Yeah, this is a fundamental problem. Luckily, arithmetic expressions are always left- or right-recursive, never middle-recursive. That means they're recognizable by a regular grammar, even if the parse tree doesn't match what you'd expect:
expr = number (('*' | '+') number)*
You can replace number by (number | [ '(' expr ')' ]) to add support for parentheses as well.
My solution was to add special syntax which makes rules like this automatically:
expr = number : num
.operators infix left '*' : times
.operators infix left '+' : plus
Thanks, the eg I tried before works now, I must have misinterpreted the output.
Nice, a language can be recognized, even if a different parse tree.
I vaguely recall the shunting yard algorithm... am I right in characterising your solution as a second level of parsing? It's not "pure", but from a practical point of view, it's no worse than back-references in PCRE. The practical issue is just of ui usability.
My solution was to add special syntax which makes rules like this automatically:
While the parse tree is built, the operators and operands are rearranged into the expected parse tree using https://en.wikipedia.org/wiki/Shunting-yard_algorithm. Here's an interactive example with some more operators: https://ianh.github.io/owl/try/#expr