object Book {
val calc = Prod(Sum( (Sum(Number(2) , Number(3))),Number(1) ),Number(5))
                                                  //> calc  : Prod = Prod(Sum(Sum(Number(2),Number(3)),Number(1)),Number(5))
val calc2 = Div(Sum(Number(28),Number(2)), Prod(Number(5),Number(2)))
                                                  //> calc2  : Div = Div(Sum(Number(28),Number(2)),Prod(Number(5),Number(2)))
calc.show                                         //> res0: String = (((2 + 3) + 1) * 5)
calc.eval                                         //> res1: Int = 30

calc2.show                                        //> res2: String = ((28 + 2) / (5 * 2))
calc2.eval                                        //> res3: Int = 3
}
trait Expr{
def eval: Int = {
this match {
case Number(x) => x
case Sum(e1,e2) => e1.eval + e2.eval
case Prod(e1,e2) => e1.eval * e2.eval
case Div(e1,e2) => e1.eval / e2.eval
}
}

def show: String = {
this match {
case Number(x) => x.toString
case Sum(e1,e2) => "("+e1.show + " + " + e2.show+")"
case Prod(e1,e2) => "("+e1.show + " * " + e2.show+")"
case Div(e1,e2) => "("+e1.show + " / " + e2.show+")"
}
}
}

case class Number(n: Int) extends Expr
case class Sum(e1: Expr, e2: Expr) extends Expr
case class Prod(e1: Expr, e2: Expr) extends Expr
case class Div(e1: Expr, e2: Expr) extends Expr