Is this the only reason not to have a data type? (Sorry, I wasn't totally following the GADT-nastics!) That is, if, for a moment, we just assume a different operator for composing lenses, then will a data/newtype work?

Now, if (as I understand it), under IV (assuming it work), it works for lens libraries iff they use a data/newtype for the lens (so that their instance is the instance for ->, I'm guessing)...... then, I say using a different operator for compose is a small price to pay. (Well, as I said before, I'd actually prefer a different compose operator!)

Mind you, I might be totally mis-understanding the arguments and reasoning!