#### 4.3.7 Integrating Types and Classes

The object system maps the space of classes into the space of types. Every class that has a proper name has a corresponding type with the same name.

The proper name of every class is a valid type specifier. In addition, every class object is a valid type specifier. Thus the expression `(typep object class)` evaluates to true if the class of object is class itself or a subclass of class. The evaluation of the expression `(subtypep class1 class2)` returns the values true and true if `class1` is a subclass of `class2` or if they are the same class; otherwise it returns the values false and true. If I is an instance of some class C named S and C is an instance of standard-class, the evaluation of the expression `(type-of I\/)` returns S if S is the proper name of C; otherwise, it returns C.

Because the names of classes and class objects are type specifiers, they may be used in the special form the and in type declarations.

Many but not all of the predefined type specifiers have a corresponding class with the same proper name as the type. These type specifiers are listed in Figure~4–8. For example, the type array has a corresponding class named array. No type specifier that is a list, such as `(vector double-float 100)`, has a corresponding class. The operator deftype does not create any classes.

Each class that corresponds to a predefined type specifier can be implemented in one of three ways, at the discretion of each implementation. It can be a standard class, a structure class,

or a system class.

A built-in class is one whose generalized instances have restricted capabilities or special representations. Attempting to use defclass to define subclasses of a built-in-class signals an error. Calling make-instance to create a generalized instance of a built-in class signals an error. Calling slot-value on a generalized instance of a built-in class signals an error. Redefining a built-in class or using change-class to change the class of an object to or from a built-in class signals an error. However, built-in classes can be used as parameter specializers in methods.

It is possible to determine whether a class is a built-in class by checking the metaclass. A standard class is an instance of the class standard-class, a built-in class is an instance of the class built-in-class, and a structure class is an instance of the class structure-class.

Each structure type created by defstruct without using the `:type` option has a corresponding class. This class is a generalized instance of the class structure-class. The `:include` option of defstruct creates a direct subclass of the class that corresponds to the included structure type.

It is implementation-dependent whether slots are involved in the operation of functions defined in this specification on instances of classes defined in this specification, except when slots are explicitly defined by this specification.

If in a particular implementation a class defined in this specification has slots that are not defined by this specfication, the names of these slots must not be external symbols of packages defined in this specification nor otherwise accessible in the `CL-USER` package.

The purpose of specifying that many of the standard type specifiers have a corresponding class is to enable users to write methods that discriminate on these types. Method selection requires that a class precedence list can be determined for each class.

The hierarchical relationships among the type specifiers are mirrored by relationships among the classes corresponding to those types.

Figure~4–8 lists the set of classes that correspond to predefined type specifiers.

     arithmetic-error                 generic-function   simple-error
     array                            hash-table         simple-type-error
     bit-vector                       integer            simple-warning
     broadcast-stream                 list               standard-class
     built-in-class                   logical-pathname   standard-generic-function
     cell-error                       method             standard-method
     character                        method-combination standard-object
     class                            null               storage-condition
     complex                          number             stream
     concatenated-stream              package            stream-error
     condition                        package-error      string
     cons                             parse-error        string-stream
     control-error                    pathname           structure-class
     division-by-zero                 print-not-readable structure-object
     echo-stream                      program-error      style-warning
     end-of-file                      random-state       symbol
     error                            ratio              synonym-stream
     file-error                       rational           t
     file-stream                      reader-error       two-way-stream
     float                            readtable          type-error
     floating-point-inexact           real               unbound-slot
     floating-point-invalid-operation restart            unbound-variable
     floating-point-overflow          sequence           undefined-function
     floating-point-underflow         serious-condition  vector
     function                         simple-condition   warning

           Figure 4–8: Classes that correspond to pre-defined type specifiers

The class precedence list information specified in the entries for each of these classes are those that are required by the object system.

Individual implementations may be extended to define other type specifiers to have a corresponding class. Individual implementations may be extended to add other subclass relationships and to add other elements to the class precedence lists as long as they do not violate the type relationships and disjointness requirements specified by this standard. A standard class defined with no direct superclasses is guaranteed to be disjoint from all of the classes in the table, except for the class named t.