Diagrams.Prelude

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

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.

module Data.Default.Class

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

Defined in Data.Colour.Internal

Methods

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

ColourOps Colour

Defined in Data.Colour.Internal

Methods

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

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

Num a => Monoid (Colour a)

Defined in Data.Colour.Internal

Methods

mempty :: Colour a

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

mconcat :: [Colour a] -> Colour a

Num a => Semigroup (Colour a)

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

a ~ Double => Color (Colour a)

Defined in Diagrams.Attributes

Methods

toAlphaColour :: Colour a -> AlphaColour Double

fromAlphaColour :: AlphaColour Double -> Colour a

Parseable (Colour Double)

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

Defined in Diagrams.Backend.CmdLine

Methods

parser :: Parser (Colour Double)

Eq a => Eq (Colour a)

Defined in Data.Colour.Internal

Methods

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

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

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

Defined in Data.Colour.Internal

Methods

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

ColourOps AlphaColour

Defined in Data.Colour.Internal

Methods

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

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

Num a => Monoid (AlphaColour a)

Defined in Data.Colour.Internal

Methods

mempty :: AlphaColour a

mappend :: AlphaColour a -> AlphaColour a -> AlphaColour a

mconcat :: [AlphaColour a] -> AlphaColour a

Num a => Semigroup (AlphaColour a)

AlphaColour forms a monoid with over and transparent.

Defined in Data.Colour.Internal

Methods

(<>) :: AlphaColour a -> AlphaColour a -> AlphaColour a

sconcat :: NonEmpty (AlphaColour a) -> AlphaColour a

stimes :: Integral b => b -> AlphaColour a -> AlphaColour a

a ~ Double => Color (AlphaColour a)

Defined in Diagrams.Attributes

Methods

toAlphaColour :: AlphaColour a -> AlphaColour Double

fromAlphaColour :: AlphaColour Double -> AlphaColour a

Parseable (AlphaColour Double)

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

Defined in Diagrams.Backend.CmdLine

Methods

parser :: Parser (AlphaColour Double)

Eq a => Eq (AlphaColour a)

Defined in Data.Colour.Internal

Methods

(==) :: AlphaColour a -> AlphaColour a -> Bool

(/=) :: AlphaColour a -> AlphaColour a -> Bool

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 AlphaColour

Defined in Data.Colour.Internal

Methods

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

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

ColourOps Colour

Defined in Data.Colour.Internal

Methods

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

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

A large list of color names.

yellowgreen :: (Ord a, Floating a) => Colour a

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

springgreen :: (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

saddlebrown :: (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

palevioletred :: (Ord a, Floating a) => Colour a

paleturquoise :: (Ord a, Floating a) => Colour a

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

palegoldenrod :: (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

navajowhite :: (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

midnightblue :: (Ord a, Floating a) => Colour a

mediumvioletred :: (Ord a, Floating a) => Colour a

mediumturquoise :: (Ord a, Floating a) => Colour a

mediumspringgreen :: (Ord a, Floating a) => Colour a

mediumslateblue :: (Ord a, Floating a) => Colour a

mediumseagreen :: (Ord a, Floating a) => Colour a

mediumpurple :: (Ord a, Floating a) => Colour a

mediumorchid :: (Ord a, Floating a) => Colour a

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

mediumaquamarine :: (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

lightyellow :: (Ord a, Floating a) => Colour a

lightsteelblue :: (Ord a, Floating a) => Colour a

lightslategrey :: (Ord a, Floating a) => Colour a

lightslategray :: (Ord a, Floating a) => Colour a

lightskyblue :: (Ord a, Floating a) => Colour a

lightseagreen :: (Ord a, Floating a) => Colour a

lightsalmon :: (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

lightgoldenrodyellow :: (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

lemonchiffon :: (Ord a, Floating a) => Colour a

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

lavenderblush :: (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

greenyellow :: (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

forestgreen :: (Ord a, Floating a) => Colour a

floralwhite :: (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

deepskyblue :: (Ord a, Floating a) => Colour a

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

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

darkturquoise :: (Ord a, Floating a) => Colour a

darkslategrey :: (Ord a, Floating a) => Colour a

darkslategray :: (Ord a, Floating a) => Colour a

darkslateblue :: (Ord a, Floating a) => Colour a

darkseagreen :: (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

darkolivegreen :: (Ord a, Floating a) => Colour a

darkmagenta :: (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

darkgoldenrod :: (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

cornflowerblue :: (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

blanchedalmond :: (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

antiquewhite :: (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.

module Data.Colour.SRGB

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

module Data.Semigroup

For computing with vectors.

module Linear.Vector

For computing with points and vectors.

module Linear.Affine

For computing with dot products and norm.

module Linear.Metric

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

module Data.Active

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:

• at
• contains
• .>
• <.>
• index
• indices
• none
• coerce
• indexed
• inside
• levels
• ...
• children
• transform
• outside
• argument
• beside
• singular

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

Functors representing data structures that can be transformed to structures of the same shape by performing an Applicative (or, therefore, Monad) action on each element from left to right.

A more detailed description of what same shape means, the various methods, how traversals are constructed, and example advanced use-cases can be found in the Overview section of Data.Traversable.

For the class laws see the Laws section of Data.Traversable.

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_.

Examples

Basic usage:

In the first two examples we show each evaluated action mapping to the output structure.

>>> traverse Just [1,2,3,4]
Just [1,2,3,4]

>>> traverse id [Right 1, Right 2, Right 3, Right 4]
Right [1,2,3,4]

In the next examples, we show that Nothing and Left values short circuit the created structure.

>>> traverse (const Nothing) [1,2,3,4]
Nothing

>>> traverse (\x -> if odd x then Just x else Nothing)  [1,2,3,4]
Nothing

>>> traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]
Left 0

Instances

Traversable ZipList

Since: base-4.9.0.0

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 Complex

Since: base-4.9.0.0

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 Identity

Since: base-4.9.0.0

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

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

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 Down

Since: base-4.12.0.0

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 First

Since: base-4.9.0.0

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

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 Max

Since: base-4.9.0.0

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 Min

Since: base-4.9.0.0

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 Dual

Since: base-4.8.0.0

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 Product

Since: base-4.8.0.0

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 Sum

Since: base-4.8.0.0

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 Par1

Since: base-4.9.0.0

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 IntMap

Traverses in order of increasing key.

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 Digit

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 Elem

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 FingerTree

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 Node

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 Seq

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 ViewL

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

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 Tree

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 Interval

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 Plucker

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

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

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 V1

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 V2

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 V3

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 V4

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 Deletable

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 Recommend

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 Split

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 Array

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 SmallArray

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 Maybe

Defined in Data.Strict.Maybe

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 Vector

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 NonEmpty

Since: base-4.9.0.0

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 Maybe

Since: base-2.1

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 Solo

Since: base-4.15

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Solo a -> f (Solo b)

sequenceA :: Applicative f => Solo (f a) -> f (Solo a)

mapM :: Monad m => (a -> m b) -> Solo a -> m (Solo b)

sequence :: Monad m => Solo (m a) -> m (Solo a)

Traversable []

Since: base-2.1

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 (Either a)

Since: base-4.7.0.0

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 (Proxy :: Type -> Type)

Since: base-4.7.0.0

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 (Arg a)

Since: base-4.9.0.0

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)

Ix i => Traversable (Array i)

Since: base-2.1

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 (U1 :: Type -> Type)

Since: base-4.9.0.0

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 (UAddr :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UAddr a -> f (UAddr b)

sequenceA :: Applicative f => UAddr (f a) -> f (UAddr a)

mapM :: Monad m => (a -> m b) -> UAddr a -> m (UAddr b)

sequence :: Monad m => UAddr (m a) -> m (UAddr a)

Traversable (UChar :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UChar a -> f (UChar b)

sequenceA :: Applicative f => UChar (f a) -> f (UChar a)

mapM :: Monad m => (a -> m b) -> UChar a -> m (UChar b)

sequence :: Monad m => UChar (m a) -> m (UChar a)

Traversable (UDouble :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b)

sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a)

mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b)

sequence :: Monad m => UDouble (m a) -> m (UDouble a)

Traversable (UFloat :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b)

sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a)

mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b)

sequence :: Monad m => UFloat (m a) -> m (UFloat a)

Traversable (UInt :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UInt a -> f (UInt b)

sequenceA :: Applicative f => UInt (f a) -> f (UInt a)

mapM :: Monad m => (a -> m b) -> UInt a -> m (UInt b)

sequence :: Monad m => UInt (m a) -> m (UInt a)

Traversable (UWord :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UWord a -> f (UWord b)

sequenceA :: Applicative f => UWord (f a) -> f (UWord a)

mapM :: Monad m => (a -> m b) -> UWord a -> m (UWord b)

sequence :: Monad m => UWord (m a) -> m (UWord a)

Traversable (V1 :: Type -> Type)

Since: base-4.9.0.0

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 (Map k)

Traverses in order of increasing key.

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)

(Monad m, Traversable m) => Traversable (CatchT m)

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)

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)

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)

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)

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)

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 (Level i)

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 (Point f)

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 (Inf p)

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 (Either e)

Defined in Data.Strict.Either

Methods

traverse :: Applicative f => (a -> f b) -> Either e a -> f (Either e b)

sequenceA :: Applicative f => Either e (f a) -> f (Either e a)

mapM :: Monad m => (a -> m b) -> Either e a -> m (Either e b)

sequence :: Monad m => Either e (m a) -> m (Either e a)

Traversable (These a)

Defined in Data.Strict.These

Methods

traverse :: Applicative f => (a0 -> f b) -> These a a0 -> f (These a b)

sequenceA :: Applicative f => These a (f a0) -> f (These a a0)

mapM :: Monad m => (a0 -> m b) -> These a a0 -> m (These a b)

sequence :: Monad m => These a (m a0) -> m (These a a0)

Traversable (Pair e)

Defined in Data.Strict.Tuple

Methods

traverse :: Applicative f => (a -> f b) -> Pair e a -> f (Pair e b)

sequenceA :: Applicative f => Pair e (f a) -> f (Pair e a)

mapM :: Monad m => (a -> m b) -> Pair e a -> m (Pair e b)

sequence :: Monad m => Pair e (m a) -> m (Pair e a)

Traversable (These a)

Defined in Data.These

Methods

traverse :: Applicative f => (a0 -> f b) -> These a a0 -> f (These a b)

sequenceA :: Applicative f => These a (f a0) -> f (These a a0)

mapM :: Monad m => (a0 -> m b) -> These a a0 -> m (These a b)

sequence :: Monad m => These a (m a0) -> m (These a a0)

Traversable f => Traversable (ListT f)

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 f => Traversable (MaybeT f)

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)

Traversable (HashMap k)

Defined in Data.HashMap.Internal

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 ((,) a)

Since: base-4.7.0.0

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)

Traversable (Const m :: Type -> Type)

Since: base-4.7.0.0

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

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

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)

Traversable f => Traversable (Rec1 f)

Since: base-4.9.0.0

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)

Bitraversable p => Traversable (Fix p)

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)

Bitraversable p => Traversable (Join p)

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)

Traversable f => Traversable (CofreeF f a)

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)

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 (FreeF f a)

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)

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 (AlongsideLeft f b)

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)

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)

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 (Tagged s)

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 (Backwards f)

Derived instance.

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 (ErrorT e f)

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 (ExceptT e f)

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 (IdentityT f)

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 (WriterT w f)

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)

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 (Constant a :: Type -> Type)

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 (Reverse f)

Traverse from right to left.

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 f, Traversable g) => Traversable (Product f g)

Since: base-4.9.0.0

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

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 f, Traversable g) => Traversable (f :*: g)

Since: base-4.9.0.0

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

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 (K1 i c :: Type -> Type)

Since: base-4.9.0.0

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 (Magma i t b)

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 (Forget r a :: Type -> TYPE LiftedRep)

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 f, Traversable g) => Traversable (Compose f g)

Since: base-4.9.0.0

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)

(Traversable f, Traversable g) => Traversable (f :.: g)

Since: base-4.9.0.0

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 (M1 i c f)

Since: base-4.9.0.0

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 (Clown f a :: Type -> Type)

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)

Bitraversable p => Traversable (Flip p a)

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 g => Traversable (Joker g a)

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 (WrappedBifunctor p a)

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 (f a), Traversable (g a)) => Traversable (Product f g a)

Defined in Data.Bifunctor.Product

Methods

traverse :: Applicative f0 => (a0 -> f0 b) -> Product f g a a0 -> f0 (Product f g a b)

sequenceA :: Applicative f0 => Product f g a (f0 a0) -> f0 (Product f g a a0)

mapM :: Monad m => (a0 -> m b) -> Product f g a a0 -> m (Product f g a b)

sequence :: Monad m => Product f g a (m a0) -> m (Product f g a a0)

(Traversable (f a), Traversable (g a)) => Traversable (Sum f g a)

Defined in Data.Bifunctor.Sum

Methods

traverse :: Applicative f0 => (a0 -> f0 b) -> Sum f g a a0 -> f0 (Sum f g a b)

sequenceA :: Applicative f0 => Sum f g a (f0 a0) -> f0 (Sum f g a a0)

mapM :: Monad m => (a0 -> m b) -> Sum f g a a0 -> m (Sum f g a b)

sequence :: Monad m => Sum f g a (m a0) -> m (Sum f g a a0)

(Traversable f, Bitraversable p) => Traversable (Tannen f p a)

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)

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 :: (a' -> a) -> (Predicate a -> Predicate a')
  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:

Identity

contramap id = id

Composition

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

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' -> a) -> f a -> 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 Comparison

A Comparison is a Contravariant Functor, because contramap can apply its function argument to each input of the comparison function.

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Comparison a -> 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.

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Equivalence a -> Equivalence a'

(>$) :: b -> Equivalence b -> Equivalence a

Contravariant Predicate

A Predicate is a Contravariant Functor, because contramap can apply its function argument to the input of the predicate.

Without newtypes contramap f equals precomposing with f (= (. f)).

contramap :: (a' -> a) -> (Predicate a -> Predicate a')
contramap f (Predicate g) = Predicate (g . f)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Predicate a -> Predicate a'

(>$) :: b -> Predicate b -> Predicate a

Contravariant (Op a)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a0) -> Op a a0 -> Op a a'

(>$) :: b -> Op a b -> Op a a0

Contravariant (Proxy :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Proxy a -> Proxy a'

(>$) :: b -> Proxy b -> Proxy a

Contravariant (U1 :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> U1 a -> U1 a'

(>$) :: b -> U1 b -> U1 a

Contravariant (V1 :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> V1 a -> V1 a'

(>$) :: b -> V1 b -> V1 a

Contravariant f => Contravariant (Indexing f)

Defined in Control.Lens.Internal.Indexed

Methods

contramap :: (a' -> a) -> Indexing f a -> Indexing f a'

(>$) :: b -> Indexing f b -> Indexing f a

Contravariant f => Contravariant (Indexing64 f)

Defined in Control.Lens.Internal.Indexed

Methods

contramap :: (a' -> a) -> Indexing64 f a -> Indexing64 f a'

(>$) :: b -> Indexing64 f b -> Indexing64 f a

Contravariant m => Contravariant (ListT m)

Defined in Control.Monad.Trans.List

Methods

contramap :: (a' -> a) -> ListT m a -> ListT m a'

(>$) :: b -> ListT m b -> ListT m a

Contravariant m => Contravariant (MaybeT m)

Defined in Control.Monad.Trans.Maybe

Methods

contramap :: (a' -> a) -> MaybeT m a -> MaybeT m a'

(>$) :: b -> MaybeT m b -> MaybeT m a

Contravariant (Const a :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a0) -> Const a a0 -> Const a a'

(>$) :: b -> Const a b -> Const a a0

Contravariant f => Contravariant (Alt f)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Alt f a -> Alt f a'

(>$) :: b -> Alt f b -> Alt f a

Contravariant f => Contravariant (Rec1 f)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Rec1 f a -> Rec1 f a'

(>$) :: b -> Rec1 f b -> Rec1 f a

(Contravariant f, Functor g) => Contravariant (ComposeCF f g)

Defined in Data.Functor.Contravariant.Compose

Methods

contramap :: (a' -> a) -> ComposeCF f g a -> ComposeCF f g a'

(>$) :: b -> ComposeCF f g b -> ComposeCF f g a

(Functor f, Contravariant g) => Contravariant (ComposeFC f g)

Defined in Data.Functor.Contravariant.Compose

Methods

contramap :: (a' -> a) -> ComposeFC f g a -> ComposeFC f g a'

(>$) :: b -> ComposeFC f g b -> ComposeFC f g a

Contravariant f => Contravariant (AlongsideLeft f b)

Defined in Control.Lens.Internal.Getter

Methods

contramap :: (a' -> a) -> AlongsideLeft f b a -> AlongsideLeft f b a'

(>$) :: b0 -> AlongsideLeft f b b0 -> AlongsideLeft f b a

Contravariant f => Contravariant (AlongsideRight f a)

Defined in Control.Lens.Internal.Getter

Methods

contramap :: (a' -> a0) -> AlongsideRight f a a0 -> AlongsideRight f a a'

(>$) :: b -> AlongsideRight f a b -> AlongsideRight f a a0

Contravariant f => Contravariant (Backwards f)

Derived instance.

Defined in Control.Applicative.Backwards

Methods

contramap :: (a' -> a) -> Backwards f a -> Backwards f a'

(>$) :: b -> Backwards f b -> Backwards f a

Contravariant m => Contravariant (ErrorT e m)

Defined in Control.Monad.Trans.Error

Methods

contramap :: (a' -> a) -> ErrorT e m a -> ErrorT e m a'

(>$) :: b -> ErrorT e m b -> ErrorT e m a

Contravariant m => Contravariant (ExceptT e m)

Defined in Control.Monad.Trans.Except

Methods

contramap :: (a' -> a) -> ExceptT e m a -> ExceptT e m a'

(>$) :: b -> ExceptT e m b -> ExceptT e m a

Contravariant f => Contravariant (IdentityT f)

Defined in Control.Monad.Trans.Identity

Methods

contramap :: (a' -> a) -> IdentityT f a -> IdentityT f a'

(>$) :: b -> IdentityT f b -> IdentityT f a

Contravariant m => Contravariant (ReaderT r m)

Defined in Control.Monad.Trans.Reader

Methods

contramap :: (a' -> a) -> ReaderT r m a -> ReaderT r m a'

(>$) :: b -> ReaderT r m b -> ReaderT r m a

Contravariant m => Contravariant (StateT s m)

Defined in Control.Monad.Trans.State.Lazy

Methods

contramap :: (a' -> a) -> StateT s m a -> StateT s m a'

(>$) :: b -> StateT s m b -> StateT s m a

Contravariant m => Contravariant (StateT s m)

Defined in Control.Monad.Trans.State.Strict

Methods

contramap :: (a' -> a) -> StateT s m a -> StateT s m a'

(>$) :: b -> StateT s m b -> StateT s m a

Contravariant m => Contravariant (WriterT w m)

Defined in Control.Monad.Trans.Writer.Lazy

Methods

contramap :: (a' -> a) -> WriterT w m a -> WriterT w m a'

(>$) :: b -> WriterT w m b -> WriterT w m a

Contravariant m => Contravariant (WriterT w m)

Defined in Control.Monad.Trans.Writer.Strict

Methods

contramap :: (a' -> a) -> WriterT w m a -> WriterT w m a'

(>$) :: b -> WriterT w m b -> WriterT w m a

Contravariant (Constant a :: Type -> Type)

Defined in Data.Functor.Constant

Methods

contramap :: (a' -> a0) -> Constant a a0 -> Constant a a'

(>$) :: b -> Constant a b -> Constant a a0

Contravariant f => Contravariant (Reverse f)

Derived instance.

Defined in Data.Functor.Reverse

Methods

contramap :: (a' -> a) -> Reverse f a -> Reverse f a'

(>$) :: b -> Reverse f b -> Reverse f a

(Contravariant f, Contravariant g) => Contravariant (Product f g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Product f g a -> Product f g a'

(>$) :: b -> Product f g b -> Product f g a

(Contravariant f, Contravariant g) => Contravariant (Sum f g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Sum f g a -> Sum f g a'

(>$) :: b -> Sum f g b -> Sum f g a

(Contravariant f, Contravariant g) => Contravariant (f :*: g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> (f :*: g) a -> (f :*: g) a'

(>$) :: b -> (f :*: g) b -> (f :*: g) a

(Contravariant f, Contravariant g) => Contravariant (f :+: g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> (f :+: g) a -> (f :+: g) a'

(>$) :: b -> (f :+: g) b -> (f :+: g) a

Contravariant (K1 i c :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> K1 i c a -> K1 i c a'

(>$) :: b -> K1 i c b -> K1 i c a

Contravariant (Forget r a :: Type -> TYPE LiftedRep)

Defined in Data.Profunctor.Types

Methods

contramap :: (a' -> a0) -> Forget r a a0 -> Forget r a a'

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

Contravariant f => Contravariant (Star f a)

Defined in Data.Profunctor.Types

Methods

contramap :: (a' -> a0) -> Star f a a0 -> Star f a a'

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

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

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Compose f g a -> Compose f g a'

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

(Functor f, Contravariant g) => Contravariant (f :.: g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> (f :.: g) a -> (f :.: g) a'

(>$) :: b -> (f :.: g) b -> (f :.: g) a

Contravariant f => Contravariant (M1 i c f)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> M1 i c f a -> M1 i c f a'

(>$) :: b -> M1 i c f b -> M1 i c f a

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

Defined in Control.Lens.Internal.Bazaar

Methods

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

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

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

Defined in Control.Lens.Internal.Bazaar

Methods

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

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

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

Defined in Control.Lens.Internal.Context

Methods

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

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

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

Defined in Control.Lens.Internal.Magma

Methods

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

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

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

Defined in Control.Monad.Trans.RWS.Lazy

Methods

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

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

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

Defined in Control.Monad.Trans.RWS.Strict

Methods

contramap :: (a' -> a) -> RWST r w s m a -> 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 id ≡ id

If you supply first and second, ensure:

first id ≡ id
second id ≡ id

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

>>> 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

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 Arg

Since: base-4.9.0.0

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 Either

Defined in Data.Strict.Either

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 These

Defined in Data.Strict.These

Methods

bimap :: (a -> b) -> (c -> d) -> These a c -> These b d

first :: (a -> b) -> These a c -> These b c

second :: (b -> c) -> These a b -> These a c

Bifunctor Pair

Defined in Data.Strict.Tuple

Methods

bimap :: (a -> b) -> (c -> d) -> Pair a c -> Pair b d

first :: (a -> b) -> Pair a c -> Pair b c

second :: (b -> c) -> Pair a b -> Pair a c

Bifunctor These

Defined in Data.These

Methods

bimap :: (a -> b) -> (c -> d) -> These a c -> These b d

first :: (a -> b) -> These a c -> These b c

second :: (b -> c) -> These a b -> These a c

Bifunctor (,)

Since: base-4.8.0.0

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

Since: base-4.8.0.0

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 (CofreeF f)

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 (FreeF f)

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 (AlongsideLeft f)

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)

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)

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)

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 ((,,) x1)

Since: base-4.8.0.0

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

Since: base-4.9.0.0

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

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)

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

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 p => Bifunctor (Flip p)

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 g => Bifunctor (Joker g :: Type -> Type -> Type)

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 (WrappedBifunctor p)

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

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

Since: base-4.8.0.0

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

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

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

Since: base-4.8.0.0

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)

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

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

Since: base-4.8.0.0

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)

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

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

• runIdentity :: a

Instances

Representable Identity

Defined in Data.Functor.Rep

Associated Types

type Rep Identity

Methods

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

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

MonadFix Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

Foldable Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

Eq1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

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

Ord1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

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

Read1 Identity

Since: base-4.9.0.0

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

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

Traversable Identity

Since: base-4.9.0.0

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)

Applicative Identity

Since: base-4.8.0.0

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

Functor Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

Monad Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

return :: a -> Identity a

Comonad Identity

Defined in Control.Comonad

Methods

extract :: Identity a -> a

duplicate :: Identity a -> Identity (Identity a)

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

ComonadApply Identity

Defined in Control.Comonad

Methods

(<@>) :: Identity (a -> b) -> Identity a -> Identity b

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

(<@) :: Identity a -> Identity b -> Identity a

Distributive Identity

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)

Hashable1 Identity

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.

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)

Affine Identity

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

Metric Identity

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

R1 Identity

Defined in Linear.V1

Methods

_x :: Lens' (Identity a) a

Additive Identity

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

Apply Identity

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

Bind Identity

Defined in Data.Functor.Bind.Class

Methods

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

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

Traversable1 Identity

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)

Generic1 Identity

Defined in Data.Functor.Identity

Associated Types

type Rep1 Identity :: k -> Type

Methods

from1 :: forall (a :: k). Identity a -> Rep1 Identity a

to1 :: forall (a :: k). Rep1 Identity a -> Identity a

FoldableWithIndex () Identity

Defined in WithIndex

Methods

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

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

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

FunctorWithIndex () Identity

Defined in WithIndex

Methods

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

TraversableWithIndex () Identity

Defined in WithIndex

Methods

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

Cosieve ReifiedGetter Identity

Defined in Control.Lens.Reified

Methods

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

Sieve ReifiedGetter Identity

Defined in Control.Lens.Reified

Methods

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

Comonad w => ComonadCofree Identity (CoiterT w)

Defined in Control.Comonad.Trans.Coiter

Methods

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

Monad m => MonadFree Identity (IterT m)

Defined in Control.Monad.Trans.Iter

Methods

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

Unbox a => Vector Vector (Identity a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: Mutable Vector s (Identity a) -> ST s (Vector (Identity a))

basicUnsafeThaw :: Vector (Identity a) -> ST s (Mutable Vector s (Identity a))

basicLength :: Vector (Identity a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Identity a) -> Vector (Identity a)

basicUnsafeIndexM :: Vector (Identity a) -> Int -> Box (Identity a)

basicUnsafeCopy :: Mutable Vector s (Identity a) -> Vector (Identity a) -> ST s ()

elemseq :: Vector (Identity a) -> Identity a -> b -> b

Unbox a => MVector MVector (Identity a)

Defined in Data.Vector.Unboxed.Base

Methods

basicLength :: MVector s (Identity a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Identity a) -> MVector s (Identity a)

basicOverlaps :: MVector s (Identity a) -> MVector s (Identity a) -> Bool

basicUnsafeNew :: Int -> ST s (MVector s (Identity a))

basicInitialize :: MVector s (Identity a) -> ST s ()

basicUnsafeReplicate :: Int -> Identity a -> ST s (MVector s (Identity a))

basicUnsafeRead :: MVector s (Identity a) -> Int -> ST s (Identity a)

basicUnsafeWrite :: MVector s (Identity a) -> Int -> Identity a -> ST s ()

basicClear :: MVector s (Identity a) -> ST s ()

basicSet :: MVector s (Identity a) -> Identity a -> ST s ()

basicUnsafeCopy :: MVector s (Identity a) -> MVector s (Identity a) -> ST s ()

basicUnsafeMove :: MVector s (Identity a) -> MVector s (Identity a) -> ST s ()

basicUnsafeGrow :: MVector s (Identity a) -> Int -> ST s (MVector s (Identity a))

Data a => Data (Identity a)

Since: base-4.9.0.0

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 :: forall r r'. (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)

IsString a => IsString (Identity a)

Since: base-4.9.0.0

Defined in Data.String

Methods

fromString :: String -> Identity a

Storable a => Storable (Identity a)

Since: base-4.9.0.0

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 ()

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

mempty :: Identity a

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

mconcat :: [Identity a] -> Identity a

Semigroup a => Semigroup (Identity a)

Since: base-4.9.0.0

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

Bits a => Bits (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(.&.) :: Identity a -> Identity a -> Identity a

(.|.) :: Identity a -> Identity a -> Identity a

xor :: Identity a -> Identity a -> Identity a

complement :: Identity a -> Identity a

shift :: Identity a -> Int -> Identity a

rotate :: Identity a -> Int -> Identity a

zeroBits :: Identity a

bit :: Int -> Identity a

setBit :: Identity a -> Int -> Identity a

clearBit :: Identity a -> Int -> Identity a

complementBit :: Identity a -> Int -> Identity a

testBit :: Identity a -> Int -> Bool

bitSizeMaybe :: Identity a -> Maybe Int

bitSize :: Identity a -> Int

isSigned :: Identity a -> Bool

shiftL :: Identity a -> Int -> Identity a

unsafeShiftL :: Identity a -> Int -> Identity a

shiftR :: Identity a -> Int -> Identity a

unsafeShiftR :: Identity a -> Int -> Identity a

rotateL :: Identity a -> Int -> Identity a

rotateR :: Identity a -> Int -> Identity a

popCount :: Identity a -> Int

FiniteBits a => FiniteBits (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

finiteBitSize :: Identity a -> Int

countLeadingZeros :: Identity a -> Int

countTrailingZeros :: Identity a -> Int

Bounded a => Bounded (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

minBound :: Identity a

maxBound :: Identity a

Enum a => Enum (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

succ :: Identity a -> Identity a

pred :: Identity a -> Identity a

toEnum :: Int -> Identity a

fromEnum :: Identity a -> Int

enumFrom :: Identity a -> [Identity a]

enumFromThen :: Identity a -> Identity a -> [Identity a]

enumFromTo :: Identity a -> Identity a -> [Identity a]

enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a]

Floating a => Floating (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

pi :: Identity a

exp :: Identity a -> Identity a

log :: Identity a -> Identity a

sqrt :: Identity a -> Identity a

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

logBase :: Identity a -> Identity a -> Identity a

sin :: Identity a -> Identity a

cos :: Identity a -> Identity a

tan :: Identity a -> Identity a

asin :: Identity a -> Identity a

acos :: Identity a -> Identity a

atan :: Identity a -> Identity a

sinh :: Identity a -> Identity a

cosh :: Identity a -> Identity a

tanh :: Identity a -> Identity a

asinh :: Identity a -> Identity a

acosh :: Identity a -> Identity a

atanh :: Identity a -> Identity a

log1p :: Identity a -> Identity a

expm1 :: Identity a -> Identity a

log1pexp :: Identity a -> Identity a

log1mexp :: Identity a -> Identity a

RealFloat a => RealFloat (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

floatRadix :: Identity a -> Integer

floatDigits :: Identity a -> Int

floatRange :: Identity a -> (Int, Int)

decodeFloat :: Identity a -> (Integer, Int)

encodeFloat :: Integer -> Int -> Identity a

exponent :: Identity a -> Int

significand :: Identity a -> Identity a

scaleFloat :: Int -> Identity a -> Identity a

isNaN :: Identity a -> Bool

isInfinite :: Identity a -> Bool

isDenormalized :: Identity a -> Bool

isNegativeZero :: Identity a -> Bool

isIEEE :: Identity a -> Bool

atan2 :: Identity a -> Identity a -> Identity a

Generic (Identity a)

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

Ix a => Ix (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

range :: (Identity a, Identity a) -> [Identity a]

index :: (Identity a, Identity a) -> Identity a -> Int

unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int

inRange :: (Identity a, Identity a) -> Identity a -> Bool

rangeSize :: (Identity a, Identity a) -> Int

unsafeRangeSize :: (Identity a, Identity a) -> Int

Num a => Num (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(+) :: Identity a -> Identity a -> Identity a

(-) :: Identity a -> Identity a -> Identity a

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

negate :: Identity a -> Identity a

abs :: Identity a -> Identity a

signum :: Identity a -> Identity a

fromInteger :: Integer -> 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

Defined in Data.Functor.Identity

Methods

readsPrec :: Int -> ReadS (Identity a)

readList :: ReadS [Identity a]

readPrec :: ReadPrec (Identity a)

readListPrec :: ReadPrec [Identity a]

Fractional a => Fractional (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(/) :: Identity a -> Identity a -> Identity a

recip :: Identity a -> Identity a

fromRational :: Rational -> Identity a

Integral a => Integral (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

quot :: Identity a -> Identity a -> Identity a

rem :: Identity a -> Identity a -> Identity a

div :: Identity a -> Identity a -> Identity a

mod :: Identity a -> Identity a -> Identity a

quotRem :: Identity a -> Identity a -> (Identity a, Identity a)

divMod :: Identity a -> Identity a -> (Identity a, Identity a)

toInteger :: Identity a -> Integer

Real a => Real (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

toRational :: Identity a -> Rational

RealFrac a => RealFrac (Identity a)

Since: base-4.9.0.0

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

Defined in Data.Functor.Identity

Methods

showsPrec :: Int -> Identity a -> ShowS

show :: Identity a -> String

showList :: [Identity a] -> ShowS

Eq a => Eq (Identity a)

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

Ord a => Ord (Identity a)

Since: base-4.8.0.0

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

Abelian a => Abelian (Identity a)

Defined in Data.Group

Cyclic a => Cyclic (Identity a)

Defined in Data.Group

Methods

generator :: Identity a

Group a => Group (Identity a)

Identity lifts groups pointwise (at only one point).

Defined in Data.Group

Methods

invert :: Identity a -> Identity a

(~~) :: Identity a -> Identity a -> Identity a

pow :: Integral x => Identity a -> x -> Identity a

Hashable a => Hashable (Identity a)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Identity a -> Int

hash :: Identity a -> Int

Ixed (Identity a)

Defined in Control.Lens.At

Methods

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

Wrapped (Identity a)

Defined in Control.Lens.Wrapped

Associated Types

type Unwrapped (Identity a)

Methods

_Wrapped' :: Iso' (Identity a) (Unwrapped (Identity a))

Prim a => Prim (Identity a)

Since: primitive-0.6.5.0

Defined in Data.Primitive.Types

Methods

sizeOf# :: Identity a -> Int#

alignment# :: Identity a -> Int#

indexByteArray# :: ByteArray# -> Int# -> Identity a

readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Identity a #)

writeByteAr