It's perfectly ordinary for a compiler to be written in the language it compiles. One way to achieve this would be to write a complete compiler for language L in some other language, and then to write a new compiler for L in L. A more interesting approach would be to write a minimal compiler for a subset of L in some other language, and then use this minimal subset to improve the compiler, making it less minimal increasing the available subset of L. In this way, a complete compiler can be built.
