Final answer:
To rewrite BNF for operator precedence and associativity, non-terminal symbols are defined to represent precedence levels, with specific rules arranged for multiplication to be right-associative. Expressions define addition and have lower precedence, while terms handle right-associative multiplication.
Step-by-step explanation:
To rewrite the BNF (Backus-Naur Form) to give precedence to the multiplication operator (*) and force it to be right-associative, the grammar needs to be adjusted so that multiplications are processed after any additions and are grouped from right to left. In BNF, this can be accomplished by defining non-terminal symbols that represent the precedence levels and by arranging the rules appropriately.
Here is an example of how you might modify the BNF to achieve this:
- <expression> ::= <term> | <expression> '+' <term>
- <term> ::= <factor> | <term> '*' <factor>
- <factor> ::= '(' <expression> ')' | number
In this revised BNF, <term> takes care of the multiplications and forces them to be right-associative because each <term> can be made up of another <term> followed by a '*' and a <factor>, effectively causing the multiplications to group to the right. Additionally, <expression> defines the addition operation, and it has a lower precedence because it is listed first and does not recurse on itself for addition.