What is the CFG for an arithmetic expression with possible matching nested parentheses?

Question

For example, the CFG can produce: 6+(4-(5)+3) OR (7+7+(1-2)+9) OR -6+(-3+7+(9-1))

I have the following rules:

S→T|SS|(S)|e

T→exp•op•exp

nonzero→1|2|3|4|5|6|7|8|9

digit→0|1|2|3|4|5|6|7|8|9

num→nonzero•digit*

op→+|-

exp→num|(num)|op•num|(op•num)

However, the above rules can produce empty parenthesis (e.g. (()()) ) and it cannot produce the aforementioned examples.

Answer 1

I ended up with a quasi-solution:

S → S | SS | op(S) | exps

digit → 0|1|2|3|4|5|6|7|8|9

nonzero → 1|2|3|4|5|6|7|8|9

num → nonzero•digit*

exp → num | (num)

exps → op•exp•[op•exp]*

op → - | +

( → (

) → )

The solution above assumes operators must always precede numbers and opening parenthesis. This may force some unnecessary operators but it will always produce a valid mathematical expression.