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How to determine the value type in compiler when evaluate the syntax tree?

 
fei peng
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hi,every one
I post this topic in "Java in General (advanced)" also,but no result,so I post it here,
I'm writing a interpreter of a expression language by javacc,javacc works well ,it parses it ,and genrate a right syntax tree.but when I evaluate this tree,a problem appeared:
I was forced not to distinguish the different form of the value types of the identifiers in expression,and there is no type define statements,just one expression, but there is two types of value,the numric and the string(string type is only used as function argumnet),for example: in expression "a*b","a" should be numeric,but in "sum(a)" ,"a" should be string,in tree node ,they all are identifiers,how can I resolve this?
The EBNF of the language is following(just focus on the production 9-12,identifiers act as function name at the same time):
1.)formalu->logicExpression
2.)logicExpression->AndExpression {|| AndExpression}
3.)AndExpression->EqualityExpression {&& EqualityExpression}
4.)EqualityExpression->RelationalExpression {(==|!=) RelationalExpression}
5.)RelationalExpression->AdditiveExpression {(>|<|>=|<=) AdditiveExpression}
6.)AdditiveExpression->MultiplicativeExpression {(+|-) MultiplicativeExpression}
7.)MultiplicativeExpression->UnaryExpression {(*|/|%) UnaryExpression}
8.)UnaryExpression->[(+|-)]literal
9.)literal-><INTEGER_LITERAL>|<FLOATING_POINT_LITERAL>|<COLUMNNAME>|<IDENTIFIER> [arguments]|(formalu)
10.)arguments->([argumentList])
11.)argumentList->argument {,argument}
12.)argument->{argumentList}|formula
 
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