A non-special variable's environment will be captured when you create a closure over it:
(let ((x 1))
(let ((f (lambda () x)))
(let ((x 2))
(eql 2 (funcall f)))))
;;=> NIL
A special variable's lexical environment will not:
(defvar *x*) ; *x* is special
(let ((*x* 1))
(let ((f (lambda () *x*)))
(let ((*x* 2))
(eql 2 (funcall f)))))
;;=> T
Using this approach, you could easily define a macro that will expand to code like the previous that will let you determine whether a symbol is globally proclaimed special:
(defmacro specialp (symbol)
(let ((f (gensym "FUNC-")))
`(let ((,symbol 1))
(let ((,f (lambda () ,symbol)))
(let ((,symbol 2))
(eql 2 (funcall ,f)))))))
(specialp x) ;=> NIL
(specialp *x*) ;=> T
Note that this isn't a function, it's a macro. That means that the macro function for specialp is getting called with the symbols X and *X*. This is important, because we have to construct code that uses these symbols. You can't do this with a function, because there'd be no (portable) way to take a symbol and create a lexical environment that has a lexical variable with that name and a lambda function that refers to it.
This also has some risks if you try to use it with certain symbols. For instance, in SBCL, if you try to bind, e.g., *standard-output* to something that isn't a stream or a stream designator, you'll get an error:
CL-USER> (specialp *standard-output*)
; in: SPECIALP *STANDARD-OUTPUT*
; (LET ((*STANDARD-OUTPUT* 1))
; (LET ((#:FUNC-1038 (LAMBDA # *STANDARD-OUTPUT*)))
; (LET ((*STANDARD-OUTPUT* 2))
; (EQL 2 (FUNCALL #:FUNC-1038)))))
;
; caught WARNING:
; Constant 1 conflicts with its asserted type STREAM.
; See also:
; The SBCL Manual, Node "Handling of Types"
;
; compilation unit finished
; caught 1 WARNING condition
gensym
in there so thatspecialp
doesn't blow up if you pass itf
? – Horaciohorae