optics-core-0.3.0.1: Optics as an abstract interface: core definitions

Safe HaskellNone
LanguageHaskell2010

Optics.IxTraversal

Contents

Description

An IxTraversal is an indexed version of a Traversal. See the "Indexed optics" section of the overview documentation in the Optics module of the main optics package for more details on indexed optics.

Synopsis

Formation

type IxTraversal i s t a b = Optic A_Traversal (WithIx i) s t a b Source #

Type synonym for a type-modifying indexed traversal.

type IxTraversal' i s a = Optic' A_Traversal (WithIx i) s a Source #

Type synonym for a type-preserving indexed traversal.

Introduction

itraversalVL :: IxTraversalVL i s t a b -> IxTraversal i s t a b Source #

Build an indexed traversal from the van Laarhoven representation.

itraversalVL . itraverseOfid
itraverseOf . itraversalVLid

Elimination

itraverseOf :: (Is k A_Traversal, Applicative f, is `HasSingleIndex` i) => Optic k is s t a b -> (i -> a -> f b) -> s -> f t Source #

Map each element of a structure targeted by an IxTraversal (supplying the index), evaluate these actions from left to right, and collect the results.

This yields the van Laarhoven representation of an indexed traversal.

Computation

Well-formedness

itraverseOf o (const pure) ≡ pure
fmap (itraverseOf o f) . itraverseOf o g ≡ getCompose . itraverseOf o (\ i -> Compose . fmap (f i) . g i)

Additional introduction forms

See also each, which is an IxTraversal over each element of a (potentially monomorphic) container.

itraversed :: TraversableWithIndex i f => IxTraversal i (f a) (f b) a b Source #

Indexed traversal via the TraversableWithIndex class.

itraverseOf itraverseditraverse
>>> iover (itraversed <%> itraversed) (,) ["ab", "cd"]
[[((0,0),'a'),((0,1),'b')],[((1,0),'c'),((1,1),'d')]]

ignored :: IxAffineTraversal i s s a b Source #

This is the trivial empty IxAffineTraversal, i.e. the optic that targets no substructures.

This is the identity element when a Fold, AffineFold, IxFold or IxAffineFold is viewed as a monoid.

>>> 6 & ignored %~ absurd
6

elementsOf :: Is k A_Traversal => Optic k is s t a a -> (Int -> Bool) -> IxTraversal Int s t a a Source #

Traverse selected elements of a Traversal where their ordinal positions match a predicate.

elements :: Traversable f => (Int -> Bool) -> IxTraversal' Int (f a) a Source #

Traverse elements of a Traversable container where their ordinal positions match a predicate.

elementselementsOf traverse

elementOf :: Is k A_Traversal => Optic' k is s a -> Int -> IxAffineTraversal' Int s a Source #

Traverse the nth element of a Traversal if it exists.

element :: Traversable f => Int -> IxAffineTraversal' Int (f a) a Source #

Traverse the nth element of a Traversable container.

elementelementOf traversed

Additional elimination forms

iforOf :: (Is k A_Traversal, Applicative f, is `HasSingleIndex` i) => Optic k is s t a b -> s -> (i -> a -> f b) -> f t Source #

A version of itraverseOf with the arguments flipped.

imapAccumLOf :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a b -> (i -> acc -> a -> (b, acc)) -> acc -> s -> (t, acc) Source #

Generalizes mapAccumL to an arbitrary IxTraversal.

imapAccumLOf accumulates state from left to right.

mapAccumLOf o ≡ imapAccumLOf o . const

imapAccumROf :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a b -> (i -> acc -> a -> (b, acc)) -> acc -> s -> (t, acc) Source #

Generalizes mapAccumR to an arbitrary IxTraversal.

imapAccumROf accumulates state from right to left.

mapAccumROf o ≡ imapAccumROf o . const

iscanl1Of :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a a -> (i -> a -> a -> a) -> s -> t Source #

This permits the use of scanl1 over an arbitrary IxTraversal.

iscanr1Of :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a a -> (i -> a -> a -> a) -> s -> t Source #

This permits the use of scanr1 over an arbitrary IxTraversal.

ifailover :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a b -> (i -> a -> b) -> s -> Maybe t Source #

Try to map a function which uses the index over this IxTraversal, returning Nothing if the IxTraversal has no targets.

ifailover' :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a b -> (i -> a -> b) -> s -> Maybe t Source #

Version of ifailover strict in the application of the function.

Combinators

indices :: (Is k A_Traversal, is `HasSingleIndex` i) => (i -> Bool) -> Optic k is s t a a -> IxTraversal i s t a a Source #

Filter results of an IxTraversal that don't satisfy a predicate on the indices.

>>> toListOf (itraversed %& indices even) "foobar"
"foa"

ibackwards :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a b -> IxTraversal i s t a b Source #

This allows you to traverse the elements of an indexed traversal in the opposite order.

ipartsOf :: forall k is i s t a. (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a a -> IxLens [i] s t [a] [a] Source #

An indexed version of partsOf that receives the entire list of indices as its indices.

isingular :: forall k is i s a. (Is k A_Traversal, is `HasSingleIndex` i) => Optic' k is s a -> IxAffineTraversal' i s a Source #

Convert an indexed traversal to an IxAffineTraversal that visits the first element of the original traversal.

For the fold version see ipre.

>>> [1,2,3] & iover (isingular itraversed) (-)
[-1,2,3]

Since: 0.3

Subtyping

data A_Traversal :: OpticKind Source #

Tag for a traversal.

Instances
Is A_Traversal A_Fold Source # 
Instance details

Defined in Optics.Internal.Optic.Subtyping

Is A_Traversal A_Setter Source # 
Instance details

Defined in Optics.Internal.Optic.Subtyping

Is An_AffineTraversal A_Traversal Source # 
Instance details

Defined in Optics.Internal.Optic.Subtyping

Is A_Prism A_Traversal Source # 
Instance details

Defined in Optics.Internal.Optic.Subtyping

Is A_Lens A_Traversal Source # 
Instance details

Defined in Optics.Internal.Optic.Subtyping

Is An_Iso A_Traversal Source # 
Instance details

Defined in Optics.Internal.Optic.Subtyping

ToReadOnly A_Traversal s t a b Source # 
Instance details

Defined in Optics.ReadOnly

Methods

getting :: Optic A_Traversal is s t a b -> Optic' (Join A_Getter A_Traversal) is s a Source #

IxOptic A_Traversal s t a b Source # 
Instance details

Defined in Optics.Indexed.Core

Methods

noIx :: NonEmptyIndices is => Optic A_Traversal is s t a b -> Optic A_Traversal NoIx s t a b Source #

van Laarhoven encoding

The van Laarhoven representation of an IxTraversal directly expresses how it lifts an effectful operation I -> A -> F B on elements and their indices to act on structures S -> F T. Thus itraverseOf converts an IxTraversal to an IxTraversalVL.

type IxTraversalVL i s t a b = forall f. Applicative f => (i -> a -> f b) -> s -> f t Source #

Type synonym for a type-modifying van Laarhoven indexed traversal.

type IxTraversalVL' i s a = IxTraversalVL i s s a a Source #

Type synonym for a type-preserving van Laarhoven indexed traversal.

Re-exports

class (FoldableWithIndex i t, Traversable t) => TraversableWithIndex i t | t -> i where Source #

Class for Traversables that have an additional read-only index available.

Methods

itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b) Source #

Instances
TraversableWithIndex Int [] Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Int -> a -> f b) -> [a] -> f [b] Source #

TraversableWithIndex Int ZipList Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Int -> a -> f b) -> ZipList a -> f (ZipList b) Source #

TraversableWithIndex Int NonEmpty Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Int -> a -> f b) -> NonEmpty a -> f (NonEmpty b) Source #

TraversableWithIndex Int IntMap Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Int -> a -> f b) -> IntMap a -> f (IntMap b) Source #

TraversableWithIndex Int Seq Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) Source #

TraversableWithIndex () Maybe Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

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

TraversableWithIndex () Par1 Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (() -> a -> f b) -> Par1 a -> f (Par1 b) Source #

TraversableWithIndex () Identity Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

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

Ix i => TraversableWithIndex i (Array i) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (i -> a -> f b) -> Array i a -> f (Array i b) Source #

TraversableWithIndex k (Map k) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (k -> a -> f b) -> Map k a -> f (Map k b) Source #

TraversableWithIndex k ((,) k) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (k -> a -> f b) -> (k, a) -> f (k, b) Source #

TraversableWithIndex Void (V1 :: Type -> Type) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Void -> a -> f b) -> V1 a -> f (V1 b) Source #

TraversableWithIndex Void (U1 :: Type -> Type) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Void -> a -> f b) -> U1 a -> f (U1 b) Source #

TraversableWithIndex Void (Proxy :: Type -> Type) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Void -> a -> f b) -> Proxy a -> f (Proxy b) Source #

TraversableWithIndex i f => TraversableWithIndex i (Rec1 f) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f0 => (i -> a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) Source #

TraversableWithIndex i m => TraversableWithIndex i (IdentityT m) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (i -> a -> f b) -> IdentityT m a -> f (IdentityT m b) Source #

TraversableWithIndex i f => TraversableWithIndex i (Reverse f) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f0 => (i -> a -> f0 b) -> Reverse f a -> f0 (Reverse f b) Source #

TraversableWithIndex i f => TraversableWithIndex i (Backwards f) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f0 => (i -> a -> f0 b) -> Backwards f a -> f0 (Backwards f b) Source #

TraversableWithIndex Void (Const e :: Type -> Type) Source #

Since: 0.3

Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Void -> a -> f b) -> Const e a -> f (Const e b) Source #

TraversableWithIndex Void (Constant e :: Type -> Type) Source #

Since: 0.3

Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Void -> a -> f b) -> Constant e a -> f (Constant e b) Source #

TraversableWithIndex Void (K1 i c :: Type -> Type) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => (Void -> a -> f b) -> K1 i c a -> f (K1 i c b) Source #

TraversableWithIndex [Int] Tree Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f => ([Int] -> a -> f b) -> Tree a -> f (Tree b) Source #

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :+: g) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) Source #

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :*: g) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> (f :*: g) a -> f0 ((f :*: g) b) Source #

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Product f g) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> Product f g a -> f0 (Product f g b) Source #

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Sum f g) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> Sum f g a -> f0 (Sum f g b) Source #

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (f :.: g) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f0 => ((i, j) -> a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) Source #

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (Compose f g) Source # 
Instance details

Defined in Optics.Internal.Indexed.Classes

Methods

itraverse :: Applicative f0 => ((i, j) -> a -> f0 b) -> Compose f g a -> f0 (Compose f g b) Source #