trait Parser extends RegexParsers with PackratParsers {
  import LambdaAST._

    lazy val identifier:PackratParser[String]  =
      """[a-zA-Z]+""".r ^^ {_.toString}

    lazy val TERM:PackratParser[Term] = LABSTR | APP | ID | PEXPR

    lazy val PEXPR:PackratParser[Term] = "(" ~> TERM <~ ")" ^^
      { term => term }

    lazy val ID:PackratParser[Id] =
      identifier ^^ Id

    lazy val LABSTR:PackratParser[Abstraction] =
      ID ~ "." ~ TERM ^^
        { case id ~ _ ~ term => Abstraction(id,term) }

    lazy val APP:PackratParser[Application] =
      TERM ~ TERM ^^
        { case t1 ~ t2 => Application(t1,t2) }

    lazy val FUNC:PackratParser[Func] =
      ID ~ ID ~ "=" ~ TERM ^^
      { case name ~ arg ~ "=" ~ body =>
        Func(name,arg,body) }
}


object LambdaAST {

  abstract trait Term
  case class Id(id:String) extends Term
  case class Abstraction(id:Id,body:Term) extends Term
  case class Application(left:Term,right:Term) extends Term
  case class Func(name:Id,arg:Id,rhs:Term) extends Term

}