Love Pratt parsing! Not a compiler guy, but I've spent way too many hours reflecting on parsing. I remember trying to get though the dragon book so many times and reading all about formal grammar etc. Until I landed on; recursive descent parsing + Pratt for expressions. Super simple technique, and for me is sufficient. I'm sure it doesn't cover all cases, but just for toy languages it feels like we can usually do everything with 2-token lookahead.

Not to step on anyone's toes, I just don't feel that formal grammar theory is that important in practice. :^)

An even simpler way imo, is explicit functions instead of a precedence table, then the code pretty much has the same structure as EBNF.

Need to parse * before +? Begin at add, have it call parse_mul for its left and right sides, and so on.

  parse_mul() {
    left = parse_literal()
    while(is_mul_token()) { // left associative
      right = parse_literal()
      make_mul_node(left, right)
    }
  }

  parse_add() {
    left = parse_mul()
    while(is_add_token()) { // left associative
      right = parse_mul()
      make_add_node(left, right)
    }
  }

Then just add more functions as you climb up the precedence levels.

I can recommend anyone reading pratts original paper. Its written in a very cool and badass style.

https://dl.acm.org/doi/epdf/10.1145/512927.512931

You can either use the stack in an intuitive way, or you can change the tree directly in a somewhat less intuitive way without recursion. Essentially either DF or BF. I don’t see how it matters much anymore with stacks that grow automatically, but it’s good to understand.