How come there are C compilers not written by Bell Labs? ;-)
As far as I am aware, there is no prohibition on producing your own implementation of a programming language based on the description of that programming language.
You can't copy someone else's implementation without their permission.
You don't need to reverse-engineer an implementation if there is a description of what the language constructs are intended to do; and with a programming language there almost always is such a description (otherwise there's not much point to it).