ArrowChoice yields Arrows with choice, allowing distribution over coproducts.

Given two Fs (f and g), create a new F with domain the coproduct of the domains of f and g, and codomain the coproduct of the codomains of f and g. This is the sum notion to split's product.

Example:

scala> import cats.implicits._
scala> val toLong: Int => Long = _.toLong
scala> val toDouble: Float => Double = _.toDouble
scala> val f: Either[Int, Float] => Either[Long, Double] = toLong +++ toDouble
scala> f(Left(3))
res0: Either[Long,Double] = Left(3)
scala> f(Right(3))
res1: Either[Long,Double] = Right(3.0)

Create a new F that takes two inputs, but only modifies the first input

Example:

scala> import cats.implicits._
scala> import cats.arrow.Strong
scala> val f: Int => Int = _ * 2
scala> val fab = Strong[Function1].first[Int,Int,Int](f)
scala> fab((2,3))
res0: (Int, Int) = (4,3)

Lift a function into the context of an Arrow.

In the reference articles "Arrows are Promiscuous...", and in the corresponding Haskell library Control.Arrow, this function is called arr.

Given two Fs (f and g) with a common target type, create a new F with the same target type, but with a source type of either f's source type OR g's source type.

Example:

scala> import cats.implicits._
scala> val b: Boolean => String = _ + " is a boolean"
scala> val i: Int => String =  _ + " is an integer"
scala> val f: (Either[Boolean, Int]) => String = b ||| i

scala> f(Right(3))
res0: String = 3 is an integer

scala> f(Left(false))
res0: String = false is a boolean

An F that, given a source A on either the right or left side, will return that same A object.

Example:

scala> import cats.implicits._
scala> val f: (Either[Int, Int]) => Int = Choice[Function1].codiagonal[Int]

scala> f(Right(3))
res0: Int = 3

scala> f(Left(3))
res1: Int = 3

Contramap on the first type parameter and map on the second type parameter

Example:

scala> import cats.implicits._
scala> import cats.arrow.Profunctor
scala> val fab: Double => Double = x => x + 0.3
scala> val f: Int => Double = x => x.toDouble / 2
scala> val g: Double => Double = x => x * 3
scala> val h = Profunctor[Function1].dimap(fab)(f)(g)
scala> h(3)
res0: Double = 5.4

contramap on the first type parameter

Create a new computation F that merge outputs of f and g both having the same input

Example:

scala> import cats.implicits._
scala> val addEmpty: Int => Int = _ + 0
scala> val multiplyEmpty: Int => Double= _ * 1d
scala> val f: Int => (Int, Double) = addEmpty &&& multiplyEmpty
scala> f(1)
res0: (Int, Double) = (1,1.0)

Note that the arrow laws do not guarantee the non-interference between the _effects_ of f and g in the context of F. This means that f &&& g may not be equivalent to g &&& f.

map on the second type parameter

Create a new F that takes two inputs, but only modifies the second input

Example:

scala> import cats.implicits._
scala> import cats.arrow.Strong
scala> val f: Int => Int = _ * 2
scala> val fab = Strong[Function1].second[Int,Int,Int](f)
scala> fab((2,3))
res0: (Int, Int) = (2,6)

Create a new computation F that splits its input between f and g and combines the output of each.

Example:

scala> import cats.implicits._
scala> import cats.arrow.Arrow
scala> val toLong: Int => Long = _.toLong
scala> val toDouble: Float => Double = _.toDouble
scala> val f: ((Int, Float)) => (Long, Double) = Arrow[Function1].split(toLong, toDouble)
scala> f((3, 4.0f))
res0: (Long, Double) = (3,4.0)

Note that the arrow laws do not guarantee the non-interference between the _effects_ of f and g in the context of F. This means that f *** g may not be equivalent to g *** f.