(defgeneric foobar (arg0 arg1))

(defmethod foobar (arg0 arg1)
  (format t "0~%"))

(defmethod foobar (arg0 (arg1 string))
  (format t "1~%"))

(defmethod foobar ((arg0 number) (arg1 string))
  (format t "2~%"))

(defmethod foobar ((arg0 string) (arg1 number))
  (format t "3~%"))

CL-USER> (foobar 0 0)
0
NIL
CL-USER> (foobar :thing "hi")
1
NIL
CL-USER> (foobar 0 "hi")
2
NIL
CL-USER> (foobar "hi" 12)
3
NIL