lens.At

Methods

ix :: Index (Identity a) -> Traversal' (Identity a) (IxValue (Identity a)) #

Wrapped (Identity a) 
Instance details

Defined in Control.Lens.Wrapped

Associated Types

type Unwrapped (Identity a) :: Type #

Newtype (Identity a)

Since: newtype-generics-0.5.1

Instance details

Defined in Control.Newtype.Generics

Associated Types

type O (Identity a) :: Type #

Methods

pack :: O (Identity a) -> Identity a #

unpack :: Identity a -> O (Identity a) #

Generic1 Identity 
Instance details

Defined in Data.Functor.Identity

Associated Types

type Rep1 Identity :: k -> Type #

Methods

from1 :: Identity a -> Rep1 Identity a #

to1 :: Rep1 Identity a -> Identity a #

t ~ Identity b => Rewrapped (Identity a) t 
Instance details

Defined in Control.Lens.Wrapped

Each (Identity a) (Identity b) a b
each :: Traversal (Identity a) (Identity b) a b
Instance details

Defined in Control.Lens.Each

Methods

each :: Traversal (Identity a) (Identity b) a b #

Field1 (Identity a) (Identity b) a b 
Instance details

Defined in Control.Lens.Tuple

Methods

_1 :: Lens (Identity a) (Identity b) a b #

type Rep Identity 
Instance details

Defined in Data.Functor.Rep

type Rep Identity = ()
type Diff Identity 
Instance details

Defined in Linear.Affine

type StM Identity a 
Instance details

Defined in Control.Monad.Trans.Control

type StM Identity a = a
type Rep (Identity a)

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

type Rep (Identity a) = D1 (MetaData "Identity" "Data.Functor.Identity" "base" True) (C1 (MetaCons "Identity" PrefixI True) (S1 (MetaSel (Just "runIdentity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Index (Identity a) 
Instance details

Defined in Control.Lens.At

type Index (Identity a) = ()
type IxValue (Identity a) 
Instance details

Defined in Control.Lens.At

type IxValue (Identity a) = a
type Unwrapped (Identity a) 
Instance details

Defined in Control.Lens.Wrapped

type Unwrapped (Identity a) = a
type O (Identity a) 
Instance details

Defined in Control.Newtype.Generics

type O (Identity a) = a
type Rep1 Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

type Rep1 Identity = D1 (MetaData "Identity" "Data.Functor.Identity" "base" True) (C1 (MetaCons "Identity" PrefixI True) (S1 (MetaSel (Just "runIdentity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Const a (b :: k) :: forall k. Type -> k -> Type #

The Const functor.

Constructors

Const 

Fields

Instances
Generic1 (Const a :: k -> Type) 
Instance details

Defined in Data.Functor.Const

Associated Types

type Rep1 (Const a) :: k -> Type #

Methods

from1 :: Const a a0 -> Rep1 (Const a) a0 #

to1 :: Rep1 (Const a) a0 -> Const a a0 #

Bitraversable (Const :: Type -> Type -> Type)

Since: base-4.10.0.0

Instance details

Defined in Data.Bitraversable

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) #

Bifoldable (Const :: Type -> Type -> Type)

Since: base-4.10.0.0

Instance details

Defined in Data.Bifoldable

Methods

bifold :: Monoid m => Const m m -> m #

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Const a b -> m #

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Const a b -> c #

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Const a b -> c #

Bifunctor (Const :: Type -> Type -> Type)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d #

first :: (a -> b) -> Const a c -> Const b c #

second :: (b -> c) -> Const a b -> Const a c #

Eq2 (Const :: Type -> Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const a c -> Const b d -> Bool #

Ord2 (Const :: Type -> Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const a c -> Const b d -> Ordering #

Read2 (Const :: Type -> Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Const a b) #

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Const a b] #

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Const a b) #

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Const a b] #

Show2 (Const :: Type -> Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Const a b -> ShowS #

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Const a b] -> ShowS #

Biapplicative (Const :: Type -> Type -> Type) 
Instance details

Defined in Data.Biapplicative

Methods

bipure :: a -> b -> Const a b #

(<<*>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d #

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Const a d -> Const b e -> Const c f #

(*>>) :: Const a b -> Const c d -> Const c d #

(<<*) :: Const a b -> Const c d -> Const a b #

Hashable2 (Const :: Type -> Type -> Type) 
Instance details

Defined in Data.Hashable.Class

Methods

liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> Const a b -> Int #

Bitraversable1 (Const :: Type -> Type -> Type) 
Instance details

Defined in Data.Semigroup.Traversable.Class

Methods

bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Const a c -> f (Const b d) #

bisequence1 :: Apply f => Const (f a) (f b) -> f (Const a b) #

Biapply (Const :: Type -> Type -> Type) 
Instance details

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d #

(.>>) :: Const a b -> Const c d -> Const c d #

(<<.) :: Const a b -> Const c d -> Const a b #

Semigroupoid (Const :: Type -> Type -> Type) 
Instance details

Defined in Data.Semigroupoid

Methods

o :: Const j k1 -> Const i j -> Const i k1 #

Functor (Const m :: Type -> Type)

Since: base-2.1

Instance details