Henry G. Baker Nimble Computer Corporation, 16231 Meadow Ridge Way, Encino, California 91436 (818) 986-1436 (818) 986-1360 (FAX) This work was supported in part by the U.S. Department of Energy Contract No. DE-AC03-88ER80663. A later version of this paper appeared in Lisp and Symbolic Computation 5 , 3 (Sept 1992), 157-190. Abstract Common Lisp [CL84] [CL90] includes a dynamic datatype system of moderate complexity, as well as predicates for checking the types of language objects. Additionally, an interesting predicate of two "type specifiers"-- SUBTYPEP --is included in the language. This subtypep predicate provides a mechanism with which to query the Common Lisp type system regarding containment relations among the various built-in and user-defined types. While subtypep is rarely needed by an applications programmer, the efficiency of a Common Lisp implementation can depend cri...