Is Future in Scala a monad?

Why and how specifically is a Scala Future not a Monad; and would someone please compare it to something that is a Monad, like an Option?

The reason I'm asking is Daniel Westheide's The Neophyte's Guide to Scala Part 8: Welcome to the Future where I asked whether or not a Scala Future was a Monad, and the author responded that it wasn't, which threw off base. I came here to ask for a clarification.

A summary first

Futures can be considered monads if you never construct them with effectful blocks (pure, in-memory computation), or if any effects generated are not considered as part of semantic equivalence (like logging messages). However, this isn't how most people use them in practice. For most people using effectful Futures (which includes most uses of Akka and various web frameworks), they simply aren't monads.

Fortunately, a library called Scalaz provides an abstraction called Task that doesn't have any problems with or without effects.

A monad definition

Let's review briefly what a monad is. A monad must be able to define at least these two functions:

def unit[A](block: => A)
    : Future[A]

def bind[A, B](fa: Future[A])(f: A => Future[B])
    : Future[B]

And these functions must statisfy three laws:

• Left identity: bind(unit(a))(f) ≡ f(a)
• Right identity: bind(m) { unit(_) } ≡ m
• Associativity: bind(bind(m)(f))(g) ≡ bind(m) { x => bind(f(x))(g) }

These laws must hold for all possible values by definition of a monad. If they don't, then we simply don't have a monad.

There are other ways to define a monad that are more or less the same. This one is popular.

Effects lead to non-values

Almost every usage of Future that I've seen uses it for asychronous effects, input/output with an external system like a web service or a database. When we do this, a Future isn't even a value, and mathematical terms like monads only describe values.

This problem arises because Futures execute immediately upon data contruction. This messes up the ability to substitute expressions with their evaluated values (which some people call "referential transparency"). This is one way to understand why Scala's Futures are inadequate for functional programming with effects.

Here's an illustration of the problem. If we have two effects:

import scala.concurrent.Future
import scala.concurrent.ExecutionContext.Implicits._


def twoEffects =
  ( Future { println("hello") },
    Future { println("hello") } )

we will have two printings of "hello" upon calling twoEffects:

scala> twoEffects
hello
hello

scala> twoEffects
hello
hello

But if Futures were values, we should be able to factor out the common expression:

lazy val anEffect = Future { println("hello") }

def twoEffects = (anEffect, anEffect)

But this doesn't give us the same effect:

scala> twoEffects
hello

scala> twoEffects

The first call to twoEffects runs the effect and caches the result, so the effect isn't run the second time we call twoEffects.

With Futures, we end up having to think about the evaluation policy of the language. For instance, in the example above, the fact I use a lazy value rather than a strict one makes a difference in the operational semantics. This is exactly the kind of twisted reasoning functional programming is designed to avoid -- and it does it by programming with values.

Without substitution, laws break

In the presense of effects, monad laws break. Superficially, the laws appear to hold for simple cases, but the moment we begin to substitute expressions with their evaluated values, we end up with the same problems we illustrated above. We simply can't talk about mathematical concepts like monads when we don't have values in the first place.

To put it bluntly, if you use effects with your Futures, saying they're monads is not even wrong because they aren't even values.

To see how monad laws break, just factor out your effectful Future:

import scala.concurrent.Future
import scala.concurrent.ExecutionContext.Implicits._


def unit[A]
    (block: => A)
    : Future[A] =
  Future(block)

def bind[A, B]
    (fa: Future[A])
    (f: A => Future[B])
    : Future[B] =
  fa flatMap f

lazy val effect = Future { println("hello") }

Again, it will only run one time, but you need it to run twice -- once for the right-hand side of the law, and another for the left. I'll illustrate the problem for the right identity law:

scala> effect  // RHS has effect
hello

scala> bind(effect) { unit(_) }  // LHS doesn't

The implicit ExecutionContext

Without putting an ExecutionContext in implicit scope, we can't define either unit or bind in our monad. This is because the Scala API for Futures has these signature:

object Future {
  // what we need to define unit
  def apply[T]
      (body: ⇒ T)
      (implicit executor: ExecutionContext)
      : Future[T]
}

trait Future {
   // what we need to define bind
   flatMap[S]
       (f: T ⇒ Future[S])
       (implicit executor: ExecutionContext)
       : Future[S]
}

As a "convenience" to the user, the standard library encourages users to define an execution context in implicit scope, but I think this is a huge hole in the API that just leads to defects. One scope of the computation may have one execution context defined while another scope can have another context defined.

Perhaps you can ignore the problem if you define an instance of unit and bind that pins both operations to a single context and use this instance consistently. But this is not what people do most of the time. Most of the time, people use Futures with for-yield comprehensions that become map and flatMap calls. To make for-yield comprehensions work, an execution context must be defined at some non-global implicit scope (because for-yield doesn't provide a way to specify additional parameters to the map and flatMap calls).

To be clear, Scala lets you use lots of things with for-yield comprehensions that aren't actually monads, so don't believe that you have a monad just because it works with for-yield syntax.

A better way

There's a nice library for Scala called Scalaz that has an abstraction called scalaz.concurrent.Task. This abstraction doesn't run effects upon data construction as the standard library Future does. Furthermore, Task actually is a monad. We compose Task monadically (we can use for-yield comprehensions if we like), and no effects run while we're composing. We have our final program when we have composed a single expression evaluating to Task[Unit]. This ends up being our equivalent of a "main" function, and we can finally run it.

Here's an example illustrating how we can substitute Task expressions with their respective evaluated values:

import scalaz.concurrent.Task
import scalaz.IList
import scalaz.syntax.traverse._


def twoEffects =
  IList(
    Task delay { println("hello") },
    Task delay { println("hello") }).sequence_

We will have two printings of "hello" upon calling twoEffects:

scala> twoEffects.run
hello
hello

And if we factor out the common effect,

lazy val anEffect = Task delay { println("hello") }

def twoEffects =
  IList(anEffect, anEffect).sequence_

we get what we'd expect:

scala> twoEffects.run
hello
hello

In fact, it doesn't really matter that whether we use a lazy value or a strict value with Task; we get hello printed out twice either way.

If you want to functionally program, consider using Task everywhere you may use Futures. If an API forces Futures upon you, you can convert the Future to a Task:

import concurrent.
  { ExecutionContext, Future, Promise }
import util.Try
import scalaz.\/
import scalaz.concurrent.Task


def fromScalaDeferred[A]
    (future: => Future[A])
    (ec: ExecutionContext)
    : Task[A] =
  Task
    .delay { unsafeFromScala(future)(ec) }
    .flatMap(identity)

def unsafeToScala[A]
    (task: Task[A])
    : Future[A] = {
  val p = Promise[A]
  task.runAsync { res =>
    res.fold(p failure _, p success _)
  }
  p.future
}

private def unsafeFromScala[A]
    (future: Future[A])
    (ec: ExecutionContext)
    : Task[A] =
  Task.async(
    handlerConversion
      .andThen { future.onComplete(_)(ec) })

private def handlerConversion[A]
    : ((Throwable \/ A) => Unit)
      => Try[A]
      => Unit =
  callback =>
    { t: Try[A] => \/ fromTryCatch t.get }
      .andThen(callback)

The "unsafe" functions run the Task, exposing any internal effects as side-effects. So try not to call any of these "unsafe" functions until you've composed one giant Task for your entire program.

I believe a Future is a Monad, with the following definitions:

def unit[A](x: A): Future[A] = Future.successful(x)

def bind[A, B](m: Future[A])(fun: A => Future[B]): Future[B] = fut.flatMap(fun)

Considering the three laws:

1. Left identity:

   Future.successful(a).flatMap(f) is equivalent to f(a). Check.

2. Right identity:

   m.flatMap(Future.successful _) is equivalent to m (minus some possible performance implications). Check.

3. Associativity m.flatMap(f).flatMap(g) is equivalent to m.flatMap(x => f(x).flatMap(g)). Check.

Rebuttal to "Without substitution, laws break"

The meaning of equivalent in the monad laws, as I understand it, is you could replace one side of the expression with the other side in your code without changing the behavior of the program. Assuming you always use the same execution context, I think that is the case. In the example @sukant gave, it would have had the same issue if it had used Option instead of Future. I don't think the fact that the futures are evaluated eagerly is relevant.

As the other commenters have suggested, you are mistaken. Scala's Future type has the monadic properties:

import scala.concurrent.Future
import scala.concurrent.ExecutionContext.Implicits._

def unit[A](block: => A): Future[A] = Future(block)
def bind[A, B](fut: Future[A])(fun: A => Future[B]): Future[B] = fut.flatMap(fun)

This is why you can use for-comprehension syntax with futures in Scala.