object Program {
  case class Equality(left: Expression, right: Expression) {
    override def toString(): String =
      left.toString() + "=" + right.toString()

    def reduce(): Equality =
      Equality(left.reduce(), right.reduce())
  }

  abstract class Expression {
    def reduce(): Expression =
      this
  }

  case class Add(left: Expression, right: Expression) extends Expression {
    override def reduce(): Expression =
      (left.reduce(), right.reduce()) match {
        case (Number(left), Number(right)) =>
          Number(left + right)

        //3x + 8x = 11x
        case (Mul(Number(value), Var(name)), Mul(Number(otherValue), Var(otherName))) if name == otherName =>
          Mul(Var(name), Number(value * otherValue))

        case (left, right) =>
          Add(left, right)
      }

    override def toString(): String =
      "(" + left.toString() + "+" + right.toString() + ")"
  }

  case class Mul(left: Expression, right: Expression) extends Expression {
    override def reduce(): Expression =
      (left.reduce(), right.reduce()) match {
        case (Number(left), Number(right)) =>
          Number(left * right)

        case (left, right) =>
          Mul(left, right)
      }

    override def toString(): String =
      "(" + left.toString() + "*" + right.toString() + ")"
  }

  case class Number(value: BigDecimal) extends Expression {
    override def toString(): String =
      value.toString()
  }

  case class Var(name: String) extends Expression {
    override def toString(): String =
      name
  }

  def main(args: Array[String]) {
    val e = Add(Mul(Number(3), Var("x")), Mul(Number(4), Var("x")))

    println("antes do reduce = " + e.toString())
    println("depois do reduce = " + e.reduce.toString())
  }
}