Parsing arithmetic expressions

Question

I'm studying the dragon book and can't wait to write an expression parser.

In order to deal with negative number input, my lexer reads digits when meet the symbol '-' to return a number token.

"-4+2" Will get (-4,number) (+,operator) (2,number)

but then I found that it can't do things as easy as "4-2" because

(4,number) (-2,number) It's a wrong syntax.

One of my solution is doing some pre-processing before evaluating an expression, such as appending a zero if the first token is a minus. I'm wondering how you guys deal with this situation?

Thanks.

Answer 1

You should have the following grammar, but not make "-" number into a token.

number := DIGIT+

unary := number
unary := "-" unary

expr := expr "+" unary
expr := expr "-" unary
...

As there are unary expressions, it is not a operator-precedence grammar. You should parse it with a more complex parser.

Answer 2

my lexer reads digits when meet the symbol '-' to return a negative number

Don't. Unary operators should be dealt with by the parser, not the lexer.

One of my solution is doing some pre-processing before evaluating an expression, such as appending a zero if the first token is a minus.

No. Fix the problem.

When you're in a hole, stop digging.