antlr - "The following sets of rules are mutually left-recursive" -

i have tried write grammar recognize expressions like:

(a + max(b) ) / ( c - average(a) ) if( > average(a), 0, 1 )  x / (max(x) 

unfortunately antlr3 fails these errors:

error(210): following sets of rules mutually left-recursive [unaryexpression, additiveexpression, primaryexpression, formula, multiplicativeexpression]

error(211): derivedkeywords.g:110:13: [fatal] rule booleanterm has non-ll(*) decision due recursive rule invocations reachable alts 1,2. resolve left-factoring or using syntactic predicates or using backtrack=true option.

error(206): derivedkeywords.g:110:13: alternative 1: after matching input such decision cannot predict comes next due recursion overflow additiveexpression formula

i have spent hours trying fix these, great if @ least me fix first problem. thanks

code:

    grammar derivedkeywords; options { output=ast; //backtrack=true; } ws    : (    ' ' | '\t' | '\n' | '\r' )             { skip(); }       ;  //for numbers digit       :     '0'..'9'       ; //for both integer , real number number       :     (digit)+ ( '.' (digit)+ )?( ('e'|'e')('+'|'-')?(digit)+ )?       ;  // boolean operatos , : 'and'; or : 'or'; not : 'not'; eq : '='; neq : '!='; gt : '>'; lt : '<'; gte : '>='; lte : '<='; comma : ',';  // token functions if : 'if'; max : 'max'; min : 'min'; average : 'average';   variable :   'a'..'z' ('a'..'z' | '0'..'9')*          ; // operators  lparen      :     '('   ;      rparen            :     ')'   ;  div         :     '/'   ;      plus              :     '+'         ; minus       :     '-'   ;      star              :     '*'         ;   expression : formula;  formula          :   functionexpression         |   additiveexpression          |   lparen! a=formula rparen! // first problem         ;  additiveexpression        : a=multiplicativeexpression ( (minus^ | plus^ )   b=multiplicativeexpression )*        ;   multiplicativeexpression       : a=unaryexpression ( (star^ | div^ ) b=unaryexpression )*         ;  unaryexpression       :     minus^ u=unaryexpression        |     primaryexpression        ;  functionexpression          : f=functionoperator lparen e=formula rparen          |  if lparen b=booleanexpression comma p=formula comma s=formula rparen         ;    functionoperator :      max | min | average;   primaryexpression       :     number        // used scientific numbers       |     digit        |     variable        |     formula     ;  // boolean stuff booleanexpression              : orexpression;  orexpression :  a=andexpression (or^ b=andexpression )*                 ; andexpression              :   a=notexpression (and^ b=notexpression )*                 ;  notexpression             : not^ t=booleanterm              | booleanterm             ;  booleanoperator :     gt | lt | eq | gte | lte | neq;   booleanterm : a=formula op=booleanoperator b=formula                              | lparen! booleanterm rparen! // second problem ; 

error(210): following sets of rules mutually left-recursive [unaryexpression, additiveexpression, primaryexpression, formula, multiplicativeexpression]

- means if parser enters unaryexpression rule, has possibility match additiveexpression, primaryexpression, formula, multiplicativeexpression , unaryexpression again without ever consuming single token input - cannot decide whether use rules or not, because if uses rules, input same.

you're trying allow subexpressions in expressions sequence of rules - need make sure path consume left parenthesis of subexpression. formula alternative in primaryexpression should changed lparen formula rparen, , rest of grammar adjusted accordingly.