Syntax for restricted width string types

Subtyped strings are only really useful if you can guarantee that it
indeed has that subtype (e.g. doesn't contain NULL). That means that
only the "owner" of the subtype should be able to set a string to that
subtype.

Isn't it a set you would really want, like
string("upper_cased"|"no_nulls") or should you throw away/regain type
information for calls to functions which accepts different types?