Optics: a hands-on introduction in Scala

Optics: purely functional abstractions to manipulate immutable objects

Here’s a dummy 👶 domain model:

case class Street(number: Int, name: String); 
case class Address(city: String, street: Street); 
case class Company(name: String, address: Address); 
case class Employee(name: String, company: Company, salary: Int)
    defined class Street
    defined class Address
    defined class Company
    defined class Employee

Case classes in Scala are used to define immutable and algebraic data types. They have built-in support for:
– pattern matching
– comparison by structure
copy method which helps for immutable updates

Let’s define an employee 👩:

val employee = Employee("Monica", Company("Bestmile", Address("Lausanne", Street(58, "rhodanie"))), 100)
    employee: Employee = Employee(Monica,Company(Bestmile,Address(Lausanne,Street(58,rhodanie))),100)

Now let’s say we want to upper case the street name. Here’s how we can do it using copy:

  company = employee.company.copy(
    address = employee.company.address.copy(
      street = employee.company.address.street.copy(
        name = employee.company.address.street.name.capitalize // luckily capitalize exists
    res3: Employee = Employee(Monica,Company(Bestmile,Address(Lausanne,Street(58,Rhodanie))),100)

Pretty convoluted 🙄. That’s when the Lens optic becomes useful, as we’ll see next.

Lens: magnifying glass 🔍 for immutable data structures

Lens is like a zoom for data structures. Let’s import the monocle library version of Lens first (we’ll look at scalaz later):

import monocle.Lens
import monocle.macros.GenLens
    import monocle.Lens
    import monocle.macros.GenLens

Let’s define a lens on the company field of Employee:

val companyLens: Lens[Employee, Company] = GenLens[Employee](_.company)
    companyLens: Lens[Employee, Company] = $sess.cmd5Wrapper$Helper$$anon$1@49802b39

GenLens is a helper scala macro provided by monocle.macros.GenLens. A macro is code running at compilation time and emitting code for the actual compilation stage. It emits creation code for our companyLens object by introspecting the passed-in selection lambda function.

Here’s what we can now do with our lens:

val foobarCompany = Company("FooBar", Address("Lausanne", Street(58,"rhodanie")))

    foobarCompany: Company = Company(FooBar,Address(Lausanne,Street(58,rhodanie)))
    res6_1: Employee = Employee(Monica,Company(FooBar,Address(Lausanne,Street(58,rhodanie))),100)

Note that Lens.set is a curried method, i.e. it defines two parameter lists:
1. value to be set
1. object to set it onto

Therefore, one could also do:

val foobarCompanySetter = companyLens.set(foobarCompany)
    foobarCompanySetter: Employee => Employee = <function1>

And we get a function which can be applied to many employees to set their company to foobar:

// foobarCompanySetter(bob)
// foobarCompanySetter(paul) 
// etc.
    res8: Employee = Employee(Monica,Company(FooBar,Address(Lausanne,Street(58,rhodanie))),100)

🤔 Our initial objective actually was to uppercase the street name. Let’s see how this can help us get there.

We can define in a similar way lenses for the address field of Company, for the street field of Address, and the name field of Street:

val addressLens    = GenLens[Company](_.address)
val streetLens     = GenLens[Address](_.street)
val streetNameLens = GenLens[Street](_.name)
    addressLens: Lens[Company, Address] = $sess.cmd9Wrapper$Helper$$anon$1@72dfba8e
    streetLens: Lens[Address, Street] = $sess.cmd9Wrapper$Helper$$anon$2@2bf5fb3d
    streetNameLens: Lens[Street, String] = $sess.cmd9Wrapper$Helper$$anon$3@1eb2bad4

We now have the pieces to compose a lens to zoom 🔍 into the street name, all the way from the outside of an employee (so to speak 🤭):

val employeeStreetNameLens = companyLens composeLens addressLens composeLens streetLens composeLens streetNameLens
    employeeStreetNameLens: monocle.PLens[Employee, Employee, String, String] = monocle.PLens$$anon$1@fd5814b

or expressed in a more compact (but also more cryptic) syntax:

val employeeStreetNameLens = companyLens ^|-> addressLens ^|-> streetLens ^|-> streetNameLens
    employeeStreetNameLens: monocle.PLens[Employee, Employee, String, String] = monocle.PLens$$anon$1@1a18e104

We can now apply this to our employee!

    res12: Employee = Employee(Monica,Company(Bestmile,Address(Lausanne,Street(58,Rhodanie))),100)


Here’s the same example with scalaz:

import scalaz.Lens._
import scalaz.@>
    import scalaz.Lens._
    import scalaz.@>
val companyL: Employee @> Company = lensu((employee, company) => employee.copy(company = company), _.company)
val addressL: Company @> Address = lensu((company, address) => company.copy(address = address), _.address)
val streetL: Address @> Street = lensu((address, street) => address.copy(street = street), _.street)
val streetNameL: Street @> String = lensu((street, name) => street.copy(name = name), _.name) 
    companyL: Employee @> Company = scalaz.LensFunctions$$anon$5@7e479cf2
    addressL: Company @> Address = scalaz.LensFunctions$$anon$5@351133fe
    streetL: Address @> Street = scalaz.LensFunctions$$anon$5@4b7b15ab
    streetNameL: Street @> String = scalaz.LensFunctions$$anon$5@171e38e

Composition is carried out with the 🐟 >=> operator (Kleisli composition with Lens):

val employeeStreetNameL = companyL >=> addressL >=> streetL >=> streetNameL
    employeeStreetNameL: scalaz.LensFamily[Employee, Employee, String, String] = scalaz.LensFamilyFunctions$$anon$4@255b80bb
employeeStreetNameL.mod(_.capitalize, employee)
    res16: Employee = Employee(Monica,Company(Bestmile,Address(Lausanne,Street(58,Rhodanie))),100)

Back to monocle: we can even zoom-in further than the street name, directly into the String type onto the first char.

Since a String can be empty, the first char is optional. We can use headOption, a special optic for such cases:

import monocle.function.Cons.headOption

val deepLens = companyLens ^|-> addressLens ^|-> streetLens ^|-> streetNameLens ^|-? headOption
    import monocle.function.Cons.headOption

    deepLens: monocle.POptional[Employee, Employee, Char, Char] = monocle.POptional$$anon$1@11cd893d
    res18: Employee = Employee(Monica,Company(Bestmile,Address(Lausanne,Street(58,Rhodanie))),100)

Note that using monocle‘s various functions and macros under the syntax namespace, one can create lenses directly on the object:

import monocle.macros.syntax.lens._

    import monocle.macros.syntax.lens._

    res19_1: Employee = Employee(Monica,Company(Bestmile,Address(Lausanne,Street(58,Rhodanie))),100)

Beyond lenses

There are different kinds of optics in monocle. They almost all compose with each other. Here’s a diagram of all the types, from the most general to the most specific.

Iso: a “mirror” for immutable structures

Iso converts elements of type S into elements of type A when S has the same “shape” as A. Consider the following case class:

case class Person(name: String, age: Int)
    defined class Person

Person is equivalent to a tuple (String, Int) and a tuple (String, Int) is equivalent to Person. We can define “bridges” between types of the same shape that way:

case class Person(name: String, age: Int)
case class PersonParam(newName: String, newAge: Int)

import monocle.macros.GenIso

// iso to tuple for both types
val personToTuple = GenIso.fields[Person]
val personParamToTuple = GenIso.fields[PersonParam]

// param -> tuple -> person
val paramToPerson =  personParamToTuple composeIso personToTuple.reverse

// applied on Monica
paramToPerson.get(PersonParam("Monica", 21))
// res0: Person = Person(Monica,21)

Prism 💎 : pick a color from the 🌈

A Prism is an optic used to select part of a Sum type (also known as Coproduct), typically a sealed trait.

It’s a type with two parameters Prism[S, A]: S is the Sum, A a part of the Sum.

Here’s an example Command sealed trait:

case class Coordinates(x: Double, y: Double)

sealed trait Command
case class DriveToPickup(target: Coordinates, passengers: Int) extends Command
case class DriveToStation(stationCoordinates: Coordinates) extends Command
case class DriveToDropoff(target: Coordinates, passengers: Int) extends Command
case object EmergencyStop extends Command
case object EmergencyResume extends Command
    defined class Coordinates
    defined trait Command
    defined class DriveToPickup
    defined class DriveToStation
    defined class DriveToDropoff
    defined object EmergencyStop
    defined object EmergencyResume

Now let’s say we want to define a generic logging function which logs coordinates involved in Command instances:

def logAnyCoordinates(command: Command) = ???

That would be the usual implementation:

def logAnyCoordinatesUsual(command: Command) = {
  val coordinates = 
  command match {
    case DriveToPickup(c, _)  => Some(c)
    case DriveToDropoff(c, _) => Some(c)
    case DriveToStation(c)    => Some(c)
    case _ => None
  println(coordinates.map(c =>  s"x=${c.x}, y=${c.y}").getOrElse(""))
    defined function logAnyCoordinatesUsual
logAnyCoordinatesUsual(DriveToDropoff(Coordinates(1.0, 2.0), 2))
logAnyCoordinatesUsual(DriveToStation(Coordinates(5.0, 2.0)))
logAnyCoordinatesUsual(DriveToDropoff(Coordinates(42, 42), 42))
    x=1.0, y=2.0

    x=5.0, y=2.0

    x=42.0, y=42.0

That’s ok, but here are some drawbacks:

  • This is evolution-fragile: if the Sum changes shape, code needs to be touched.

  • This sort of selection code is likely to end up duplicated in various places depending on the needs of each method.

  • It only describes one thing: extracting the value from the Sum type

But most importantly: it’s super boring code! 😴 😝
Let’s look at another, more generic way to do this using a combination of Prism and Lens.

First, we need some imports and a helper method (which unfortunately isn’t part of monocle)

import monocle._
import monocle.Optional
import monocle.macros.{GenLens, GenPrism}

implicit class RichOptional[A, B](self: Optional[A, B]) {
  def merge(optional: Optional[A, B]): Optional[A, B] =
    Optional[A, B](a => self.getOption(a).orElse(optional.getOption(a)))(b => a => self.setOption(b)(a).getOrElse(optional.set(b)(a)))
    import monocle._
    import monocle.Optional
    import monocle.macros.{GenLens, GenPrism}

    defined class RichOptional

Using a combination of Prism and Lens, we can define an Optional which acts as sort of pointer on all coordinates in the Command sealed trait:

val commandCoordinatesOptional = 
GenPrism[Command, DriveToPickup] ^|-> GenLens[DriveToPickup](_.target) merge
GenPrism[Command, DriveToStation] ^|-> GenLens[DriveToStation](_.stationCoordinates) merge
GenPrism[Command, DriveToDropoff] ^|-> GenLens[DriveToDropoff](_.target)
    commandCoordinatesOptional: Optional[Command, Coordinates] = monocle.Optional$$anon$6@7276fe7a

The combination of Prism then “zoom-in” using ^|-> and Lens leads to an Optional, an optic that represents a value which can be there or not. Then we use horizontal composition between Optional instances with merge.

We can now rewrite our logging function to take advantage of this:

def logAnyCoordinatesCool(command: Command) = {
  println(commandCoordinatesOptional.getOption(command).map(c => s"x=${c.x}, y=${c.y}").getOrElse(""))
    defined function logAnyCoordinatesCool
logAnyCoordinatesCool(DriveToDropoff(Coordinates(1.0, 2.0), 2))
logAnyCoordinatesCool(DriveToStation(Coordinates(5.0, 2.0)))
logAnyCoordinatesCool(DriveToDropoff(Coordinates(42, 42), 42))
    x=1.0, y=2.0

    x=5.0, y=2.0

    x=42.0, y=42.0

Even more 🆒 is the ability to update the coordinates for all! We can now define:

def offsetByOne(coordinates: Coordinates) = coordinates.copy(x = coordinates.x + 1, y = coordinates.y + 1)

def offsetCoordinatesByOne(command: Command) = commandCoordinatesOptional.modify(offsetByOne)(command)
    defined function offsetByOne
    defined function offsetCoordinatesByOne
offsetCoordinatesByOne(DriveToDropoff(Coordinates(1.0, 2.0), 2))
offsetCoordinatesByOne(DriveToStation(Coordinates(5.0, 2.0)))
offsetCoordinatesByOne(DriveToDropoff(Coordinates(42, 42), 42))
    res8_0: Command = DriveToDropoff(Coordinates(2.0,3.0),2)
    res8_1: Command = EmergencyStop
    res8_2: Command = DriveToStation(Coordinates(6.0,3.0))
    res8_3: Command = EmergencyResume
    res8_4: Command = DriveToDropoff(Coordinates(43.0,43.0),42)

Traversal ➿: many eyes see it all 🕷️

Traversal can focus into all elements inside of a container (e.g. List, Vector, Option). In more generic terms, it allows to focus from a type S into 0 to n values of type A.

For instance, let’s say each vehicle keeps a journal 📒 of commands:

case class Vehicle(name: String, id: Int)
case class VehicleCommandsJournal(vehicle: Vehicle, commands: List[Command])
    defined class Vehicle
    defined class VehicleCommandsJournal

Here’s a journal with some commands:

val journal = VehicleCommandsJournal(
  Vehicle("Navia1", 1),
    DriveToPickup(Coordinates(1.0, 2.0), 2),
    DriveToDropoff(Coordinates(5.0, 3.0), 2),
    DriveToStation(Coordinates(5.0, 2.0)),
    journal: VehicleCommandsJournal = VehicleCommandsJournal(Vehicle(Navia1,1),List(DriveToPickup(Coordinates(1.0,2.0),2), DriveToDropoff(Coordinates(5.0,3.0),2), DriveToStation(Coordinates(5.0,2.0)), EmergencyStop))

Let’s see if we can carry out our coordinates offset stunt. First, we need some more imports:

import monocle.Traversal
import scalaz.std.list.listInstance // we need scalaz Traverse type class instance for List in scope
    import monocle.Traversal
    import scalaz.std.list.listInstance // we need scalaz Traverse type class instance for List in scope

We can now define a traversal for commands in the journal:

val commandsLens = GenLens[VehicleCommandsJournal](_.commands) // first the lens
val commandsCoordinatesTraversal = commandsLens ^|->> fromTraverse[List, Command, Command] // compose with the commands traversal
    commandsLens: monocle.package.Lens[VehicleCommandsJournal, List[Command]] = $sess.cmd12Wrapper$Helper$$anon$1@446a2d03
    commandsCoordinatesTraversal: PTraversal[VehicleCommandsJournal, VehicleCommandsJournal, Command, Command] = monocle.PTraversal$$anon$2@7d066293

We can use this Traversal instance to define an offset function which works on VehicleCommandsJournal:

def offsetAllCoordinatesByOne(journal: VehicleCommandsJournal) = 
    defined function offsetAllCoordinatesByOne

And now let’s apply it to our small journal:

    res14: VehicleCommandsJournal = VehicleCommandsJournal(Vehicle(Navia1,1),List(DriveToPickup(Coordinates(2.0,3.0),2), DriveToDropoff(Coordinates(6.0,4.0),2), DriveToStation(Coordinates(6.0,3.0)), EmergencyStop))



We’ve seen how to zoom-in on elements based on structure using Lens and other optics. We can also focus on elements based on data using monocle‘s various typeclasses.

To illustrate this, let’s define a structure which maps employees 👥👥 per company 🏭:

case class EmployeesPerCompany(employees: Map[Company, List[Employee]])
    defined class EmployeesPerCompany

We have two companies around here:

val bm = Company("Bestmile", Address("Lausanne", Street(58, "rhodanie")))
val pmi = Company("Phil International", Address("Lausanne", Street(50, "Rhodanie")))
    bm: Company = Company(Bestmile,Address(Lausanne,Street(58,rhodanie)))
    pmi: Company = Company(Phil International,Address(Lausanne,Street(50,Rhodanie)))

And various employees:

val employeesPerCompany = EmployeesPerCompany(List(
    Employee("Monica", bm, salary = 100),
    Employee("Bob", bm, salary = 90),
    Employee("Alice", bm, salary = 110),
    Employee("Alfred", bm, salary = 105),
    Employee("Picsou", pmi, salary = 1000),
    Employee("Donald", pmi, salary = 2000))
    employeesPerCompany: EmployeesPerCompany = EmployeesPerCompany(
        Company(Phil International,Address(Lausanne,Street(50,Rhodanie))) -> List(
          Employee(Picsou,Company(Phil International,Address(Lausanne,Street(50,Rhodanie))),1000),
          Employee(Donald,Company(Phil International,Address(Lausanne,Street(50,Rhodanie))),2000)
        Company(Bestmile,Address(Lausanne,Street(58,rhodanie))) -> List(

Notice the injustice 🤑💸? In the world of optics, it’s easy to correct this. We first need a lens on the salary field of Employee:

val salaryLens = GenLens[Employee](_.salary)
    salaryLens: monocle.package.Lens[Employee, Int] = $sess.cmd32Wrapper$Helper$$anon$1@710493f1

Then some imports:

import monocle.function.At.at      // to get At typeclass
import monocle.function.Each.each  // to get Each typeclass 
import monocle.std.map._           // to get Map typeclass instance for At
import monocle.std.list._          // to get List typeclass instance for Each 
    import monocle.function.At.at      // to get At typeclass
    import monocle.function.Each.each  // to get Each typeclass 
    import monocle.std.map._           // to get Map typeclass instance for At
    import monocle.std.list._          // to get List typeclass instance for Each 

We can now do:

val corrected = (employeesPerCompany.lens(_.employees) 
     ^|-> at(pmi) 
     ^|->> each ^|->> each 
     ^|-> salaryLens
).modify(_ / 10)
    corrected: EmployeesPerCompany = EmployeesPerCompany(
        Company(Phil International,Address(Lausanne,Street(50,Rhodanie))) -> List(
          Employee(Picsou,Company(Phil International,Address(Lausanne,Street(50,Rhodanie))),100),
          Employee(Donald,Company(Phil International,Address(Lausanne,Street(50,Rhodanie))),200)
        Company(Bestmile,Address(Lausanne,Street(58,rhodanie))) -> List(

Of course, let’s not forget 😏:

     ^|-> at(bm) 
     ^|->> each ^|->> each 
     ^|-> salaryLens
).modify(_ * 10)
    res35: EmployeesPerCompany = EmployeesPerCompany(
        Company(Philip Morris International,Address(Lausanne,Street(50,Rhodanie))) -> List(
          Employee(Picsou,Company(Philip Morris International,Address(Lausanne,Street(50,Rhodanie))),100),
          Employee(Donald,Company(Philip Morris International,Address(Lausanne,Street(50,Rhodanie))),200)
        Company(Bestmile,Address(Lausanne,Street(58,rhodanie))) -> List(

For more information




For Javascripters:


Port of monocle for TS

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