There's Prolog and its Definite Clause Grammars (DCG) formalism. Here's a DCG for a tiny subset of natural English (copied from wikipedia [1]):

  sentence --> noun_phrase, verb_phrase.
  noun_phrase --> det, noun.
  verb_phrase --> verb, noun_phrase.
  det --> [the].
  det --> [a].
  noun --> [cat].
  noun --> [bat].
  verb --> [eats].

The syntax is just like BNF. "-->" is "::=", terms in []'s are terminals and the rest are nonterminals. Nonterminals can have arguments and there's special syntax to include entire Prolog programs in the body of rules.

I discovered DCGs at the end of my CS degree when I was working on my graduation project, a Magic: the Gathering expert system written in Prolog. I needed a way to script cards for my rules engine, to translate expressions in the M:tG ability text language to function calls in the engine. I really wanted to write a parser using the standard parser generator tools, but I thought it would be too much work for a graduate project. Then I found out about DCGs. With DCGs I could write grammar rules like this:

  tap(X,Y) --> (['Tap'];[tap]), target(X,Y), (condition ; []), {permanent_Type(Y)}.
  tap(X,Y) --> (['Tap'];[tap]), all(X,Y), (condition ; []).

And that would not only parse, but also _generate_ ability text like "Tap target Kavu" or "Tap all Goblins target player controls" etc. So as a side effect of adding a bunch of abilities to my engine, I also had a generator for new M:tG cards.

[Edit: to be clear, the grammar rules above are already, by themselves, a parser for abilities that start with "tap". The Prolog interpreter executes those grammar rules as a program and instantiates their variables in the process. To integrate them with the engine all I had to do was write engine functions that called the nonterminals in the grammar and read the values of variables like X and Y in tap(X,Y).]

Admittedly, my grammar was limited because I didn't have the time to hand-code a grammar for the entirety of M:tG ability text, as it was at the time (I graduated 2011). In any case my rules engine was also limited (I had no planeswalkers and static effects were only partially implemented, if I remember correctly; because the rules for static effects are a bit arcane). But I managed to cover a good subset of the rules and cards, so it was possible to play a basic game with creatures with activated and triggered abilities and with non-creature spells [2].

The important detail is that DCGs are syntactic sugar for ordinary Prolog, so I could code my parser in the same language as my engine and my player. My biggest problem was really to draw an imaginary line between the parser and the other two components, because the easiest thing would be to allow them to know about each other and be infinitely entangled in a big ball of mess.

Anyway, yeah, there's something out there that is perfectly suited for creating DSLs, if you have the patience [3]. The tradeoff is that you have to learn Prolog. I suspect this is a cost too high for many who just want an easy-to-use tool.

Btw, you can't easily run my degree project unfortunately. Like an idiot I wrote it for a proprietary Prolog system and although I tried to port it to the free and open-source SWI-Prolog, it's been a nightmare of incompatibilities. The ported project is here but it breaks unexpectedly all the time:

https://github.com/stassa/Gleemin

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[1] https://en.wikipedia.org/wiki/Definite_clause_grammar#Exampl...

[2] I also had an alpha-beta minimax AI player. Not that good though. I wanted to program a player with background knowledge of M:tG but I didn't have the time.

[3] Or you can learn them from examples... See Experiment 3 on page 19 of the pdf, here:

https://link.springer.com/article/10.1007/s10994-020-05945-w