Common Lisp, I understand, *defines* a string as an array of characters
	(where arrays are mutable in both ways, I believe).

Indeed.  After
    (setq x (make-array 4 :element-type 'character
                          :initial-element #\space
                          :adjustable t))
you'll find that
    (stringp x)
is true.  You'll also be able to do
    (adjust-array x 6 :initial-element #\*)
after which x prints as
    "    **"
without losing its identity.
(Ok, so [CLtL2 p 33]: "the type string [is] the union of one or more
specialized vector types, the types of whose elements are subtypes of
the type character" and "vectors" don't have the :adjustable option set.)

 Subtypes of string include
	 simple-string, ...

	So:
	        String
	                ImmutableString
	                        Symbol
	
	Sounds good to me.
	
Sounds inside-out to me.  A String can do anything that an ImmutableString
can, not the other way around.
	ReadableString
        |
	+--Symbol
	|
	+--String
looks rather better.  Symbols have guarnateed uniqueness, which _adds_
something to ReadableString; Strings have mutability, which _adds_
something to ReadableString.