README.md

layout	title	permalink
docs-optics	Setter	/optics/setter/

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]({{'/arrow/typeclasses/functor' | relative_url }}). 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]({{'/optics/lens' | relative_url }}), 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{:target="_blank"} in the form of test cases for internal verification of lawful instances and third party apps creating their own setters.