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. :^)
I think even the theory of Regular Languages is overdone: You can get the essence of what NFAs are without really needing NFAs. You can get O(n) string matching without formally implementing NFAs, or using any other formal model like regex-derivatives. In fact, thinking in terms of NFAs makes it harder to see how to implement negation (or "complement" if you prefer to call it that) efficiently. It's still only linear time!
The need for NFA/DFA/derivative models is unnecessary because ultimately, REG is just DSPACE(O(1)). That's it. Thinking in any other way is confusing the map with the territory. Furthermore, REG is extremely robust, because we also have REG = DSPACE(o(log log n)) = NSPACE(o(log log n)) = 1-DSPACE(o(log n)).
Until you need to do more than all-or-nothing parsing :) see tree-sitter for example, or any other efficient LSP implementation of incremental parsing.
Quick other one: To parse infix expressions, every time you see "x·y | (z | w)", find the operator of least binding power: In my example, I've given "|" less binding power than "·". Anyway, this visually breaks the expression into two halves: "x·y" and "(z | w)". Recursively parse those two subexpressions. Essentially, that's it.
The symbols "·" and "|" don't mean anything - I've chosen them to be visually intuitive: The "|" is supposed to look like a physical divider. Also, bracketed expressions "(...)" or "{...}" should be parsed first.
Wikipedia mentions that a variant of this got used in FORTRAN I. You could also speed up my naive O(n^2) approach by using Cartesian trees, which you can build using something suspiciously resembling precedence climbing.
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.
Not to step on anyone's toes, I just don't feel that formal grammar theory is that important in practice. :^)
exactly this ! a thousand times this !
The need for NFA/DFA/derivative models is unnecessary because ultimately, REG is just DSPACE(O(1)). That's it. Thinking in any other way is confusing the map with the territory. Furthermore, REG is extremely robust, because we also have REG = DSPACE(o(log log n)) = NSPACE(o(log log n)) = 1-DSPACE(o(log n)).
The symbols "·" and "|" don't mean anything - I've chosen them to be visually intuitive: The "|" is supposed to look like a physical divider. Also, bracketed expressions "(...)" or "{...}" should be parsed first.
Wikipedia mentions that a variant of this got used in FORTRAN I. You could also speed up my naive O(n^2) approach by using Cartesian trees, which you can build using something suspiciously resembling precedence climbing.
https://dl.acm.org/doi/epdf/10.1145/512927.512931
Need to parse * before +? Begin at add, have it call parse_mul for its left and right sides, and so on.
Then just add more functions as you climb up the precedence levels.