First example of Harrison's "Handbook of Practical Logic and Automated Reasoning" in Scala

harr1.sc

sealed abstract class Expr
case class Variable(name: String) extends Expr
case class Const(value: Int) extends Expr
case class Add(left: Expr, right: Expr) extends Expr
case class Mult(left: Expr, right: Expr) extends Expr

object Simplify {
  def one(e: Expr): Expr = e match {
    case Add(Const(0), r)         => r
    case Add(l, Const(0))         => l
    case Add(Const(a), Const(b))  => Const(a + b)
    case Mult(Const(0), r)        => Const(0)
    case Mult(l, Const(0))        => Const(0)
    case Mult(Const(1), r)        => r
    case Mult(l, Const(1))        => l
    case Mult(Const(a), Const(b)) => Const(a * b)
    case _                        => e
  }
  def all(e: Expr): Expr = e match {
    case Add(l, r)  => one(Add(all(l), all(r)))
    case Mult(l, r) => one(Mult(all(l), all(r)))
    case _          => e
  }
}

object Main {
  def printExpr(e: Expr) = e match {
    case Const(x) => print(x)
    case _        => print("The expression could not be simplified to a constant.")
  }
  def main(args: Array[String]) {
    var e = Add(Mult(Add(Const(1), Mult(Const(0), Variable("x"))), Const(3)), Const(12))
    var s = Simplify.all(e)
    printExpr(s)
  }
}