package Main

abstract class Term

case class Var(name: String) extends Term

case class Fun(arg: String, body: Term) extends Term

case class Appli(f: Term, v: Term) extends Term

object TermTest extends App {

  def printTerm(term: Term) {

    term match {

      case Var(n) =>

        print("" + n)

      case Fun(x, b) =>

        print("^" + x + ".")

        printTerm(b)

      case Appli(f, v) =>

        Console.print("(")

        printTerm(f)

        print(" ")

        printTerm(v)

        print(")")

    }

  }

  def isIdentityFun(term: Term): Boolean = term match {

    case Fun(x, Var(y)) if x == y => true

    case _ => false

  }

  val id = Fun("x", Var("x"))

  println("id: " + id)

  val t = Fun("x", Fun("y", Appli(Var("x"), Var("y"))))

  println("t: " + t)

  printTerm(t)

  println

  println(isIdentityFun(id))

  println(isIdentityFun(t))

}