Java programme to implement a simple parser

Question

the following syntax shows how an arithmetic expression may be constructed in a simple language....
<expression> ::= <term> | <addop><term> | <expression><addop><term>
<term> ::= <primary> | <term> <multop> <primary>
<primary> ::= <digit> | <letter> | ( <expression> )
<digit> ::= 0 | 1 | 2 | ... | 9
<letter> ::= a | b | c | ... | y | z
<multop> ::= * | /
<addop> ::= + | -
i have been asked to write a Java program which determines whether a given character string is a legal expression according to the rules above. it should take in a string as input when it runs, for example,
a*b+(c-d)
The output from the program should be a single uppercase word:
TRUE - if the expression is legal FALSE - if it is not
You may assume the expression contains no spaces, and that all operands are single lower-case characters.
So far i have had some ideas but need a bit of help.
begin      
if term(string) then TRUE;
OTHERWISE      
if addop(first char of string) and term(rest of string) then TRUE; OTHERWISE      
for each <addop> in the string           
if expression(start of string up to addop) and term(string after addop)
          then TRUE;
OTHERWISE FALSE
end
Any help would be great, cheers

Answer 1

Here's a giveaway; it's a proper LL1 grammar that recognizes expressions:expression : term exprtail ;
exprtail : addop term exprtail | <empty> ;
term : factor termtail ;
termtail : mulop factor termtail | < empty> ;
factor : + factor | - factor | element ;
element : constant | identifier | ( expression ) ;
constant : 0 | 1 | 2 ... 9 ;
identifier : a | b | c ... z ;If you want to build your recursive parse by hand, all you have to do is
to translate every grammar rule to a Java method:Expression expression() {
   return exprtail(term());
Expression exprtail(Expression expr) {
   while (token().type == addop) {
      expr= buildExpression(token().token, expr, term());
      nextToken();
   return expr;
}etc. etc.
kind regards,
Jos