| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Optics.IxTraversal
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
- type IxTraversal i s t a b = Optic A_Traversal (WithIx i) s t a b
- type IxTraversal' i s a = Optic' A_Traversal (WithIx i) s a
- itraversalVL :: IxTraversalVL i s t a b -> IxTraversal i s t a b
- itraverseOf :: (Is k A_Traversal, Applicative f, is `HasSingleIndex` i) => Optic k is s t a b -> (i -> a -> f b) -> s -> f t
- itraversed :: TraversableWithIndex i f => IxTraversal i (f a) (f b) a b
- ignored :: IxAffineTraversal i s s a b
- elementsOf :: Is k A_Traversal => Optic k is s t a a -> (Int -> Bool) -> IxTraversal Int s t a a
- elements :: Traversable f => (Int -> Bool) -> IxTraversal' Int (f a) a
- elementOf :: Is k A_Traversal => Optic' k is s a -> Int -> IxAffineTraversal' Int s a
- element :: Traversable f => Int -> IxAffineTraversal' Int (f a) a
- iforOf :: (Is k A_Traversal, Applicative f, is `HasSingleIndex` i) => Optic k is s t a b -> s -> (i -> a -> f b) -> f t
- imapAccumLOf :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a b -> (i -> acc -> a -> (b, acc)) -> acc -> s -> (t, acc)
- imapAccumROf :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a b -> (i -> acc -> a -> (b, acc)) -> acc -> s -> (t, acc)
- iscanl1Of :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a a -> (i -> a -> a -> a) -> s -> t
- iscanr1Of :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a a -> (i -> a -> a -> a) -> s -> t
- ifailover :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a b -> (i -> a -> b) -> s -> Maybe t
- ifailover' :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a b -> (i -> a -> b) -> s -> Maybe t
- indices :: (Is k A_Traversal, is `HasSingleIndex` i) => (i -> Bool) -> Optic k is s t a a -> IxTraversal i s t a a
- ibackwards :: (Is k A_Traversal, is `HasSingleIndex` i) => Optic k is s t a b -> IxTraversal i s t a b
- 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]
- isingular :: forall k is i s a. (Is k A_Traversal, is `HasSingleIndex` i) => Optic' k is s a -> IxAffineTraversal' i s a
- iadjoin :: (Is k A_Traversal, Is l A_Traversal, is `HasSingleIndex` i) => Optic' k is s a -> Optic' l is s a -> IxTraversal' i s a
- data A_Traversal :: OpticKind
- type IxTraversalVL i s t a b = forall f. Applicative f => (i -> a -> f b) -> s -> f t
- type IxTraversalVL' i s a = IxTraversalVL i s s a a
- class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i (t :: Type -> Type) | t -> i where
- itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b)
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.itraverseOf≡iditraverseOf.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 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
itraverseOf(itraversalVLf) ≡ f
Well-formedness
itraverseOfo (constpure) ≡purefmap(itraverseOfo f) .itraverseOfo g ≡getCompose.itraverseOfo (\ 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.
itraverseOfitraversed≡itraverse
>>>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,
IxAffineFold, Traversal or
IxTraversal is viewed as a monoid.
>>>6 & ignored %~ absurd6
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.
elements≡elementsOftraverse
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.
element≡elementOftraversed
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.
mapAccumLOfo ≡imapAccumLOfo.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.
mapAccumROfo ≡imapAccumROfo.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
Monoid structure
IxTraversal admits a (partial) monoid structure where iadjoin
combines non-overlapping indexed traversals, and the identity element is
ignored (which traverses no elements).
If you merely need an IxFold, you can use indexed traversals as indexed
folds and combine them with one of the monoid structures on indexed folds
(see Optics.IxFold). In particular, isumming can be used to
concatenate results from two traversals, and ifailing will returns
results from the second traversal only if the first returns no results.
There is no Semigroup or Monoid instance for IxTraversal, because
there is not a unique choice of monoid to use that works for all optics,
and the (<>) operator could not be used to combine optics of different
kinds.
iadjoin :: (Is k A_Traversal, Is l A_Traversal, is `HasSingleIndex` i) => Optic' k is s a -> Optic' l is s a -> IxTraversal' i s a infixr 6 Source #
Combine two disjoint indexed traversals into one.
>>>iover (_1 % itraversed `iadjoin` _2 % itraversed) (+) ([0, 0, 0], (3, 5))([0,1,2],(3,8))
Note: if the argument traversals are not disjoint, the result will not
respect the IxTraversal laws, because it will visit the same element multiple
times. See section 7 of
Understanding Idiomatic Traversals Backwards and Forwards
by Bird et al. for why this is illegal.
>>>iview (ipartsOf (each `iadjoin` each)) ("x","y")([0,1,0,1],["x","y","x","y"])>>>iset (ipartsOf (each `iadjoin` each)) (const ["a","b","c","d"]) ("x","y")("c","d")
For the IxFold version see isumming.
Since: 0.4
Subtyping
data A_Traversal :: OpticKind Source #
Tag for a traversal.
Instances
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 (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i (t :: Type -> Type) | t -> i where #
A Traversable with an additional index.
An instance must satisfy a (modified) form of the Traversable laws:
itraverse(constIdentity) ≡Identityfmap(itraversef).itraverseg ≡getCompose.itraverse(\i ->Compose.fmap(f i).g i)
Minimal complete definition
Nothing
Methods
itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b) #
Traverse an indexed container.
itraverse≡itraverseOfitraversed