Bifunctor

Bifunctor takes two type parameters instead of one, and is a functor in both of these parameters. It defines a function bimap, which allows for mapping over both arguments at the same time. Its signature is as follows:

def bimap[A, B, C, D](fab: F[A, B])(f: A => C, g: B => D): F[C, D]

Either as a Bifunctor

Probably the most widely used Bifunctor instance is the Either data type.

Say you have a value that is either an error or a ZonedDateTime instance. You also want to react to both possibilities - if there was a failure, you want to convert it to your own DomainError, and if the result was a success, you want to convert it to an UNIX timestamp.

import cats._
import cats.implicits._
import java.time._

case class DomainError(message: String)

def dateTimeFromUser: Either[Throwable, ZonedDateTime] = 
  Right(ZonedDateTime.now())  // Example definition
dateTimeFromUser.bimap(
  error => DomainError(error.getMessage),
  dateTime => dateTime.toEpochSecond
)
// res0: Either[DomainError, Long] = Right(value = 1663770320L)

Bifunctor also defines a convenience function called leftMap, which is defined as follows:

def leftMap[A, B, C](fab: F[A, B])(f: A => C): F[C, B] = bimap(fab)(f, identity)

There is no rightMap however - use map instead. The reasoning behind this is that in Cats, the instances of Bifunctor are also mostly instances of Functor, as it is the case with Either.

Tuple2 as a Bifunctor

Another very popular Bifunctor is that for the Tuple2 data type, or (A, B) for types A and B.

Let's say we have a list of balances and want divide them by the number of months in the lifetime of the account holder. The balances are given in cents. A bit contrived, but we want an average contribution per month to the given account. We want the result in dollars per month. The lifetime is given in the number of years the account has been active.

val records: List[(Int, Int)] = List((450000, 3), (770000, 4), (990000, 2), (2100, 4), (43300, 3))
// records: List[(Int, Int)] = List(
//   (450000, 3),
//   (770000, 4),
//   (990000, 2),
//   (2100, 4),
//   (43300, 3)
// )

def calculateContributionPerMonth(balance: Int, lifetime: Int) = balance / lifetime

val result: List[Int] =
  records.map(
      record => record.bimap(
        cents => cents / 100,
        years => 12 * years
      )
    ).map((calculateContributionPerMonth _).tupled)
// result: List[Int] = List(125, 160, 412, 0, 12)

As you can see, this instance makes it convenient to process two related pieces of data in independent ways, especially when there is no state relationship between the two until processing is complete.

Note that, just as with the bifunctor for Either, we do not have a rightMap function since the relevant instances of Bifunctor induce a Functor in the second argument, so we just use map.