MonadLaws.scala

object monadLaws extends App {
  // To qualify as a monald, a type has to satisfy three laws:

  // Associativity
  // (m flatMap f) flatMap g = m flatMap (x => f(x) flatMap g)
  val f = (a: Int) => List(a)
  val g = (a: Int) => List(a - 1, a + 1)
  val m1 = 1 to 2

  val r1 = m1 flatMap f flatMap g
  val r2 = m1 flatMap (x => f(x) flatMap g)
  assert(r1 == r2)


  // Left identity:
  //   unit(x) flatMap f == f(x)
  val unit = (a: Int) => List(a)

  assert(unit(2).flatMap(f) == f(2))

  // Right identity:
  //   m flatMap unit = m
  assert(List(2).flatMap(unit) == List(2))
  assert(List(2).flatMap((a: Int) => List(a)) == List(2))
}