Hello folks,
I promised you in How to live in a pure world I would have written a full article showing an example of how to deal with IO functionally and here it is!

I will use Kotlin and its functional companion library: Arrow.

A brief history of Arrow

Arrow was born as a merge of two functional libraries in the Kotlin universe: FunKtionale and Kategory. The contributors of the two libraries decided to join forces and so Arrow was born.

Like other libraries in other programming languages (like ScalaZ and Cats in Scala), Arrow tried to provide the same concepts of typed functional programming that were born in the Haskell universe: so they started out defining some core data types (Option, Try, Either, Validated, etc.) and a bunch of typeclasses like Functor, Semigroup, Monoid, Monad, and the likes (much more to be true).

The current version of Arrow is 0.11.0-SNAPSHOT. Arrow 0.11.0 should be released by September 2020, and the first major release should come out by the end of the year, even if it will not be marked as 1.0 but as 1.4, following the Kotlin compiler version (because of Arrow Meta).

What the team is working on to target the first stable release is to simplify and stabilize the api.

For example, they have already deprecated and they are going to remove the Try<A> data type, because it favors an eager evaluation of code that can have side effects, in favor of Either<E, A>. If you think about it you could say that:

typealias Try<A> = Either<Throwable, A> 

and the non-eager evaluation is granted by the fact that, aside for right/left value constructors, the function Either.catch() you use to wrap throwing blocks accepts only a suspended block (more on this later).

The same kind of simplification occurred also for Option<A>. There were some questions in the Kotlin community towards the actual need for such a data type, given the Kotlin language features nullable types. So Arrow maintainers have decided to ditch the Option data type in favor of nullable types or, once again, Eithers, providing also easy means to go from nullable types to Eithers. Example:

val a: A? = null 
val b: Either<Unit, A> = Either.fromNullable(a)
// and if you like you can define  
typealias Option<A> = Either<Unit, A> 

Monads

Before addressing the title question about whether or not IO should be modeled as a Monad, let's talk a bit about monads.

What is a Monad?

Last time I haven't spent much time on the subject because I wanted to focus more on the reason why IO operations were intrinsically impure

So, without further ado, here is maybe the most concise definition you could find about what a Monad is:

A monad is a monoid in the category of endofunctors.

The problem is this definition requires you to know what is a monoid, a category, and an endofunctor.

I'll try to provide you a short definition of all three.

Monoid

A monoid is a semigroup with a unit element, that respects the monoid laws. A semigroup is a set A with an internal operation, usually called combine, that is associative.

interface Semigroup<A> {
    fun combine(a: A, b: A): A
}

interface Monoid<A>: Semigroup<A> {
    val empty: A
}

The monoids laws are

1. associativity (because it's a semigroup): for all a,b,c in A it must be true that combine(a,combine(b,c)) = combine(combine(a,b),c)
2. left identity: for all a in A combine(empty,a) = a
3. right identity: for all a in A combine(a,empty) = a

Category

This is a bit more abstract. A category C is a pair (O, M) where

• O is a collection of objects (we are not interested in better defining them)
• M is a collection of morphisms that connects an object A in O to an object B (m: A -> B)

For C to be a category it must obey to the category laws:

1. There must exist for every A in O an identity morphism 1_A: A -> A
2. There must exist an operation, called composition, indicated by . such that for every 2 morphisms in M, f: A -> B and g: B -> C, it exists a morphism g . f: A -> C. This operation must have 2 properties
   1. associativity: for every 3 morphism in M, f: A -> B, g: B -> C and h: C -> D then it must be true that (f . g) . h = f . (g . h)
   2. identity: for every f: A -> B then 1_A . f = f . 1_B

Why are categories relevant for programmers? Well, because you can say that a programming language is a category where

• O is the collection of its types
• M are the functions
• The composition of morphism is the composition of functions.

Functor

What is a functor? It's a map between categories that preserves the category structure. To be more precise, given 2 categories C and D, F is a functor if

• for every object X in C, it maps an F(X) in D
• for every morphism f: A -> B in C it maps the morphism F(f) = F(A) -> F(B) in D
• for every X in C it maps the identity morphism in C into the identity morphism in D, i.e. F(1_xC) = 1_F(X)D
• for every two morphism in C, f and g, F(f . g) = F(f) . F(g)

An endofunctor is just a functor from a category C into C itself.

Given the previous parallelism drawn between a category and a programming language, you might be wondering: what is an endofunctor in a programming language?
Well, if you think about it, it should be something that maps its types (the objects) but also its functions (the morphisms) between the basic types (from the original category) into functions between the mapped types (in the new category, the one where all the objects have the form F<X>).

So an endofunctor F in Kc (the Kotlin types category) is a pair F = (F(X), lift) where

• F(X) is a type constructor (i.e. F(X) is a new type in Kc)

• lift is a function
  

      fun <A,B> lift(f:(A) -> B): F<A> -> F<B>
  

I guess all this might seem a bit abstract, so an example might help.

Ex.: Option<A> is a functor.

Why? Because it is a type constructor (from A to Option<A>) and it exist a lift function

    fun <A,B> lift(f:(A) -> B): Option<A> -> Option<B> = 
        { a: Option<A> -> a.map(f) }

Putting it all together

From all the definition above we can come back to a more operative definition of a monad: a monad is a type constructor with three functions

// pseudo code (to actually encode a generic monad one has to encode first the concept of higher kinded types)
interface Monad<A> {
    fun of(t: A): Monad<A> = // omitted
    fun <B> map(ma: Monad<A>, f: (A) -> B): Monad<B> = // omitted
    fun <B> flatMap(ma: Monad<A>, f: (A) -> Monad<B>): Monad<B> = // omitted
}

that obeys to the following laws

• left identity: flatMap(of(x), f) = f(x)
• right identity: flatMap(x, of) = x
• associativity: flatMap(flatMap(ma, f), g) = flatMap(mx) {x -> flatMap(f(x), g) }

Note: the actual encoding in Arrow of Monads is a bit different, the above pseudo-code was made just to give a general idea.

IO monad

IO is a monad and in Arrow is undergoing the same simplification process shown above for the core data types: more specifically it's going to be deprecated and removed from the library (this time not in favor of Either).

The reasons in this case are different.

The first one is that Kotlin has a language feature (suspended functions and coroutines) that can better express the intent of a data type like IO<A>, with native support in the language.

Secondly, if you ever try to write actual programs using IO, you will probably end up with something like IO<Either<E, A>>, that is not so ergonomic to work with.

Let's see it with an example (finally, am I right?)

data class FileName(val path: String)
data class Employee(
  val lastName: String, 
  val firstName: String, 
  val birthDate: LocalDate, 
  val emailAddress: EmailAddress
)
data class EmailAddress(val value: String)

sealed class ProgramError
data class ReadFileError(val path: String): ProgramError()
data class ParseError(val source: String): ProgramError()
data class MailSendingError(
  val emailMessage: EmailMessage
): ProgramError()

typealias Program = 
    (FileName) -> IO<Either<ProgramError, Unit>>
typealias LoadEmployees = 
    (FileName) -> IO<Either<ProgramError, List<Employee>>>
typealias EmployeeFilter = (Employee) -> Boolean
typealias SendBirthdayGreetings = 
    (Employee) -> IO<Either<ProgramError, Unit>>

fun createSendGreetingsFunction(
    loadEmployees: LoadEmployees,
    employeeBornToday: EmployeeFilter,
    sendBirthDayGreetingMail: SendBirthdayGreetings
): Program = { sourceFile: FileName ->
    EitherT(loadEmployees(sourceFile)).flatMap { employees ->
        employees
            .filter(employeeBornToday)
            .map { e -> EitherT(sendBirthDayGreetingMail(e)) }
            .sequence().map { Unit }
    }.value().fix()
}

This is a snippet of code from my take on the birthday greetings kata by Matteo Vaccari (full code here, tag io-either-version-arrow-0.10.5).

The code per se is pretty straightforward: it will load a list of employees from a csv file, filter the employees born today and then send them a birthday greeting email.

To execute the program description built using IOs one need to do something like the following at the edge of his/her world (the main function, your rest controller, etc.)

val program = sendGreetingsToAll(FileName("/fixtures/bigFile.csv"))
program.unsafeRunSync()

NOTE: one common mistake one can make is to continuously create and run IOs. That is not the way (or it is not supposed to be). You should build your entire description of what your program does and then only run it once at the end of your world (so to speak).

The following are the functions in the previous snippet of code that have a side effect and have been modeled with IO

typealias LoadEmployees = 
    (FileName) -> IO<Either<ProgramError, List<Employee>>>
typealias SendBirthdayGreetings = 
    (Employee) -> IO<Either<ProgramError, Unit>>
typealias Program = 
    (FileName) -> IO<Either<ProgramError, Unit>>

What is the issue with them?
Well, it's something related to their composition.
Given that their return type is an Either nested inside an IO, working with it becomes a little cumbersome because, even if they are both Monads (IO and Either), and monads should make it easier to sequence transformations, having two nested monads you should first map or flatMap on the external one, IO, and then on the internal one, Either.

One would have hoped to be able to write

val f: (A) -> IO<Either, B> = // omitted
val a: IO<Either<E, A>> = // whatever
val b: IO<Either<E, B>> = a.flatMap(f)

But it's not possible. You have to write something like this

val f: (A) -> IO<Either, B> = // omitted
val ioA: IO<Either<E, A>> = // whatever
val ioB: IO<Either<E, B>> = 
    ioA.flatMap { eitherA: Either<E, A> -> 
        eitherA.fold(
            { e: E -> IO.just(e.left()) }, 
            { theActualA: A -> f(theActualA) }  
        )

That's the reason why you have seen in my previous snippet that EitherT. What is it? It is a Monad Transformer and let you compose two nested monads in case the inner one is an Either; in lemon terms, it's a data type that wraps the IO<Either<E, A>> and let you regain the easiness of sequencing operations.

Let's see how that would apply in the last example

val f: (A) -> IO<Either, B> = // omitted
val ioA: IO<Either<E, A>> = // whatever
val ioB: IO<Either<E, B>> = 
    EitherT(ioA).flatMap { theActualA: A -> 
        EitherT(f(theActualA)) 
    }.value().fix()

Monad transformers solve a problem, i.e. the fact that two Monads cannot be generically composed to produce another monad; the question is: is it the right problem to solve?
We have introduced IO to re-gain purity and referential transparency but it also adds already one wrapper layer around our impure logic; if, when we are using IO in real life, we end up having an IO<Either<E, A>>, and to work with it we have to use an EitherT, adding another extra layer with both a cognitive and performance overhead, one might ask: is it worth it?

Suspended functions

The answer is: maybe no. In Arrow 0.11.0-SNAPSHOT the maintainers decided to ditch the IO monad in favour of suspended functions. What does it mean? Let's have a look at the sendBirthdayGreetings example revised

typealias LoadEmployees = 
    suspend (FileName) -> Either<ProgramError, List<Employee>>
typealias EmployeeFilter = (Employee) -> Boolean
typealias SendBirthdayGreetings = 
    suspend (Employee) -> Either<ProgramError, Unit>
typealias SendGreetings = 
    suspend (FileName) -> Either<ProgramError, Unit>

fun createSendGreetingsFunction(
    loadEmployees: LoadEmployees,
    employeeBornToday: EmployeeFilter,
    sendBirthDayGreetingMail: SendBirthdayGreetings
): SendGreetings = { sourceFile: FileName ->
    loadEmployees(sourceFile).flatMap { employees ->
        employees
            .filter(employeeBornToday)
            .map { e -> sendBirthDayGreetingMail(e) }
            .sequence().map { Unit }
    }
}

Can you spot the difference? That's right here it is

typealias LoadEmployees = 
    suspend (FileName) -> Either<ProgramError, List<Employee>>
typealias SendBirthdayGreetings = 
    suspend (Employee) -> Either<ProgramError, Unit>
typealias SendGreetings = 
    suspend (FileName) -> Either<ProgramError, Unit>

All the functions that returned an IO<Either<ProgramError, A>> in the previous version, now simply return an Either<ProgramError, A> but are marked as suspend, signaling they need a safe environment to be executed (arrow-fx-coroutines provides such an environment).

So the suspend functions take the place of functions returning IO because they are, for all intent and purposes, delayed and conveying the same concept as the IO monad: something impure is going on.

Here is how you could run the previous function at the end of your world (in my case in the acceptance test)

import arrow.fx.coroutines.Environment

Environment().unsafeRunSync {
    sendGreetingsToAll(FileName("/fixtures/bigFile.csv"))
}        

Easy, no?

Conclusion

IO: to be a Monad or not to be?

Arrow guys answer is: no, thank you. We have already a Kotlin construct that is more than enough to describe impure interactions with the external world: suspended functions.

What else? I don't know, I only hope to have given you a feel of how to use IO, monad, or not, in a real-life example.

References

• Arrow docs
• Bartosz Milewski category theory for programmers: videos, book
• Giulio Canti functional programming notes (only for those of you who speak Italian and are versed in Typescript)
• Scott Wlaschin visual explanation of the elevated world
• A nice little post explaining functors, applicatives, monoids and monads in pictures