optics-research

Discovering magic abilities of optics concept with Kotlin

Inspired by Arrow Optics and Monocle

Problem

Let's examine example of immutable data types composition with nested hierarchy.

data class Street(val number: Int, val name: String)
data class Address(val city: String, val street: Street)
data class Company(val name: String, val address: Address)
data class Employee(val name: String, val company: Company)

Assume that we have instance of Employee and need to update street name of it's company. We could use copy method generated by Kotlin data classes:

employee.copy(
    company = employee.company.copy( 
        address = employee.company.address.copy(
            street = employee.company.address.street.copy(
                name = employee.company.address.street.name.capitalize()
            )
        )
    )
)

The deeper the hierarchy of types composition we have, the more code is required to modify each next inner field.

Lens

Let's introduce class Lens that abstracts the concepts of getting and setting the portion (called focus) of some structure S in functional way:

class Lens<S, F>(
    val get: (S) -> F,
    val set: (S, F) -> S
) {
    fun modify(s: S, update: (F) -> F): S {
        return set(s, get(s).let(update))
    }
}

Then we can create Lens instance for every field used in our path to deeply nested target:

val Employee.Companion.company = Lens(
    get = Employee::company,
    set = { s, f -> s.copy(company = f) }
)

val Company.Companion.address = Lens(
    get = Company::address,
    set = { s, f -> s.copy(addres = f) }
)

val Address.Companion.street = Lens(
    get = Address::street,
    set = { s, f -> s.copy(street = f) }
)

val Street.Companion.name = Lens(
    get = Street::name,
    set = { s, f -> s.copy(name = f) }
)

Given types of Lens<A, B> and Lens<B, C> we can compose them to Lens<A, C> with function at. So we can modify target field from employee with composed Lens<Employee, String>:

Employee.company
    .at(Company.address) 
    .at(Adress.street)
    .at(Street.name)
    .modify(employee, String::capitalize)

Optional ([OptLens])

Now let's change type Employee to have the list of companies instead of single company.

/* ... */
data class Employee(val name: String, val companies: List<Company>)

And try to create new instance of Employee by updating the first item in companies list without optics.

employee.copy(
    companies = employee.companies.mapIndexed { index, company -> 
        if (index == 0) {
            company.copy(
                address = company.address.copy(
                    street = company.address.street.copy(
                        name = company.address.street.name.capitalize()
                    )
                )
            )
        } else {
            company
        }
    }
)

With composition of Lens it could be expressed like this:

Employee.companies
    .atPosition(0)
    .at(Company.address) 
    .at(Adress.street)
    .at(Street.name)
    .modify(employee, String::capitalize)

Traversal

TBD

Optics code generation

TBD

Roadmap

• Lens
• ListTraversal
• Optional
• Prism
• Optics DSL
• Find solution for generic Traversals (HKT required?)
• Property tests for optic laws
• Performance benchmarks