ANTLR: grammar for the R5RS lexical structure, problem with numbers

i'm implementing an IDE for scheme in eclipse using DLTK. So far, i am programming the grammar to recognize the lexical structure.

i'm following the official EBNF which can be viewed here:

http://rose-r5rs.googlecode.com/hg/doc/r5rs-grammar.html

i can't get a simple form of the numbers grammar getting worked. for example the decimal numbers, i have

grammar r5rsnumbers;

options {
  language = Java;
}


program:
NUMBER;

// NUMBERS


NUMBER : /*NUM_2 | NUM_8 |*/ NUM_10; //| NUM_16;
fragment NUM_10 : PREFIX_10 COMPLEX_10;
fragment COMPLEX_10 
: REAL_10 (
            '@' REAL_10
            | '+' (
                    UREAL_10 'i'
                    | 'i'
                    )?  
            | '-' (
                    UREAL_10 'i'
                    | 'i'
                    )?
            )?
    | '+' (
        UREAL_10 'i'
        | 'i'
        )?  
    | '-' (
        UREAL_10 'i'
        | 'i'
        )?;

fragment REAL_10 : SIGN UREAL_10;
fragment UREAL_10 
    : UINTEGER_10 ('/' UINTEGER_10)?
    | DECIMAL_10;
fragment UINTEGER_10 : DIGIT_10+ '#'*;

fragment DECIMAL_10 
    : UINTEGER_10 SUFFIX
    | '.' DIGIT_10+ '#'* SUFFIX
    | DIGIT_10+ '.' DIGIT_10* '#'* SUFFIX
    | DIGIT_10+ '#'+ '.' '#'* SUFFIX;

fragment PREFIX_10 
    : RADIX_10  EXACTNESS
    | EXACTNESS RADIX_10;

fragment DIGIT : '0'..'9';
fragment EMPTY : '""'; // empty is the empty string
fragment SUFFIX : EMPTY | EXPONENT_MARKER SIGN DIGIT_10+;
fragment EXPONENT_MARKER : 'e' | 's' | 'f' | 'd' | 'l';
fragment SIGN : EMPTY | '+' |  '-';
fragment EXACTNESS : EMPTY | '#i' | '#e';
fragment RADIX_10 : EMPTY | '#d';
fragment DIGIT_10 : DIGIT;

the problem is, it is not recognizing anything. i don't understand the warning i get from the PREFIX_10 or how to solve it. if i don't use fragment in the rules, the file isn't compiling since he complains about the DIGIT_10 rule matching the same input as almost all other prior rules.

it's the same with num_2, 开发者_如何转开发num_8 and num_16

plus, i am not sure with my solution of the empty-string.

how do i get around here?

---

Note that your ANTLR rule:

EMPTY : '""';

does not match an empty string, but two double quotes.

But you don't want a lexer rule to match only an empty string: that will cause it to go in an infinite loop since there are an infinite amount of empty strings in any string/source.

So the BNF rules:

<real 10>
    ::= <sign> <ureal 10>

<sign>
    ::= <empty> | {+} | {-}

should not be translated as the following ANTLR rules:

REAL_10 
  :  SIGN UREAL_10
  ;

SIGN 
  :  EMPTY 
  |  '+' 
  |  '-'
  ;

but like this instead:

REAL_10 
  :  SIGN? UREAL_10
  ;

SIGN 
  :  '+' 
  |  '-'
  ;

Also note that your rule:

fragment COMPLEX_10 
: REAL_10 (
            '@' REAL_10
            | '+' (
                    UREAL_10 'i'
                    | 'i'
                    )?  
            | '-' (
                    UREAL_10 'i'
                    | 'i'
                    )?
            )?
    | '+' (
        UREAL_10 'i'
        | 'i'
        )?  
    | '-' (
        UREAL_10 'i'
        | 'i'
        )?;

is a bit hard to read. Indenting it differently might make this a bit easier to comprehend:

fragment COMPLEX_10
  :  REAL_10 ( '@' REAL_10 
             | '+' (UREAL_10 'i' | 'i')? 
             | '-' (UREAL_10 'i' | 'i')?
             )?
  |  '+' (UREAL_10 'i' | 'i')?  
  |  '-' (UREAL_10 'i' | 'i')?
  ;

which could be simplified by writing:

fragment COMPLEX_10
  :  REAL_10 ('@' REAL_10)?
  |  REAL_10? ('+' | '-') UREAL_10? 'i'
  ;

Also be aware that many BNF notations make no distinction between lower- and uppercase literals. So instead of writing 'i' in your ANTLR grammar, you might want to use ('i' | 'I') instead.

EDIT

Sebastian wrote:

but i'm still having problems with the PREFIX_10 rule: fragment PREFIX_10 : RADIX_10? EXACTNESS? | EXACTNESS? RADIX_10?; which tells me that alternative 2 can never be matched, although it should match #i #d and #d #i with the 2 alternatives seperately or am i doing something wrong here?

There are a couple of things wrong with the (fragment) rule PREFIX_10:

fragment PREFIX_10 
  :  RADIX_10? EXACTNESS? // alternative 1
  |  EXACTNESS? RADIX_10? // alternative 2
  ;

For one, both match an empty string. Because alternative 1 will always match an empty string, alternative 2 would never match, which is what ANTLR was telling you.

Now, looking at the BNF rules:

<exactness>
    ::= <empty> | {#i} | {#e}

<prefix 10>
    ::= <radix 10> <exactness>
      | <exactness> <radix 10>

<radix 10>
    ::= <empty> {#d}

(Note that <empty> {#d} equals {#d}, so the <empty> is IMO just misplaced. All other radii don't have and <empty> part)

I'd translate those into the following (untested!) ANTLR rules:

fragment EXACTNESS
  :  '#i' 
  |  '#e'
  ;

fragment PREFIX_10
  :  RADIX_10 EXACTNESS?
  |  EXACTNESS RADIX_10 // **
  ;

fragment RADIX_10
  :  '#d'
  ;

** Note that it's not:

fragment PREFIX_10
  :  RADIX_10 EXACTNESS? // matches '#d'
  |  EXACTNESS? RADIX_10 // matches '#d'
  ;

because the lexer does not know through which alternative to match #d.

And in case the BNF rule for <radix 10> should be like this (ie. they forgot to place a |):

<radix 10>
    ::= <empty> 
      | {#d}

then the ANTLR PREFIX_10 should still look like:

fragment PREFIX_10
  :  RADIX_10 EXACTNESS?
  |  EXACTNESS RADIX_10
  ;

but then all other rules that use PREFIX_10 should make PREFIX_10 optional.

HTH