Have people heard of the following top-down parsing algorithm for mathematical expressions:

  1. Replace any expression that's within parentheses by its parse tree by using recursion
  2. Find the lowest precedence operator, breaking ties however you'd like. Call this lowest precedence operator OP.
  3. View the whole unparsed expression as `x OP y`
  4. Generate a parse tree for x and for y. Call them P(x) and P(y).
  5. Return ["OP", P(x), P(y)].

For 2, I don’t think you can break ties however you like because this would give you random left or right associativity https://en.m.wikipedia.org/wiki/Operator_associativity For example 2-4-7 would be either (2-4)-7 or 2-(4-7), depending on how you broke the tie.