Writing your own optics


In order to work with optics, you need to create them for your specific data type. Consider the following data types:

enum PublicationState {
    case draft
    case published(Date)

struct Article {
    let title: String
    let subtitle: Option<String>
    let state: PublicationState
    let tags: [String]

We can also create some sample values to apply our optics to:

let state = PublicationState.published(Date())
let article = Article(title: "Working with optics in Swift",
                      subtitle: .some("Learn to use BowOptics"),
                      state: .draft,
                      tags: ["fp", "swift", "bow"])

In the following sections, we will describe how to create each of the optics for those types, where they are applicable.


Iso<S, A> represents an isomorphism between types S and A. That means we can transform from an S to an A and back to S with a pair of functions, and we will get the original value. Similarly, we can start with an A, transform it to an S and back to an A without losing information. This does not mean S and A are equal, but it implies their structures are equivalent.

An example of an Iso can be found in product types. In our running example, Article is a product type composed of a String, an optional String, a PublicationState and an Array of String. But we could also represent the same information using a tuple of 4 elements, and we would be able to get a tuple from an article, and vice versa. That is, we can build an Iso<Article, (String, Option<String>, PublicationState, [String])>.

To do so, we need a pair of functions. To go from tuple to Article, we can use Article.init, since the types in the tuple are already in the same order the initializer expects them. To go from Article to tuple we need to destructure the Article:

func toTuple(_ article: Article) -> (String, Option<String>, PublicationState, [String]) {
    return (article.title, article.subtitle, article.state, article.tags)

With this function, creating an Iso between these types is as easy as:

let iso = Iso<Article, (String, Option<String>, PublicationState, [String])>(get: toTuple, reverseGet: Article.init)

The Iso initializer expects two functions: get, to go from S to A, and reverseGet to go from A to S, which is exactly what our two functions are doing.

Using Iso

We can transform an article into a tuple with the iso we just created:

iso.get(article) // returns ("Working with optics", .some("Learn to use BowOptics"), .draft, ["fp", "swift", "bow"])

Or we can make an Article out of a tuple:

iso.reverseGet(("FP in Swift", .none(), .draft, [])) // Creates an Article(title: "FP in Swift", subtitle: .none(), state: .draft, tags: [])


Getter<S, A> allows us to get a value A out of a structure S. For instance, we can make a Getter to extract the title of an Article. In that case, we need to make a Getter<Article, String>:

let titleGetter = Getter<Article, String>(get: { article in article.title })

Using Getter

As you can guess, we can use a Getter to get a property of a structure. Using the recently created titleGetter, we can apply it to our article:

titleGetter.get(article) // Returns "Working with optics in Swift"


Similarly, a Setter<S, A> allows us to set a new value of type A or modify the existing one in a structure S. Since we are dealing with immutable data structures, that involves making a copy of the structure that changes the focused value. We can add the following method to Article in order to get copies with modified fields seamlessly:

extension Article {
    func copy(withTitle title: String? = nil,
              withSubtitle subtitle: Option<String>? = nil,
              withState state: PublicationState? = nil,
              withTags tags: [String]? = nil) -> Article {
        return Article(title: title ?? self.title,
                       subtitle: subtitle ?? self.subtitle,
                       state: state ?? self.state,
                       tags: tags ?? self.tags)

This copy method provides multiple overloads to make a copy of the receiver object and modify only certain fields. If an argument is passed, the copy will have it; otherwise, the current value of the object is taken.

Using this, let’s proceed to write a Setter for the title of an Article. To create a Setter, we can pass two closures that specify how an article is modified with a function f that modifies its title, and how to set a new title for an article. We can write a Setter<Article, String>:

let titleSetter = Setter<Article, String>(
    modify: { article, f in article.copy(withTitle: f(article.title)) },
    set: { article, newTitle in article.copy(withTitle: newTitle) })

Using Setter

Similar to Getter, we can use a Setter to set a property in a structure. Using the titleSetter created above, we can set a new title for the article we had:

titleSetter.set(article, "All about Optics") // Returns Article(title: "All about optics", subtitle: .some("Learn to use BowOptics"), state: .draft, tags: ["fp", "swift", "bow"])

It is important to note that the original article remains the same; the Setter creates a copy where all values are the same except the one focused by the Setter.

We don’t have to pass a new value; we can also transform the title of the article:

titleSetter.modify(article, { str in str.uppercased() }) // Returns Article(title: "WORKING WITH OPTICS IN SWIFT", subtitle: .some("Learn to use BowOptics"), state: .draft, tags: ["fp", "swift", "bow"])


If we combine the power of Getter and Setter into a single optic, we have a Lens. A Lens<S, A> is an optic that lets us get, set or modify a value A out of a structure S.

We can provide a Lens to get/set the title of an Article by providing these two functions:

let titleLens = Lens<Article, String>(
    get: { article in article.title },
    set: { article, newTitle in article.copy(withTitle: newTitle) })

Using Lens

Using Lens is like using Getter and Setter, in the same optic. You can retrieve and modify the focus of the Lens. Using the Lens we just created:

// Gets the title

// Sets a new title
titleLens.set(article, "All about Optics")

// Modifies the existing title
titleLens.modify(article, { str in str.uppercased() })


In the previous optics, title is always present in an Article. However, if we focus on its subtitle, we can see it is an Option<String>. We can still write a Lens whose focus is Option<String>, but for the sake of composition, it would be better to remove that optionality.

To do so, we can use the AffineTraversal<S, A>, which lets us focus on a value A that may be absent in a structure S, just like the case of the article subtitle. An AffineTraversal needs two functions to be initialized. The setter function just needs to make a copy of the article with the new value. The getter function is a bit trickier. It returns an Either; if the focus is present in the structure, it returns an Either.right containing it; otherwise, it returns an Either.left with the original article.

let subtitleAffineTraversal = AffineTraversal<Article, String>(
    set: { article, newSubtitle in article.copy(withSubtitle: .some(newSubtitle)) },
    getOrModify: { article in article.subtitle.fold({ Either.left(article) }, Either.right) })

Using AffineTraversal

Using AffineTraversal is quite similar to using a Lens. We can get an Option of the focus or set it to a new value:

subtitleAffineTraversal.getOption(article) // Returns .some("Learn to use BowOptics")
subtitleAffineTraversal.set(article, "") // Returns Article(title: "Working with optics in Swift", subtitle: .some(""), state: .draft, tags: ["fp", "swift", "bow"])

If we try to modify an article, it will return a new article with the modified subtitle, or the original article if the subtitle was not present.

let articleWithoutSubtitle = Article(title: "Not interesing", subtitle: .none(), state: .draft, tags: [])
subtitleAffineTraversal.modify(articleWithoutSubtitle, { str in str.lowercased() }) // Returns the same article as it does not have a subtitle


All the optics above work for product types. When it comes to sum types, we need to use Prism. Prism<S, A> is an optic that lets us focus on a value A that is present under certain circumstances in the structure S.

Sum types in Swift are usually represented by enum, so focusing on one of the cases does not guarantee that it is always going to be there.

As an example, consider the PublicationState described above. If we want to focus on the published side and get the Date of publication, we need to create a Prism<PublicationState, Date>. As usual, we need two functions. The getter lets us get Either the date (right, if we received a PublicationState that is in the state we are focusing) or the original state (left, if we are in another case of the PublicationState). The other function lets us build a state from a given Date.

let publishedPrism = Prism<PublicationState, Date>(
    getOrModify: { state in
        guard case let .published(date) = state else {
            return Either.left(state)
        return Either.right(date)
    }, reverseGet: PublicationState.published)

Using Prism

We can use the Prism above to get the publication date from a state:

publishedPrism.getOption(state) // Returns an Option with the date that we set when we created it

However, in the case of a PublishedState.draft, this Prism cannot get a Date, so it will return an empty Option:

publishedPrism.getOption(.draft) // Returns .none()


The optics presented so far have only one focus. Is it possible to have multiple foci? The Fold and Traversal optics have 0 to n foci.

Fold is a generalization of Foldable. Fold<S, A> describes an optic that can focus on several A values in a structure S and can transform and fold them into a summary value.

This is usually the case of fields that contain collections of elements and we want to focus on them individually. In the case of Article, if we write a Lens for the tags, it lets us focus on all tags as a whole, not on each individual tag.

let tagsLens = Lens<Article, [String]>(
    get: { article in article.tags },
    set: { article, newTags in article.copy(withTags: newTags) })

We can get a Fold<Article, String> that lets us have foci to each individual tag. In this case, we can leverage an existing Fold<[A], A>; i.e. for any array, it gives us a Fold to focus on each item of the array. It is available in Array<Element>.fold. With that, we can compose it with the tagsLens to get a Fold:

let tagsFold: Fold<Article, String> = tagsLens + Array<String>.fold

Using Fold

Once we have a Fold, we can use it for different purposes, like counting the number of tags:

tagsFold.size(article) // Returns 3

Or find a tag with a specific criteria:

tagsFold.find(article, { tag in tag.count == 2 }) // Returns .some("fp")


Finally, Traversal is a generalization of Traverse. Traversal<S, A> lets us focus on multiple A values in a structure S to get, set or modify them. Like in the case for Fold, it is useful for fields that contain collections of elements. Likeways, there is a Traversal<[A], A> available for any array in Array<Element>.traversal. With that, we can compose it with the tagsLens to get a Traversal:

let tagsTraversal: Traversal<Article, String> = tagsLens + Array<String>.traversal

Using Traversal

The Traversal for tags that we have created lets us modify all of them with a function:

tagsTraversal.modify(article, { str in str.uppercased() }) // Uppercases all tags

Or check if there is a tag that matches a predicate:

tagsTraversal.exists(article, { str in str == "advanced" }) // Returns false as the article does not have any "advanced" tag

There are many more operations that are available for each optic that the ones shown in this page. For a complete reference, check the API documentation for each optic.