// ===
sbt.version=1.2.8

ThisBuild / scalaVersion     := "2.13.0"
ThisBuild / version          := "0.1.0-SNAPSHOT"
ThisBuild / organization     := "com.example"
ThisBuild / organizationName := "example"

lazy val root = (project in file("."))
  .settings(
    name := "check_cont_monad_law",
    libraryDependencies += "org.scalacheck" %% "scalacheck" % "1.14.0" % Test
  )

// ===

package example

import org.scalacheck.{Prop, Properties}

final case class Cont[R, A](run: (A => R) => R) {
  def map[B](f: A => B): Cont[R, B] = Cont(br => run(f andThen br))
  def flatMap[B](f: A => Cont[R, B]): Cont[R, B] =
    Cont(br => run(f(_).run(br)))
}
object Cont {
  def pure[R, A](a: A): Cont[R, A] = Cont(_(a))
}

class ContMonadSpec extends Properties("Monad[Cont[R, ?]]") {

  def inc(i: Int): Cont[Int, Int] = Cont(_(i + 1))
  def add_![R](s: String): Cont[String, String] = Cont(_(s + "!"))
  def add_?[R](s: String): Cont[String, String] = Cont(_(s + "?"))

  property("rightIdentity") = Prop.forAll { i: Int =>
    inc(i).flatMap(Cont.pure).run(identity) == inc(i).run(identity)
  }
  property("leftIdentity") = Prop.forAll { i: Int =>
    Cont.pure[Int, Int](i).flatMap(inc).run(identity) == inc(i).run(identity)
  }
  property("associativity") = Prop.forAll { s: String =>
    Cont.pure(s).flatMap(add_!).flatMap(add_?).run(identity) ==
      Cont.pure(s).flatMap(a => add_!(a).flatMap(add_?)).run(identity)
  }
}

// ===

sbt:check_cont_monad_law> test
[info] + Monad[Cont[R, ?]].rightIdentity: OK, passed 100 tests.
[info] + Monad[Cont[R, ?]].leftIdentity: OK, passed 100 tests.
[info] + Monad[Cont[R, ?]].associativity: OK, passed 100 tests.
[info] Passed: Total 3, Failed 0, Errors 0, Passed 3
[success] Total time: 1 s, completed 2019/09/15 19:49:36