Setter
A Setter is an optic that can see into a structure and set or modify its focus.
It is a generalization of Functor#map. Given a Functor<F>, we can apply a function (A) -> B to Kind<F, A> and get Kind<F, B>. We can think of Kind<F, A> as a structure S that has a focus A.
So, given a PSetter<S, T, A, B>, we can apply a function (A) -> B to S and get T.
Functor.map(fa: Kind<F, A>, f: (A) -> B) -> Kind<F, B>PSetter.modify(s: S, f: (A) -> B): T
You can get a Setter for any existing Functor.
To create your own Setter, you need to define how to apply (A) -> B to S.
A Setter<Player, Int> can set and modify the value of Player. So we need to define how to apply a function (Int) -> Int to Player.
Composition
Unlike a regular set function, a Setter composes. Similar to a Lens, we can compose Setters to focus into nested structures and set or modify a value.
Setter can be composed with all optics but Getter and Fold. It results in the following optics:
| Iso | Lens | Prism | Optional | Getter | Setter | Fold | Traversal | |
|---|---|---|---|---|---|---|---|---|
| Setter | Setter | Setter | Setter | Setter | X | Setter | X | Setter |
Polymorphic setter
When dealing with polymorphic types, we can also have polymorphic setters that allow us to morph the type of the focus.
Previously, when we used a Setter<ListKOf<Int>, Int>, it was able to morph the Int values in the constructed type ListK<Int>.
With a PSetter<ListKOf<Int>, ListKOf<String>, Int, String>, we can morph an Int value to a String value and thus also morph the type from ListK<Int> to ListK<String>.
Laws
Arrow provides SetterLaws in the form of test cases for internal verification of lawful instances and third party apps creating their own setters.