alt Hacker NewsGDSL is written in C++ with use of STL, templates and lambdas, so it's 2600 lines of such C++ source code. There is no self-hosting: neither the LISP compiler nor the C compiler can compile itself. No operating system is implemented, the word kernel in the title means something else.
FYI Here is a 700-line subset-of-C compiler which can compile itself: https://github.com/valdanylchuk/xcc700 . FYI The linker and the libc are not included.
Kernel as used in the title means shared processing core, not necessarily an OS kernel, which probably deserves clarification. As for Lisp and C, those are meant to be subset demonstrations not yet full compilers, thus the phrasing. The compiler you linked is also a subset of C with only what's needed for a minimal compiler.
I’ve been working towards making it self hosting eventually, which is why there’s the start of code for generics in GDSL-C, though that’s a significant project which will take significant time. Add to that, a lot of people would prefer to write handlers in C++ rather than learn a new language. So it may stay as a C++ project for a while.
That being said, I was also hesitant to post this until I had it self hosting, but I decided that being able to implement even the demonstrated subsets was interesting enough to be worth sharing. This is a project in progress, and I hope to expand it massively in the months to come.