Antlr lexer tokens that match similar strings, what if the greedy lexer makes a mistake?

Question

It seems that sometimes the Antlr lexer makes a bad choice on which rule to use when tokenizing a stream of characters... I'm trying to figure out how to help Antlr make the obvious-to-a-human right choice. I want to parse text like this:

d/dt(x)=a
a=d/dt
d=3
dt=4

This is an unfortunate syntax that an existing language uses and I'm trying to write a parser for. The "d/dt(x)" is representing the left hand side of a differential equation. Ignore the lingo if you must, just know that it is not "d" divided by "dt". However, the second occurrence of "d/dt" really is "d" divided by "dt".

Here's my grammar:

grammar diffeq_grammar;

program :   (statement? NEWLINE)*;

statement
    :   diffeq
    |   assignment;

diffeq  :   DDT ID ')' '=' ID;

assignment
    :   ID '=' NUMBER
    |   ID '=' ID '/' ID
    ;

DDT :   'd/dt(';
ID  :   'a'..'z'+;
NUMBER  :   '0'..'9'+;
NEWLINE :   '\r\n'|'\r'|'\n';

When using this grammar the lexer grabs the first "d/dt(" and turns it to the token DDT. Perfect! Now later the lexer sees the second "d" followed by a "/" and says "hmmm, I can match this as an ID and a '/' or I can be greedy and match DDT". The lexer chooses to be greedy... but little does it know, there is no "(" a few characters later in the input stream. When the lexer looks for the missing "(" it throws a MismatchedTokenException!

The only solution I've found so far, is to move all the rules into the parser with a grammar like:

grammar diffeq_grammar;

program :   (statement? NEWLINE)*;

statement
    :   diffeq
    |   assignment;

diffeq  :   ddt id ')' '=' id;

assignment
    :   id '=' number
    |   id '=' id '/' id
    ;

ddt :   'd' '/' 'd' 't' '(';
id  :   CHAR+;
number  :   DIGIT+;
CHAR    :   'a'..'z';
DIGIT   :   '0'..'9';
NEWLINE :   '\r\n'|'\r'|'\n';

This is a fine solution if I didn't already have thousands of lines of working code that depend on the first grammar working. After spending 2 days researching this problem I have come to the conclusion that a lexer... really ought to be able to distinguish the two cases. At some point the Antlr lexer is deciding between two rules: DDT and ID. It chooses DDT because the lexer is greedy. But when matching DDT fails, I'd like the lexer to go back to using ID.

I'm okay with using predicates or other tricks as long as the grammar remains basically the same (i.e., the rules in the lexer, stay in the lexer. And most rules are left untouched.).

Ideally I can modify the lexer rule for DDT with any valid Antlr code... and be done.

My target language is Java.

Thanks!

UPDATE

Thank you guys for some great answers!! I accepted the answer that best fit my question. The actual solution I used is in my own answer (not the accepted answer), and there are more answers that could have worked. Readers, check out all the answers; some of them may suit your case better than mine.

Answer 1

I'm okay with using predicates or other tricks as long as the grammar remains basically the same (i.e., the rules in the lexer, stay in the lexer. And most rules are left untouched.).

In that case, force the lexer to look ahead in the char-stream to make sure there really is "d/dt(" using a gated syntactic predicate.

A demo:

grammar diffeq_grammar;

@parser::members {
  public static void main(String[] args) throws Exception {
    String src = 
        "d/dt(x)=a\n" +
        "a=d/dt\n" +
        "d=3\n" +
        "dt=4\n";
    diffeq_grammarLexer lexer = new diffeq_grammarLexer(new ANTLRStringStream(src));
    diffeq_grammarParser parser = new diffeq_grammarParser(new CommonTokenStream(lexer));
    parser.program();
  }
}

@lexer::members {
  private boolean ahead(String text) {
    for(int i = 0; i < text.length(); i++) {
      if(input.LA(i + 1) != text.charAt(i)) {
        return false;
      }
    }
    return true;
  }
}

program
 : (statement? NEWLINE)* EOF
 ;

statement
 : diffeq     {System.out.println("diffeq     : " + $text);}
 | assignment {System.out.println("assignment : " + $text);}
 ;

diffeq
 : DDT ID ')' '=' ID
 ;

assignment
 : ID '=' NUMBER
 | ID '=' ID '/' ID
 ;

DDT     : {ahead("d/dt(")}?=> 'd/dt(';
ID      : 'a'..'z'+;
NUMBER  : '0'..'9'+;
NEWLINE : '\r\n' | '\r' | '\n';

If you now run the demo:

java -cp antlr-3.3.jar org.antlr.Tool diffeq_grammar.g
javac -cp antlr-3.3.jar *.java
java -cp .:antlr-3.3.jar diffeq_grammarParser

(when using Windows, replace the : with ; in the last command)

you will see the following output:

diffeq     : d/dt(x)=a
assignment : a=d/dt
assignment : d=3
assignment : dt=4