Common Lisp the Language, 2nd Edition

4.4. Type Specifiers That Combine

The following type specifier lists define a type in terms of other types or objects.

(member object1 object2 ...)

This denotes the set containing precisely those objects named. An object is of this type if and only if it is eql to one of the specified objects.

(eql object)

X3J13 voted in June 1988 (CLOS)   to add the eql type specifier. It may be used as a parameter specializer for CLOS methods (see section 28.1.6.2 and find-method). It denotes the set of the one object named; an object is of this type if and only if it is eql to object. While (eql object) denotes the same type as (member object), only (eql object) may be used as a CLOS parameter specializer.

(not type)

This denotes the set of all those objects that are not of the specified type.

(and type1 type2 ...)

This denotes the intersection of the specified types.

When typep processes an and type specifier, it always tests each of the component types in order from left to right and stops processing as soon as one component of the intersection has been found to which the object in question does not belong. In this respect an and type specifier is similar to an executable and form. The purpose of this similarity is to allow a satisfies type specifier to depend on filtering by previous type specifiers. For example, suppose there were a function primep that takes an integer and says whether it is prime. Suppose also that it is an error to give any object other than an integer to primep. Then the type specifier

(and integer (satisfies primep))

is guaranteed never to result in an error because the function primep will not be invoked unless the object in question has already been determined to be an integer.

(or type1 type2 ...)

This denotes the union of the specified types. For example, the type list by definition is the same as (or null cons). Also, the value returned by the function position is always of type (or null (integer 0 *)) (either nil or a non-negative integer).

As for and, when typep processes an or type specifier, it always tests each of the component types in order from left to right and stops processing as soon as one component of the union has been found to which the object in question belongs.