I would like to have a Gödel-numbering of the context-sensitive languages. Because there is no obvious syntactic distinction between LBAs and TMs, I cannot number the former in an immediate way. So I thought of CS grammars, but I do not think there is a bound on the alphabet size (the number of non-terminals).
Now I still think I could do it for example like this: look at TMs where the left and right ends of the input are marked and there are no transitions crossing these borders. But writing this down would be a bit of an effort, which has nothing to do with my real topic.
Therefore I am looking for some reference for a Gödel-numbering of the context-sensitive languages, which I could cite instead of working out all the details myself.