Traversal
A Traversal is an optic that can see into a structure and get, set, or modify 0 to N foci.
It is a generalization of Traverse#traverse. Given a Traverse<F>, we can apply a function (A) -> Kind<G, B> to Kind<F, A> and get Kind<G, Kind<F, B>>.
We can think of Kind<F, A> as a structure S that has a focus A. So, given a PTraversal<S, T, A, B>, we can apply a function (A) -> Kind<F, B> to S and get Kind<F, T>.
Traverse.traverse(fa: Kind<F, A>, f: (A) -> Kind<G, B>, GA: Applicative<G>): Kind<G, Kind<F, B>>PTraversal.modifyF(s: S, f: (A) -> Kind<F, B>, GA: Applicative<F>): Kind<F, T>
You can get a Traversal for any existing Traverse.
Or by using any of the constructors of Traversal.
Arrow optics also provides a number of predefined Traversal optics.
Composition
Composing Traversal can be used for accessing and modifying foci in nested structures.
Traversal can be composed with all optics, and results in the following optics:
| Iso | Lens | Prism | Optional | Getter | Setter | Fold | Traversal | |
|---|---|---|---|---|---|---|---|---|
| Traversal | Traversal | Traversal | Traversal | Traversal | Fold | Setter | Fold | Traversal |
Polymorphic Traversal
When dealing with polymorphic types, we can also have polymorphic Traversals that allow us to morph the type of the foci.
Previously, we used a Traversal<ListKOf<Int>, Int>; it was able to morph the Int values in the constructed type ListK<Int>.
With a PTraversal<ListKOf<Int>, ListKOf<String>, Int, String>, we can morph an Int to a String, and thus, also morph the type from ListK<Int> to ListK<String>.
Laws
Arrow provides TraversalLaws in the form of test cases for internal verification of lawful instances and third party apps creating their own traversal.