Applicative in Scala Cats

I always heard about Applicative, but I don’t know what really is. So, I write this post to understand myself. Below picture is from and example is from mastering advanced Scala.

What is Applicative?

During programming, you will encounter this situation.

def getSome(a: Int): Option[Int] = Some(a)

def getNone(a: Int): Option[Int] = None

def add(a: Int, b: Int): Int = a + b

val aOpt = getSome(1)

val bOpt = getSome(2)

And I want to get aOpt and bOpt add together using add. But aOpt and bOpt is Option. So, the usual way to do is by using flatMap and map like this.

aOpt.flatMap(a => => add(a, b)))
// res0: Option[Int] = Some(3)

In here, we can use Applicative.

What is Applicative?

I don’t know that my understanding of Applicative is right. But I think, Applicative is


Very famous picture about Applicative.

In here there is a wrapped value: 2. And there is a wrapped function. We unwrapped both function and value, and process some operation and wrap it again! And we can also adapt these things to above example.

import cats.instances.option._
import cats.Applicative

Applicative[Option].map2(aOpt, bOpt)(add)
// res1: Option[Int] = Some(3)

We can also use like this.

import cats.syntax.all._

(aOpt |@| bOpt).map(add)

Monad extends Applicative

@typeclass trait Monad[F[_]] extends FlatMap[F] with Applicative[F] {
  override def map[A, B](fa: F[A])(f: A => B): F[B] =
  flatMap(fa)(a => pure(f(a)))

As you can see, Monad extends Applicative. And Applicative extends Functor. So, hierarchy is ‘Monad <: Applicative <: Functor’

Tip – Traverse

While studying with Mastering Advanced Scala, there are some tips in Applicative, So, I write down this. If there is a List[Int] and want all element adapt ‘getSome’ function, for example

val ints = List(1,2,3,4,5)
// res3: List[Option[Int]] = List(Some(1), Some(2), Some(3), Some(4), Some(5))

The result is ‘List(Some(1), Some(2), Some(3), Some(4), Some(5))’ and if you want to make ‘Some(List(1, 2, 3, 4, 5))’ you can use Traverse like this.

import cats.Traverse
import cats.instances.list._
import cats.instances.option._


// res4: Option[List[Int]] = Some(List(1, 2, 3, 4, 5))

This will return None if any element return None

def getSomeOrNone(a: Int): Option[Int] =
  if(a % 2 == 0) Some(a)
  else None


// res5: Option[List[Int]] = None


Cartesian Product in Scala Cats

During work, I have some problem handling three future at the same time. First future return a long value and second and third future receive the parameter from the first return and return a tuple.

The code is like this.

for {
  long <- futureLong()
  int <- futureInt(long)
  char <- futureChar(long)
} yield (int, char)

Of course for comprehension operates step by step, so, futureInt is called after futureLong is finished and futureChar is called after futureInt is finished. So, It takes too much time to get a final return value.

So, I changed codes like this.

val longVal: Future[Long] = futureLong()

val intVal: Future[Int] = for {
  long <- futureLong()
  int <- futureInt(long)
} yield int

val charVal: Future[Char] = for {
  long <- futureLong()
  char <- futureChar(long)
} yield char

val forComp: (Int, Char) = Await.result(for {
  int <- intVal
  char <- charVal
} yield (int, char), 5 second)

Yes, It works as I want. But, there is duplicated codes like, ‘long <- futureLong()’. During thinking a long time, my coworker, Liam, recommends using  Cartesian Product.

What is Cartesian Product?

Cartesian Product is very simple. It’s just a product of two Sets. For example, if there are two sets A = {1,2,3} and B = {‘a’, ‘b’, ‘c’}, Cartesian Product of A X B is

{(1, ‘a’), (1, ‘b’), (1, ‘c’), (2, ‘a’), (2, ‘b’), (2, ‘c’), (3, ‘a’), (3, ‘b’), (3, ‘c’)}

Yes. that’s all. Of course Cartesian Product didn’t hold commutative law. For example Cartesian Product of B X A is

{(‘a’, 1), (‘a’, 2), (‘a’, 3), (‘b’, 1), (‘b’, 2), (‘b’, 3), (‘c’, 1), (‘c’, 2), (‘c’, 3)}

And different from A X B.

Cartesian Product in cats

Above example can be implemented in Scala.

import cats.instances.list._
import cats.syntax.all._

val ints: List[Int] = List(1, 2, 3, 4)
val chars: List[Char] = List('a', 'b', 'c')

(ints |@| chars).tupled
// res0: List[(Int, Char)] = List((1,a), (1,b), (1,c), (2,a), (2,b), (2,c), (3,a), (3,b), (3,c), (4,a), (4,b), (4,c))
(chars |@| ints).tupled
// res1: List[(Char, Int)] = List((a,1), (a,2), (a,3), (a,4), (b,1), (b,2), (b,3), (b,4), (c,1), (c,2), (c,3), (c,4))

(ints |@| chars).map(_ + _.toString)
// res2: List[String] = List(1a, 1b, 1c, 2a, 2b, 2c, 3a, 3b, 3c, 4a, 4b, 4c)

In Cats Cartesian Product Syntax is ‘|@|’.(Some people call it Oink, and others call Pizza box) If you call tuple, it will return List Tuple. You can also map it.

Cartesian Product in Future

Ok, let’s return to the previous problem. I need to call futureInt and futureChar at a same time. And using three for comprehension is too dirty. So, how and I solve this with Cartesian Product? It’s very simple.

for {
  long <- futureLong()
  (int, char) <- (futureInt(long) |@| futureChar(long)).tupled
} yield (int, char)

Very simple right? You can test whether this expression really operates at the same time.

In this test, the first test occurs TimeoutException and second and third pass test well. Then, we can make a conclusion that, last expression also run at the same time.

Writer Monad in cats

I already wrote a post about reader monad and It’s time to write about Writer Monad. First, I thought that Writer Monad is opposite of Reader Monad. But it’s quite different from Reader Monad. Let’s say that Writer Monad is…

Writer Monad is stack something while operating.

Hm… I think it’s not a very well summarized sentence. If any reader has nicer summarized one, comment me. Below example is from mastering advanced Scala.


type Writer id defined in cats like this.

type Writer[L, V] = WriterT[Id, L, V]

As you can see, Writer Monad accept type L & V. type L is a type which stacks something. and V is a result(return) value. Id position in WirterT is something wraps the result. Here is Id so, never mind.

You can simply use Writer Monad like.


def greetW(name: String, logged: Boolean): Writer[List[String], String] =
  Writer(List("Compose a greeting"), {
    val userName = if(logged) name else "User"
    s"Hello $userName"

def isLoggedW(name: String): Writer[List[String], Boolean] =
  Writer(List("Checking if user is logged in"), name.length == 3)

import cats.instances.list._

val name = "Joe"

val resultW: Writer[List[String], String] = for {
  logged <- isLoggedW(name)
  greeting <- greetW(name, logged)
} yield greeting
val (log, result) =

// log: List[String] = List(Checking if user is logged in, Compose a greeting)
//result: String = Hello Joe

Yes. It’s very simple. It just stacks some strings in L(List[String]) and returns value in V(String). I think it’s very useful.

How is it works?

Of course, you can have curious that how’s is it works? As you can see in ‘for comprehension’, there is nowhere to pass List[String]. But after finishing for comprehension, it splits out log: List[String] and result: String.

Let’s remind this.

For comprehension is syntactic sugar of flatMap.

You can also write like this.

val flatMapResult: Writer[List[String], String] =
  isLoggedW(name).flatMap(logged => greetW(name, logged))

It’s the same result of for comprehension statements.

Ok. It’s flatMap. Then, Let’s deep dive to WriterT.flatMap

final case class WriterT[F[_], L, V](run: F[(L, V)]) {
  def flatMap[U](f: V => WriterT[F, L, U])(implicit flatMapF: FlatMap[F], semigroupL: Semigroup[L]): WriterT[F, L, U] =
    WriterT {
      flatMapF.flatMap(run) { lv => { lv2 =>
          (semigroupL.combine(lv._1, lv2._1), lv2._2)

In this code, never mind another but line:7. In Line 7, they combine two List[String]. Stacking is occurred in here. WriterT is different from others. value run’s type is F[(L, V)] and it does flatMap with it. So we can stack List[String]

WriterT Example

WriterT is Monad Transformer of Writer. So, you can use like this.

import cats.instances.future._
import scala.concurrent.Future

def greetWFuture(name: String, logged: Boolean): WriterT[Future, List[String], String] =
  WriterT(Future(List("Compose a greeting"), {
    val userName = if(logged) name else "User"
    s"Hello $userName"

def isLoggedWFuture(name: String): WriterT[Future, List[String], Boolean] =
  WriterT(Future(List("Checking if user is logged in"), name.length == 3))

val resultWFuture: WriterT[Future, List[String], String] = for {
  logged <- isLoggedWFuture(name)
  greeting <- greetWFuture(name, logged)
} yield greeting

val futureResult: Future[(List[String], String)] =

import scala.concurrent.Await
import scala.concurrent.duration._

val (logAwait, resultAwait) = Await.result(futureResult, 2 second)

It’s very simple. We can use Writer Monad inside another Monad.

Reader Monad in cats

After studying Monad, I also curious about Reader Monad and Writer Monad. So, I write a post about it. In fact, first, I suppose to write a Reader Monad and Writer Monad at the same post, but later I decided to write separately.

Below example is from mastering advanced Scala

What is Reader Monad

At first, I thought Reader Monad is used to read something. It’s true. But another definition is effective.

Reader Monad is used to Dependency Injection.

Yes. I think it’s a better definition. Reader Monad object is like this.

object Reader {
  def apply[A, B](f: A => B): Reader[A, B] = ReaderT[Id, A, B](f)

Anonymous function f is the function we want to run. And ‘A’ will be injected later when we call like this.

ATypeInstance is an instance which type is A. And as you can see, is passed when you call run function.


First, Let’s suppose some Service like this.

trait AuthService {
  def isLogged(name: String): Boolean

class AuthServiceChar3 extends AuthService{
  override def isLogged(name: String): Boolean = name.length == 3

class AuthServiceChar5 extends AuthService{
  override def isLogged(name: String): Boolean = name.length == 5

trait UserService {
  def greet(name: String, isLogged: Boolean): String

class UserServiceDefaultUser extends UserService{
  override def greet(name: String, isLogged: Boolean): String = {
    val actualName = if(isLogged) name else "User"

    s"Hello $actualName"

class UserServiceNoDefault extends UserService{
  override def greet(name: String, isLogged: Boolean): String = {
    if(isLogged) s"Hello $name" else "No authorization"

case class Environment(userName: String, userService: UserService, authService: AuthService)

AuthService has a simple auth logic and actualized class is AuthServiceChar3 and AuthServiceChar5. And UserSertivce has a simple greet logic and actualized class is UserServiceDefaultUser and UserServiceNoDefault.

And Environment is case class which needs a user name, UserService, and AuthService. And here are some Reader Monad use environment and return something.


def isLoggedUser: Reader[Environment, Boolean] = Reader[Environment, Boolean] { env =>

def greetUser(logged: Boolean): Reader[Environment, String] = Reader[Environment, String] { env =>
  env.userService.greet(env.userName, logged)
// In Intellij if you use auto complete, Kleisli[Id, Environment, String] will be written. I will write post later
val resultR: Reader[Environment, String] = for {
  logged <- isLoggedUser
  greeting <- greetUser(logged)
} yield greeting

Value resultR is a Reader Monad get logged value from isLoggedUser and return greet String.

In here yet, we didn’t pass Environment instance. Now, let’s pass Environment.

val environment1 = Environment("Joe", new UserServiceDefaultUser, new AuthServiceChar3)

println(  // print Hello Joe

val environment2 = Environment("Joe", new UserServiceNoDefault, new AuthServiceChar5)

println(  // print No authorization

As you can see, we inject environment when we call run function. And when we inject different instance, print different output.

Pattern Matching & unapply & apply

In Scala, we use pattern matching very often. It’s made by unapply. But because we use this by making case class, I always forget how to make it. I write this post to remind me. All example uploaded in below(gist).

How to make apply & unapply

Normal Pattern Matching

Let’s say that there is a class defined like this.

class Person(val name: String, val age: Int, val weight: Int)

And we can write apply by making companion object.

object Person {
  def apply(name: String, age: Int, weight: Int): Person = new Person(name, age, weight)

We can also write unapply in companion object like this.

object Person {
  def apply(name: String, age: Int, weight: Int): Person = new Person(name, age, weight)

  def unapply(arg: Person): Option[(String, Int, Int)] =
    if(arg.age > 20) Some(, arg.age, arg.weight)
    else None

Unapply return Option Tuple. After the operation, if it returns Some, it matches to case class. If it returns None, it does not match. We can use it like this.

val young: Person = Person("Martin Junior", 14, 50)
val old: Person = Person("Martin", 29, 70)

def PatternMatching(person: Person): Unit = person match {
  case Person(name, age, weight) => println(s"name: $name, age: $age, weight: $weight")
  case _ => println(s"${} is under 20")

In apply, If age is under 20 it returns None so, young is not matched. And old is matched. Yes! it’s simple! But I have additional Curious.

How about pattern matching partial?

What if I don’t want to expose weight in pattern matching? It’s simple!

class SecretPerson(val name: String, val age: Int, val weight: Int)

object SecretPerson {
  def apply(name: String, age: Int, weight: Int): SecretPerson = new SecretPerson(name, age, weight)

  def unapply(arg: SecretPerson): Option[(String, Int)] =
  if(arg.age >= 20) Some(, arg.age)
  else None

def PatternMatchingSecret(secretPerson: SecretPerson): Unit = secretPerson match {
  case SecretPerson(name, age) => println(s"name: $name, age: $age")
  case _ => println(s"${} is under 20")

val secretYoung: SecretPerson = SecretPerson("Martin Junior", 14, 50)
val secretOld: SecretPerson = SecretPerson("Martin", 29, 70)


Just return Option Tuple without weight. It is possible!

Case class unapply overriding

How about case class? It already has pre-defined unapply. What if I also want to hide weight this time? Let’s do it!

case class CasePerson(name: String, age: Int, weight: Int)
object CasePerson {
//  Compile Error - unapply is defined twice
//  def unapply(arg: CasePerson): Option[(String, Int)] =
//    if(arg.age >= 20) Some(, arg.age)
//    else None

val caseYoung: CasePerson = CasePerson("Martin Junior", 14, 50)
val caseOld: CasePerson = CasePerson("Martin", 29, 70)

def PatternMatchingCase(casePerson: CasePerson): Unit = casePerson match {
//   case CasePerson(name, age) => println(s"name: $name, age: $age") compile error: wrong number of arguments
  case CasePerson(name, age, weight) => println(s"name: $name, age: $age, weight: $weight")
  case _ => println(s"${} is under 20")

It’s impossible. We can get compile error in override ‘unapply is defined twice’. And also in case matching part ‘wrong number of arguments’.

Covariant and Contravariant in Scala

Scala often uses type parameter and also, you can see [+A] or [-A] in many library codes. I also wonder what it is. So, I study this and discuss with my co-worker. And leave this post to understand me. (But also, any comments are always welcome!)

Special Thanks for Karellen in Kakao.

What is Covariant, Contravariant and Invariant?

In Scala School Co, Contra, In -variant is described like this.

Variance is  about “if A <: B ( A is a subtype of B), how is the relation between M[A] and M[B]?”

if A <: B… then,

Meaning Scala notation
covariant M[A] <: M[B] [+B]
contravariant M[B] <: M[A] [-B]
invariant M[B] and M[A] are not related [B]

This means for example, in Java

As you can see above,

List<Object> objects = listStr

cannot be compiled.

Because in Java List<Object> is not considered as a parent of List<String>.

But, in Scala,

It can be compiled. Because in Scala, List[Any] is considered as a parent of  List[String]. In Scala source code, List is set as covariant.

Liskov Substitution Principle

It is very natural and simple. If A <: B, we can assign Typ A variable to Type B variable.

val a: A = new A

val b: B = a

also, List[+A] can be adapted, becase List is covariant.

val a: List[A] = List[A].empty

val b: List[B] = a

Variance in class

Guess, that I want to make my own List, and class like this.

class MyList[+A] {
    def insert(element: A): A = ??? // compile error

compile error message is

Error: covariant type A occurs in contravariant position in type A of value element
def insert(element: A): A = ???

Why does that happen? Simply thinking, I make a List of type A and subtype of A can be considered as a subtype of MyList[A]. Below topic explain of this.

Rethinking of + and –

In Scala, ‘+’ means Covariant and ‘-‘ means Contravariant. Let`s forget about it. And redefine ‘+’ as ‘Can receive subtype’ and ‘-‘ as ‘Can receive Supertype’. And then, above error can be described.

As defined in Liskov principle, In element, we can assign super type of A. But, +A is covariant. So, element can be only assigned subtype. So, this is contradiction.

So, if we correct the code like this, It can be compiled.

class MyList[+A] {
    def insert[B >: A](element: B): A = ???

By the way, how about return type as A. Is this ok? Of course yes. Let`s say that C <: A

And after long, long operation, the return type is decided as C. And as Liskov law, type C can be assigned to type A.(val c: C = A)

Variance in Function

In conclusion(as you can see above), Parameter is Contravariant(-A) and return type is Covariant. Also, in Scala, Function signature is

trait Function1[-T1, +R]

Yes, it`s simplified.

The subtype of Functions

In Scala course in coursera, there is a interesting problem. (It`s motivation of this post)

There are types like this.

NoneEmpty <: IntSet

type A = IntSet => NoneEmpty

type B = NoneEmpty => IntSet

What is the relationship between A and B?

  • A <: B
  • A >: B

The answer is A <: B. Why? As Liskov Principle, A can be assigned as B. It does not feel the impact to me. So, Let`s say that

if A <: B, A can pretend as B

Yes, String can pretend as Object. And above, NoneEmpty can pretend as IntSet.

Ok, then type A (IntSet => NoneEmpty) can pretend as type B(NoneEmpty => IntSet)? Of course!

If User passes NoneEmpty to A, It can be assigned to IntSet. And after an operation, A return NoneEmpty. And NoneEmpty can be assigned to IntSet.


A can pretend as B and A <: B