## 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 adit.io 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 => bOpt.map(b => 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)
ints.map(getSome)
// 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._

Traverse[List].traverse(ints)(getSome)

// 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

Traverse[List].traverse(ints)(getSomeOrNone)

// res5: Option[List[Int]] = None

```

 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) aOpt.flatMap(a => bOpt.map(b => add(a, b))) import cats.instances.option._ import cats.Applicative Applicative[Option].map2(aOpt, bOpt)(add) import cats.syntax.all._ (aOpt |@| bOpt).map(add) val ints = List(1,2,3,4,5) ints.map(getSome) import cats.Traverse import cats.instances.list._ import cats.instances.option._ Traverse[List].traverse(ints)(getSome) def getSomeOrNone(a: Int): Option[Int] = if(a % 2 == 0) Some(a) else None Traverse[List].traverse(ints)(getSomeOrNone)

## 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.

 package org.example.ktz.blog import cats.syntax.all._ import cats.instances.future._ import org.scalatest._ import scala.concurrent.ExecutionContext.Implicits.global import scala.concurrent.duration._ import scala.concurrent.{Await, Future} class CartesianProductTest extends FlatSpec with Matchers { def futureLong(): Future[Long] = Future { Thread.sleep(2000) println("Future Long Done!") 2 } def futureInt(long: Long): Future[Int] = Future{ Thread.sleep(2000) println("Future Int Done!") long.toInt } def futureChar(long: Long): Future[Char] = Future{ Thread.sleep(2000) println("Future Char Done!") long.toChar } "Concurrent" should "for comprehension" in { val forComp: (Int, Char) = Await.result(for { long <- futureLong() int <- futureInt(long) char <- futureChar(long) } yield (int, char), 5 second) // java.util.concurrent.TimeoutException: Futures timed out after [5 seconds] } "Concurrent" should "for comprehension2" in { 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) // Work well 🙂 } "Concurrent" should "cartesian" in { val cartesion: (Int, Char) = Await.result(for { long <- futureLong() (int, char) <- (futureInt(long) |@| futureChar(long)).tupled } yield (int, char), 5 second) // Work well 🙂 } }

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.

### Example

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.

```import cats.data.Writer

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) = resultW.run

// 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 =>
flatMapF.map(f(lv._2).run) { 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.data.WriterT
import cats.instances.future._
import scala.concurrent.Future
import scala.concurrent.ExecutionContext.Implicits.global

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)] = resultWFuture.run

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.

 import cats.data.Writer 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) = resultW.run val flatMapResult: Writer[List[String], String] = isLoggedW(name).flatMap(logged => greetW(name, logged)) import cats.data.WriterT import cats.instances.future._ import scala.concurrent.Future import scala.concurrent.ExecutionContext.Implicits.global 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)] = resultWFuture.run import scala.concurrent.Await import scala.concurrent.duration._ val (logAwait, resultAwait) = Await.result(futureResult, 2 second)
view raw WriterExample.sc hosted with ❤ by GitHub

## 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.

```
readerMoandValue.run(ATypeInstance)

```

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

### Example

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.

```import cats.data.Reader

def isLoggedUser: Reader[Environment, Boolean] = Reader[Environment, Boolean] { env =>
env.authService.isLogged(env.userName)
}

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(resultR.run(environment1))  // print Hello Joe

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

println(resultR.run(environment2))  // print No authorization

```

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

 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) import cats.data.Reader def isLoggedUser: Reader[Environment, Boolean] = Reader[Environment, Boolean] { env => env.authService.isLogged(env.userName) } 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 val environment1 = Environment("Joe", new UserServiceDefaultUser, new AuthServiceChar3) println(resultR.run(environment1)) val environment2 = Environment("Joe", new UserServiceNoDefault, new AuthServiceChar5) println(resultR.run(environment2))
view raw ReaderExample.sc hosted with ❤ by GitHub

## 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

 package org.ktz.example.blog; import java.util.ArrayList; import java.util.List; public class Variance { public static void main(String[] args) { String str = ""; Object obj = str; List listStr = new ArrayList<>(); // List
view raw Variance.java hosted with ❤ by GitHub

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,

 val obj: Object = "Hello World!" val listString: List[String] = List.empty val listAny: List[Any] = listString
view raw Variance.scala hosted with ❤ by GitHub

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.

 type List[+A] = scala.collection.immutable.List[A]
view raw ScalaList.scala hosted with ❤ by GitHub

### 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