I've always thought that this would be a better definition of what a "compiler" is vs what an "interpreter" is:

A compiler, if asked to "execute" itself a million times will generate code that is still reasonably fast.

An interpreter, if asked to "execute" itself a million times, will generate code that is a million times slower.

Theoretically, one could write an interpreter specifically for the purpose of nesting other interpreters, which would then (nearly) remove itself from memory as it transfers control to the second interpreter, but I know I'm not quite insane enough to start working on such a thing.

What would be interesting about it?

seeing how many languages you could nest before the interpreter becomes too slow to be of use.