18-124853.scala

def rpn(str: String): Int = rpnPrime(str.split(' ').toList, Nil)
 
def rpnPrime(str: List[String], stack: List[Int]): Int = (str, stack) match {
  case ("+"::t, y::x::zs) => {
    println(s"str: $str, stack: $stack")
    rpnPrime(t, (x + y)   :: zs)
  }
  case ("-"::t, y::x::zs) => {
    println(s"str: $str, stack: $stack")
    rpnPrime(t, (x - y)   :: zs)
  }
  case ("*"::t, y::x::zs) => {
    println(s"str: $str, stack: $stack")
    rpnPrime(t, (x * y)   :: zs)
  }
  case ("/"::t, y::x::zs) => {
    println(s"str: $str, stack: $stack")
    rpnPrime(t, (x / y)   :: zs)
  }
  case ("%"::t, y::x::zs) => {
    println(s"str: $str, stack: $stack")
    rpnPrime(t, (x % y)   :: zs)
  }
  case (  n::t,       zs) => {
    println(s"str: $str, stack: $stack")
    rpnPrime(t, (n.toInt) :: zs)
  }
  case _ => {
    println(s"str: $str, stack: $stack")
    stack.head
  }
}
 
println(rpn("1 3 +"))
println(rpn("1 3 + 5 2 - *"))

quickrun

str: List(1, 3, +), stack: List()
str: List(3, +), stack: List(1)
str: List(+), stack: List(3, 1)
str: List(), stack: List(4)
4
str: List(1, 3, +, 5, 2, -, *), stack: List()
str: List(3, +, 5, 2, -, *), stack: List(1)
str: List(+, 5, 2, -, *), stack: List(3, 1)
str: List(5, 2, -, *), stack: List(4)
str: List(2, -, *), stack: List(5, 4)
str: List(-, *), stack: List(2, 5, 4)
str: List(*), stack: List(3, 4)
str: List(), stack: List(12)
12