FlatMapLaws

FlatMapLaws.scala

package cats.laws

import cats.FlatMap
import cats.arrow.Kleisli
import cats.syntax.apply._
import cats.syntax.flatMap._
import cats.syntax.functor._

/**
 * Laws that must be obeyed by any [[FlatMap]].
 */
class FlatMapLaws[F[_]](implicit F: FlatMap[F]) extends ApplyLaws[F] {
  def flatMapAssociativity[A, B, C](fa: F[A], f: A => F[B], g: B => F[C]): (F[C], F[C]) =
    fa.flatMap(f).flatMap(g) -> fa.flatMap(a => f(a).flatMap(g))

  def flatMapConsistentApply[A, B](fa: F[A], fab: F[A => B]): (F[B], F[B]) =
    fa.apply(fab) -> fab.flatMap(f => fa.map(f))

  /**
   * The composition of [[cats.arrow.Kleisli]] arrows is associative. This is
   * analogous to the associativity law of [[FlatMap.flatMap]].
   */
  def kleisliAssociativity[A, B, C, D](f: A => F[B], g: B => F[C], h: C => F[D], a: A): (F[D], F[D]) = {
    val (kf, kg, kh) = (Kleisli(f), Kleisli(g), Kleisli(h))
    (kh compose (kg compose kf)).run(a) -> ((kh compose kg) compose kf).run(a)
  }
}