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Version: 2.0.x

CommutativeEither

CommutativeEither[F] describes a way of combining two parameterized types F[A] and F[B] that is commutative.

Its signature is:

trait AssociativeEither[F[_]] {
  def either(fa: => F[A], fb: => F[B]): F[Either[A, B]]
}

trait CommutativeEither[F[_]] extends AssociativeEither[F]

If we import zio.prelude._ we can use the orElseEitherPar operator or its symbolic alias <|> to combine two values of a parameterized type that has a CommutativeEither instance defined for it in a commutative way.

The either operator must be commutative. So after rearranging the order of Either values the following property must hold:

fa <|> fb === fb <|> fa

This is the same as the law defined by the Commutative abstraction for concrete types, but lifted into the context of parameterized types.

The either operator runs the left value and the right value in parallel, returning the result from either the left value or the right value.

We can see this by noting that the requirement that the either operator is commutative places significant limitations on our implementation. We must choose on some basis between the left and right values but we can't run one and then if it fails run the other because that would in general not be commutative.

ZIO provides a good example of why running the left value and then running the right value if it fails is not commutative and what a commutative operator would look like.

import zio._

import java.io.IOException

val helloZIO: ZIO[Console, IOException, Either[Unit, Unit]] =
  Console.printLine("Hello").orElseEither(Console.printLine("ZIO"))
// helloZIO: ZIO[Console, IOException, Either[Unit, Unit]] = OnSuccessAndFailure(
//   trace = "repl.MdocSession.MdocApp.helloZIO(commutativeeither.md:15)",
//   first = Stateful(
//     trace = "repl.MdocSession.MdocApp.helloZIO(commutativeeither.md:15)",
//     onState = zio.FiberRef$unsafe$$anon$2$$Lambda$16469/1392082310@4746861d
//   ),
//   successK = zio.ZIO$$$Lambda$16455/131458822@28409e99,
//   failureK = zio.ZIO$$Lambda$16567/2121115595@39be44c5
// )

val zioHello: ZIO[Console, IOException, Either[Unit, Unit]] =
  Console.printLine("ZIO").orElseEither(Console.printLine("Hello"))
// zioHello: ZIO[Console, IOException, Either[Unit, Unit]] = OnSuccessAndFailure(
//   trace = "repl.MdocSession.MdocApp.zioHello(commutativeeither.md:19)",
//   first = Stateful(
//     trace = "repl.MdocSession.MdocApp.zioHello(commutativeeither.md:19)",
//     onState = zio.FiberRef$unsafe$$anon$2$$Lambda$16469/1392082310@6b2152f8
//   ),
//   successK = zio.ZIO$$$Lambda$16455/131458822@28409e99,
//   failureK = zio.ZIO$$Lambda$16567/2121115595@18a447ef
// )

If the orElseEither operator was commutative then these two programs should be the same. But they obviously are not.

The first program will print Hello to the console on one line but never print ZIO. Since the left ZIO workflow was successful the right ZIO workflow will never be run.

Similarly the second program will print ZIO to the console on one line but will never print Hello.

We have to return either of the values but the order can't matter. The raceEither operator on ZIO does just that.

It runs both effects concurrently, returning the first one to complete successfully and safely interrupting the other. With it we can make our example above satisfy the commutative law.

import zio._

import java.io.IOException

val helloZIO: ZIO[Console, IOException, Either[Unit, Unit]] =
  Console.printLine("Hello").raceEither(Console.printLine("ZIO"))
// helloZIO: ZIO[Console, IOException, Either[Unit, Unit]] = Stateful(
//   trace = "repl.MdocSession.MdocApp.<local MdocApp>.helloZIO(commutativeeither.md:33)",
//   onState = zio.ZIO$$$Lambda$16572/510475751@343cb634
// )

val zioHello: ZIO[Console, IOException, Either[Unit, Unit]] =
  Console.printLine("ZIO").raceEither(Console.printLine("Hello"))
// zioHello: ZIO[Console, IOException, Either[Unit, Unit]] = Stateful(
//   trace = "repl.MdocSession.MdocApp.<local MdocApp>.zioHello(commutativeeither.md:37)",
//   onState = zio.ZIO$$$Lambda$16572/510475751@7f6f541a
// )

Now both ZIO workflows will begin execution at the same time.

For an individual execution of this workflow either Hello or ZIO may be printed to the console, or possibly both if the loser is not interrupted before it runs. But both the left and right workflows have an equal opportunity to be run and we can say that both helloZIO and zioHello describe the same program.

We can also see this interpretation of orElseEitherPar in terms of racing in its implementation for ZStream.

import zio.stream._

def orElseEitherPar[R, E, A, B](left: => ZStream[R, E, A], right: => ZStream[R, E, B]): ZStream[R, E, Either[A, B]] =
  left.mergeEither(right)

We still run both streams concurrently but now instead of cancelling the loser we just emit elements from either stream whenever they are available. This is commutative because whatever order we merge the streams they will still be evaluated concurrently.

The difference in the implementations here reflects the fact that a ZIO always succeeds with exactly one value, whereas a ZStream can succeed with zero or more values.

So in the case of ZIO if one fiber completes execution successfully first we have nothing to do with the value from the other and so just interrupt it. In contrast, a ZStream can succeed with multiple values so we can just emit the values from either stream as they are available.

In many cases the implementation of the orElseEitherPar will involve actual concurrency but it does not need to.

To see this, consider the following instance of the CommutativeEither abstraction for Set.

import zio.prelude._

implicit val SetCommutativeEither: CommutativeEither[Set] =
  new CommutativeEither[Set] {
    def either[A, B](left: => Set[A], right: => Set[B]): Set[Either[A, B]] =
      left.map(Left(_)) ++ right.map(Right(_))
  }
// SetCommutativeEither: CommutativeEither[Set] = repl.MdocSession$MdocApp$$anon$1@1eb87f9d

In this case there is no actual concurrency going on but we are combining the left Set and right Set, wrapping their values in Left and Right respectively.

This is like the interpretation of orElseEither as concatenating two collections except normally concatenation would not be commutative since order matters. In the case of a Set the order of elements doesn't matter.

We can think of this as running each Set to get its elements until it fails by being empty.

As with the other operators for describing ways of combining parameterized types, we can also define CommutativeEither instances for data types that are contravariant or invariant. These also often do not require any actual concurrency because the logical parallelism is handled by running either the left value or the right value depending on the input.

For example, here is the instance of CommutativeEither for the Predicate data type.

trait Predicate[-A] {
  def run(a: A): Boolean
}

object Predicate {
  implicit val PredicateCommutativeEither: CommutativeEither[Predicate] =
    new CommutativeEither[Predicate] {
      def either[A, B](left: => Predicate[A], right: => Predicate[B]): Predicate[Either[A, B]] =
        new Predicate[Either[A, B]] {
          def run(either: Either[A, B]): Boolean =
            either match {
              case Left(a) => left.run(a)
              case Right(b) => right.run(b)
            }
        }
    }
}

It is commutative because no matter what order we combine the two predices, we will always send A values to the predicate that can handle A values and B values to the predicate that can handle B values. If we did something different with the A and B values other than just sending them to the predicate based on whether they were a Left or a Right then we would be at risk of violating the laws.

When a data type for which a CommutativeEither instance is defined is also covariant we can use the orElsePar operator as well.

def orElsePar[F[+_]: CommutativeEither : Covariant, A](left: => F[A], right: => F[A]): F[A] =
  left.orElseEitherPar(right).map(_.merge)

The orElsePar operator just maps over the output of the orElseEitherPar operator and merges the Either values when both the left and right values are parameterized on the same types.

This is quite useful and typically has more domain specific names. For example this is the race operator on ZIO and the merge operator on ZStream. We can think of this as just like orElseEither but eliminating the Either when the types that the left and right values are parameterized on are the same.

There is also an additional operator we can use for contravariant types called eitherWithPar.

def orElseEitherWithPar[F[-_]: CommutativeEither : Contravariant, A, B, C](
  left: => F[A],
  right: => F[B]
)(f: C => Either[A, B]): F[C] =
  left.orElseEitherPar(right).contramap(f)

This is like the orElseEitherWith defined on data types that have an AssociativeEither and Contravariant instance except it guarantees that the F[A] and F[B] values will be combined in a way that is commutative in addition to being associative.

The CommutativeEither functional abstraction, along with the CommutativeBoth abstraction, describe the two fundamental ways of combining values in parallel. We can either run both values and return both their results, as in the zipPar operator on ZIO, or we can run both values and return either of their results, as in the raceEither operator on ZIO.

As with some of the other functional abstractions for parameterized types, CommutativeEither tends to be most useful when you are defining your own parameterized types or writing generic code. If you are working with existing data types like ZIO or ZStream the operators described by this abstraction tend to already be available to you with more domain specific names.

If you are defining your own data type then exploring whether there is a way to run both values in parallel to produce either result can be a useful exercise.

If your data type describes some kind of effect then there is often a very obvious interpretation in terms of concurrency. If not it may require more thought.

Defining a CommutativeEither instance, if it exists, is a good practice to allow you to use other operators in ZIO Prelude that are defined for data types with CommutativeEither instances. It will also allow you to test that your implementation satisfies the expected laws, which can be tricky with some of these more complex types.

Finally, if you are writing generic code the CommutativeBoth and CommutativeEither abstractions describe the fundamental binary operators for combining values in parallel. So if you want to describe parallel or concurrent operators in a generic way you will definitely want to use these abstractions.