sample applicative functor in Scala that is not a monad

NotaMonad.scala

/**
 * An example of a polynomial applicative functor `1+X×X` build from two monads, 1+ and X×X, and
 * which is not a monad.
 * 
 * Idea: https://stackoverflow.com/questions/49742377/is-data-poe-a-empty-pair-a-a-a-monad/49742857#49742857
 */
object NotMonad {
  sealed trait SquarePlusOne[+A] {
    def map[B](f: A => B): SquarePlusOne[B]
  }
  case object One extends SquarePlusOne[Nothing] {
    def map[B](f: Nothing => B): SquarePlusOne[B] = One
  }
  case class Square[A](a: A, b: A) extends SquarePlusOne[A] {
    def map[B](f: A => B): SquarePlusOne[B] = Square(f(a), f(b))
  }

  def flatten[A](nm2: SquarePlusOne[SquarePlusOne[A]]): SquarePlusOne[A] = nm2 match {
    case Square(Square(a, b), Square(c, d)) => Square(a, d)
    case _                                  => One
  }
  
  def main(args : Array[String]): Unit = {
    val left1: SquarePlusOne[Int] =Square(1, 2)
    val left2: SquarePlusOne[SquarePlusOne[Int]] = Square(left1, One)
    val right1: SquarePlusOne[Int] = Square(3, 4)
    val right2: SquarePlusOne[SquarePlusOne[Int]] = Square(One, right1)
    val sample: SquarePlusOne[SquarePlusOne[SquarePlusOne[Int]]] =Square(left2, right2)
    val sample1: SquarePlusOne[SquarePlusOne[Int]]  = flatten(sample)

    assert(sample1 == Square(left1, right1), s"$sample1 vs ${Square(left1, right2)}")
    val flattenedFromOutside: SquarePlusOne[Int] = flatten(sample1)
    assert(flattenedFromOutside == Square(1, 4))

    assert(flatten(left2) == One)
    assert(flatten(right2) == One)

    val flattenedInside: SquarePlusOne[SquarePlusOne[Int]] = sample map flatten
    assert(flattenedInside == Square(One, One), s"got $flattenedInside")
    val flattenedFromInside: SquarePlusOne[Int] = flatten(flattenedInside)
    assert(flattenedFromInside == One)
  }
}