Well, virtually every production-grade compiler is self-compiling. Since you bring it up explicitly, I'm wondering what implications of begin self-compiling you have in mind?

> Meaning the LLM is able to program itself without training data about the programming language...

Could you clarify this sentence a bit? Does it mean the LLM will code in this new language without training in it before hand? Or is it going to enable the LLM to programm itself to gain some new capabilities?

Frankly, with the advent of coding agents, building a new compiler sounds about as relevant as introducing a new flavor of assembly language and then a new assembly may at least be justified by a new CPU architecture...