How is the CoffeeScript/TypeScript translator built?

Question

JavaScript

This is not the first time I hear that the "compilers" of CoffeeScript and TypeScript are written in the same languages ​​that they "compile" themselves.
But after all, in order for everything to work, first you need to "compile" this same "compiler", which is written in a language that must "compile" itself. So how does it work?

Answer 1

Well, the first versions were written in other languages, and only then, when the compiler became more or less sane, they rewrote it in itself. It turns out that the previous version of the "compiler" collects the next one.
CoffeeScript was originally in Ruby, for example.

Answer 2

The time machine is no different.