Find function's arity in Common Lisp

For interpreted functions you should be able to use function-lambda-expression.

For compiled functions, alas, this function often returns nil, so you will have to use an implementation-dependent function (clocc/port/sys.lisp):

(defun arglist (fn)
  "Return the signature of the function."
  #+allegro (excl:arglist fn)
  #+clisp (sys::arglist fn)
  #+(or cmu scl)
  (let ((f (coerce fn 'function)))
    (typecase f
      (STANDARD-GENERIC-FUNCTION (pcl:generic-function-lambda-list f))
      (EVAL:INTERPRETED-FUNCTION (eval:interpreted-function-arglist f))
      (FUNCTION (values (read-from-string (kernel:%function-arglist f))))))
  #+cormanlisp (ccl:function-lambda-list
                (typecase fn (symbol (fdefinition fn)) (t fn)))
  #+gcl (let ((fn (etypecase fn
                    (symbol fn)
                    (function (si:compiled-function-name fn)))))
          (get fn 'si:debug))
  #+lispworks (lw:function-lambda-list fn)
  #+lucid (lcl:arglist fn)
  #+sbcl (sb-introspect:function-lambda-list fn)
  #-(or allegro clisp cmu cormanlisp gcl lispworks lucid sbcl scl)
  (error 'not-implemented :proc (list 'arglist fn)))

EDIT: note that arity in CL is not really a number, since Lisp functions can accept optional, rest and keyword arguments in addition to required ones; this is why the above arglist function returns the lambda list of the argument function, not a number.

If you are only interested in functions which accept only required parameters, you would need to use something like

(defun arity (fn)
  (let ((arglist (arglist fn)))
    (if (intersection arglist lambda-list-keywords)
        (error "~S lambda list ~S contains keywords" fn arglist)
        (length arglist))))