How do you write a grammar for this arithmetic expression?

Question

This is an arithmetic expression for my language: ADD 100 MUL 5 DIV 10 SUB 7 MOD 10 4

Where ADD = addition, SUB = subtraction, MUL = multiplication, DIV = division, MOD = modulo.

The expression above can also be rewitten into the standard 100 + (5 * (10 / (7 - (10 % 4)))) , parenthesis included to mark the order of operations.

This is quite different than the standard because evaluation starts with the right most operation, that is MOD 10 4 , then the result of that is then used to evaluate the next operation, that is SUB 7 2 , where 2 is the result of the modulo operation. Parenthesis is not required for this grammar.

I have gotten hold the grammar for the standard notation from https://ruslanspivak.com/lsbasi-part6/ , here it is:

 <expr> := <term> ((ADD|SUB) <term>)*
 <term> := <factor> ((MUL|DIV|MOD) <factor>)*
 <factor> := integer

In my language, I am clueless in writing the grammar for arithmetic operations. Are modifications needed for the grammar above? Or do I need to write a completely new grammar?

Answer 1

I managed to solve this by analyzing the execution of each production in my code. To my surprise, I forgot to include an <expr> production in <factor> . Changing my code a bit my moving certain conditions and I was able to parse the sample expression above. This is the grammar for the arithmetic expression in my language:

<expr> := ((ADD|SUB) <term> <term>)* | <term>
<term> := ((MUL|DIV|MOD) <factor> <factor>)* | <factor>
<factor> := INTEGER | <expr>

The <expr> production in <factor> makes it possible to have multiple operations because it goes back to the start to parse the next operation.