Scala combinator parsers - distinguish between number strings and variable strings

Question

I'm doing Cay Horstmann's combinator parser exercises, I wonder about the best way to distinguish between strings that represent numbers and strings that represent variables in a match statement:

def factor: Parser[ExprTree] = (wholeNumber | "(" ~ expr ~ ")" | ident) ^^ {
    case a: wholeNumber  => Number(a.toInt)
    case a: String => Variable(a)
}

The second line there, "case a: wholeNumber" is not legal. I thought about a regexp, but haven't found a way to get it to work with "case".

Answer 1

I would split it up a bit and push the case analysis into the |. This is one of the advantages of combinators and really LL(*) parsing in general:

def factor: Parser[ExprTree] = ( wholeNumber ^^ { Number(_.toInt) }
                               | "(" ~> expr <~ ")" 
                               | ident ^^ { Variable(_) } )

I apologize if you're not familiar with the underscore syntax. Basically it just means "substitute the nth parameter to the enclosing function value". Thus { Variable(_) } is equivalent to { x => Variable(x) }.

Another bit of syntax magic here is the ~> and <~ operators in place of ~. These operators mean that the parsing of that term should include the syntax of both the parens, but the result should be solely determined by the result of expr. Thus, the "(" ~> expr <~ ")" matches exactly the same thing as "(" ~ expr ~ ")", but it doesn't require the extra case analysis to retrieve the inner result value from expr.