### 4.1 Introduction ¶

A type is a (possibly infinite) set of objects. An object can belong to more than one type. Types are never explicitly represented as objects by Common Lisp. Instead, they are referred to indirectly by the use of type specifiers, which are objects that denote types.

New types can be defined using deftype, defstruct, defclass, and define-condition.

The function typep, a set membership test, is used to determine whether a given object is of a given type. The function subtypep, a subset test, is used to determine whether a given type is a subtype of another given type. The function type-of returns a particular type to which a given object belongs, even though that object must belong to one or more other types as well. (For example, every object is of type t, but type-of always returns a type specifier for a type more specific than t.)

Objects, not variables, have types. Normally, any variable can have any object as its value. It is possible to declare that a variable takes on only values of a given type by making an explicit type declaration. Types are arranged in a directed acyclic graph, except for the presence of equivalences.

Declarations can be made about types using declare, proclaim, declaim, or the. For more information about declarations, see Declarations.

Among the fundamental objects of the object system are classes. A class determines the structure and behavior of a set of other objects, which are called its instances. Every object is a direct instance of a class. The class of an object determines the set of operations that can be performed on the object. For more information, see Classes.

It is possible to write functions that have behavior specialized to the class of the objects which are their arguments. For more information, see Generic Functions and Methods.

The class of the class of an object is called its metaclass . For more information about metaclasses, see Meta-Objects.