Now edited ... thank you.
The compiler was from a limited subset of TRS-80 BASIC to Z80. It was written in its own subset, so it could compile itself.
I had 16K of RAM, and that had to fit the BASIC source, the compiled version, and then that compiled version compiled the BASIC source to another compiled version in a different location, which could then be saved on tape.
Interesting times, and so foreign to today's experiences that it's hard for people to follow the details. I could write it up, but I'm pretty sure no one would derive any value from reading it. I sometimes wonder if the hand-written syntax flow charts and first draft are still somewhere in my piles of undiscarded papers. I doubt it ... it as 1979 when I was doing it, and I've moved continents since then.