権限代数

// 1992年: https://ir.nctu.edu.tw/bitstream/11536/3533/1/A1992HE70800003.pdf
// 1997年: http://msn.iecs.fcu.edu.tw/~ccc/profile/publish/ij_paper2/IJ-135.pdf
// 2000年: https://ir.nctu.edu.tw/bitstream/11536/30118/1/000166289900002.pdf

import scala.math.BigInt

sealed class PermissionCompound(protected val value: BigInt) { self =>

  def +(that: PermissionCompound): PermissionCompound = PermissionCompound(
    self.value * that.value
  )

  def -(that: PermissionCompound): Option[PermissionCompound] =
    if (self.contains(that))
      Some(
        PermissionCompound(
          self.value / that.value
        )
      )
    else
      None

  def contains(that: PermissionCompound): Boolean =
    self.value % that.value == 0

  def isDuplicated(that: PermissionCompound): Boolean =
    factorize(self.value).count(_ == that.value) >= 2

  private def factorize(x: BigInt): List[BigInt] = {
    @annotation.tailrec
    def loop(x: BigInt, a: BigInt = 2, l: List[BigInt] = Nil): List[BigInt] = a * a > x match {
      case false if x % a == 0 => loop(x / a, a, a :: l)
      case false => loop(x, a + 1, l)
      case true  => x :: l
    }
    loop(x)
  }

  override def toString: String = s"PermissionCompound($value)"
}

object PermissionCompound {
  import PermissionAtom.PermissionAtomNone
  def zero: PermissionCompound                 = PermissionAtomNone
  def apply(value: BigInt): PermissionCompound = new PermissionCompound(value)

}

sealed abstract class PermissionAtom(override protected val value: BigInt) extends PermissionCompound(value)

object PermissionAtom {
  case object PermissionAtomNone                  extends PermissionAtom(0)
  case object PermissionAtomEgs                   extends PermissionAtom(2)
  case object PermissionAtomEcpSetic              extends PermissionAtom(3)
  case object PermissionAtomEcpToeic              extends PermissionAtom(5)
  case object PermissionAtomEcpToeicPersonalCoach extends PermissionAtom(7)
  case object PermissionAtom4Skills               extends PermissionAtom(11)
  case object PermissionAtomBiz                   extends PermissionAtom(13)

  def valueOf(value: BigInt): PermissionCompound = {
    value match {
      case n if n == 2  => PermissionAtomEgs
      case n if n == 3  => PermissionAtomEcpSetic
      case n if n == 5  => PermissionAtomEcpToeic
      case n if n == 7  => PermissionAtomEcpToeicPersonalCoach
      case n if n == 11 => PermissionAtom4Skills
      case n if n == 13 => PermissionAtomBiz
    }
  }

}