Optics.IxTraversal

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.

Formation

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

Type synonym for a type-modifying indexed traversal.

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

Type synonym for a type-preserving indexed traversal.

Introduction

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

Build an indexed traversal from the van Laarhoven representation.

itraversalVL . itraverseOf ≡ id
itraverseOf . itraversalVL ≡ id

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

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

itraverseOf (itraversalVL f) ≡ f

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

Indexed traversal via the TraversableWithIndex class.

itraverseOf itraversed ≡ itraverse

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

ignored :: IxTraversal i s s a b

This is the trivial empty IxTraversal.

>>> 6 & ignored %~ absurd
6

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

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

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

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

elements ≡ elementsOf traverse

elementOf :: Is k A_Traversal => Optic k is s t a a -> Int -> IxTraversal Int s t a a

Traverse the nth element of a Traversal if it exists.

TODO: the result ideally should be an indexed affine traversal.

element :: Traversable f => Int -> IxTraversal' Int (f a) a

Traverse the nth element of a Traversable container.

element ≡ elementOf 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

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)

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)

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

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

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

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

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

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

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]

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

Subtyping

data A_Traversal :: OpticKind

Tag for a traversal.

Instances

Is A_Traversal A_Fold

Defined in Optics.Internal.Optic.Subtyping

Methods

implies :: proxy A_Traversal A_Fold p -> (Constraints A_Traversal p -> r) -> Constraints A_Fold p -> r

Is A_Traversal A_Setter

Defined in Optics.Internal.Optic.Subtyping

Methods

implies :: proxy A_Traversal A_Setter p -> (Constraints A_Traversal p -> r) -> Constraints A_Setter p -> r

Is An_AffineTraversal A_Traversal

Defined in Optics.Internal.Optic.Subtyping

Methods

implies :: proxy An_AffineTraversal A_Traversal p -> (Constraints An_AffineTraversal p -> r) -> Constraints A_Traversal p -> r

Is A_Prism A_Traversal

Defined in Optics.Internal.Optic.Subtyping

Methods

implies :: proxy A_Prism A_Traversal p -> (Constraints A_Prism p -> r) -> Constraints A_Traversal p -> r

Is A_Lens A_Traversal

Defined in Optics.Internal.Optic.Subtyping

Methods

implies :: proxy A_Lens A_Traversal p -> (Constraints A_Lens p -> r) -> Constraints A_Traversal p -> r

Is An_Iso A_Traversal

Defined in Optics.Internal.Optic.Subtyping

Methods

implies :: proxy An_Iso A_Traversal p -> (Constraints An_Iso p -> r) -> Constraints A_Traversal p -> r

ToReadOnly A_Traversal s t a b

Defined in Optics.ReadOnly

Methods

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

IxOptic A_Traversal s t a b

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

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

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

type IxTraversalVL' i s a = IxTraversalVL i s s a a

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

Re-exports

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

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

Methods

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

Instances

TraversableWithIndex Int []

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex Int ZipList

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex Int NonEmpty

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex Int IntMap

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex Int Seq

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex () Maybe

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex () Par1

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex () Identity

Defined in Optics.Internal.Indexed

Methods

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

Ix i => TraversableWithIndex i (Array i)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex k (Map k)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex k ((,) k)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex Void (V1 :: Type -> Type)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex Void (U1 :: Type -> Type)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex Void (Proxy :: Type -> Type)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex i f => TraversableWithIndex i (Rec1 f)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex i m => TraversableWithIndex i (IdentityT m)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex i f => TraversableWithIndex i (Reverse f)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex i f => TraversableWithIndex i (Backwards f)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex Void (K1 i c :: Type -> Type)

Defined in Optics.Internal.Indexed

Methods

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

TraversableWithIndex [Int] Tree

Defined in Optics.Internal.Indexed

Methods

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

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :+: g)

Defined in Optics.Internal.Indexed

Methods

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

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :*: g)

Defined in Optics.Internal.Indexed

Methods

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

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Product f g)

Defined in Optics.Internal.Indexed

Methods

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

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Sum f g)

Defined in Optics.Internal.Indexed

Methods

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

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (f :.: g)

Defined in Optics.Internal.Indexed

Methods

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

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (Compose f g)

Defined in Optics.Internal.Indexed

Methods

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