How to allow optional outermost parenthesis?

Question

I am writing a parser for certain expressions. I want to allow parentheses to be optional at the outermost level. My current parser looks like this:

class MyParser extends JavaTokenParsers {

  def expr = andExpr | orExpr | term
  def andExpr = "(" ~> expr ~ "and" ~ expr <~ ")"
  def orExpr = "(" ~> expr ~ "or" ~ expr <~ ")"
  def term = """[a-z]""".r
}

As it is, this parser accepts only fully parenthesized expressions, such as:

val s1 = "(a and b)"
val s2 = "((a and b) or c)"
val s3 = "((a and b) or (c and d))"

My question is, is there any modification I can make to this parser in order for the outermost parenthesis to be optional? I would like to accept the string:

val s4 = "(a and b) or (c and d)"

Thanks!

Answer 1

class MyParser extends JavaTokenParsers {
  // the complete parser can be either a parenthesisless "andExpr" or parenthesisless          
  // "orExpr " or "expr"
  def complete = andExpr | orExpr | expr
  def expr = parenthesis | term
  // moved the parenthesis from the andExpr and orExpr so I dont have to create
  // an extra parenthesisless andExpr and orExpr
  def parenthesis = "(" ~> (andExpr | orExpr) <~ ")"
  def andExpr = expr ~ "and" ~ expr
  def orExpr = expr ~ "or" ~ expr
  def term = """[a-z]""".r
}