Types and Classes
*****************

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.

Types
=====

Data Type Definition
--------------------

Information about type usage is located in the sections specified in Figure~4--1. Figure~4--7 lists some classes that are particularly relevant to the object system. Figure~9--1 lists the defined condition types.

  Section                                Data Type
  _________________________________________________________________________
  Classes                        Object System types
  Slots                          Object System types
  Objects                        Object System types
  Generic Functions and Methods  Object System types
  Condition System Concepts      Condition System types
  Types and Classes              Miscellaneous types
  Syntax                         All types---read and print syntax
  The Lisp Printer               All types---print syntax
  Compilation                    All types---compilation issues

           Figure 4--1: Cross-References to Data Type Information

Type Relationships
------------------

*
     The types cons, symbol, array, number, character, hash-table,

     function,

     readtable, package, pathname, stream, random-state, condition, restart, and any single other type created by defstruct,

     define-condition,

     or defclass are pairwise disjoint, except for type relations explicitly established by specifying superclasses in defclass

     or define-condition

     or the :include option of destruct.

*
     Any two types created by defstruct are disjoint unless one is a supertype of the other by virtue of the defstruct :include option.

     [Editorial Note by KMP: The comments in the source say gray suggested some change from ``common superclass'' to ``common subclass'' in the following, but the result looks suspicious to me.]

*
     Any two distinct classes created by defclass or define-condition are disjoint unless they have a common subclass or one class is a subclass of the other.

*
     An implementation may be extended to add other subtype relationships between the specified types, as long as they do not violate the type relationships and disjointness requirements specified here.  An implementation may define additional types that are subtypes or supertypes of any specified types, as long as each additional type is a subtype of type t and a supertype of type nil and the disjointness requirements are not violated.

     At the discretion of the implementation, either standard-object or structure-object might appear in any class precedence list for a system class that does not already specify either standard-object or structure-object.  If it does, it must precede the class t and follow all other standardized classes.

Type Specifiers
---------------

Type specifiers can be symbols, classes, or lists. Figure~4--2 lists symbols that are standardized atomic type specifiers, and Figure~4--3 lists standardized compound type specifier names. For syntax information, see the dictionary entry for the corresponding type specifier. It is possible to define new type specifiers using defclass, define-condition, defstruct, or deftype.

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

                 Figure 4--2: Standardized Atomic Type Specifiers

\indent If a type specifier is a list, the car of the list is a symbol, and the rest of the list is subsidiary type information.  Such a type specifier is called a compound type specifier . Except as explicitly stated otherwise, the subsidiary items can be unspecified. The unspecified subsidiary items are indicated by writing *.  For example, to completely specify a vector, the type of the elements and the length of the vector must be present.

      (vector double-float 100)

The following leaves the length unspecified:

      (vector double-float *)

The following leaves the element type unspecified:

      (vector * 100)

Suppose that two type specifiers are the same except that the first has a * where the second has a more explicit specification. Then the second denotes a subtype of the type denoted by the first.

If a list has one or more unspecified items at the end, those items can be dropped. If dropping all occurrences of * results in a singleton list, then the parentheses can be dropped as well (the list can be replaced by the symbol in its car). For example, (vector double-float *) can be abbreviated to (vector double-float), and (vector * *) can be abbreviated to (vector) and then to vector.

  and           long-float    simple-base-string
  array         member        simple-bit-vector
  base-string   mod           simple-string
  bit-vector    not           simple-vector
  complex       or            single-float
  cons          rational      string
  double-float  real          unsigned-byte
  eql           satisfies     values
  float         short-float   vector
  function      signed-byte
  integer       simple-array

  Figure 4--3: Standardized Compound Type Specifier Names

Figure 4--4 show the defined names that can be used as compound type specifier names but that cannot be used as atomic type specifiers.

  and     mod  satisfies
  eql     not  values
  member  or

  Figure 4--4: Standardized Compound-Only Type Specifier Names

New type specifiers can come into existence in two ways.

*
     Defining a structure by using defstruct without using the :type specifier or defining a class by using defclass or define-condition automatically causes the name of the structure or class to be a new type specifier symbol.

*
     deftype can be used to define derived type specifiers , which act as `abbreviations' for other type specifiers.

A class object can be used as a type specifier. When used this way, it denotes the set of all members of that class.

Figure 4--5 shows some defined names relating to types and declarations.

  coerce            defstruct  subtypep
  declaim           deftype    the
  declare           ftype      type
  defclass          locally    type-of
  define-condition  proclaim   typep

  Figure 4--5: Defined names relating to types and declarations.

Figure 4--6 shows all defined names that are type specifier names, whether for atomic type specifiers or compound type specifiers; this list is the union of the lists in Figure~4--2 and Figure~4--3.

 and                              function           simple-array
 arithmetic-error                 generic-function   simple-base-string
 array                            hash-table         simple-bit-vector
 atom                             integer            simple-condition
 base-char                        keyword            simple-error
 base-string                      list               simple-string
 bignum                           logical-pathname   simple-type-error
 bit                              long-float         simple-vector
 bit-vector                       member             simple-warning
 broadcast-stream                 method             single-float
 built-in-class                   method-combination standard-char
 cell-error                       mod                standard-class
 character                        nil                standard-generic-function
 class                            not                standard-method
 compiled-function                null               standard-object
 complex                          number             storage-condition
 concatenated-stream              or                 stream
 condition                        package            stream-error
 cons                             package-error      string
 control-error                    parse-error        string-stream
 division-by-zero                 pathname           structure-class
 double-float                     print-not-readable structure-object
 echo-stream                      program-error      style-warning
 end-of-file                      random-state       symbol
 eql                              ratio              synonym-stream
 error                            rational           t
 extended-char                    reader-error       two-way-stream
 file-error                       readtable          type-error
 file-stream                      real               unbound-slot
 fixnum                           restart            unbound-variable
 float                            satisfies          undefined-function
 floating-point-inexact           sequence           unsigned-byte
 floating-point-invalid-operation serious-condition  values
 floating-point-overflow          short-float        vector
 floating-point-underflow         signed-byte        warning

                  Figure 4--6: Standardized Type Specifier Names

Classes
=======

While the object system is general enough to describe all standardized classes (including, for example, number, hash-table, and symbol), Figure 4--7 contains a list of classes that are especially relevant to understanding the object system.

  built-in-class    method-combination         standard-object
  class             standard-class             structure-class
  generic-function  standard-generic-function  structure-object
  method            standard-method

                Figure 4--7: Object System Classes

Introduction to Classes
-----------------------

A class is an object that determines the structure and behavior of a set of other objects, which are called its instances .

A class can inherit structure and behavior from other classes. A class whose definition refers to other classes for the purpose of inheriting from them is said to be a subclass of each of those classes. The classes that are designated for purposes of inheritance are said to be superclasses of the inheriting class.

A class can have a name. The function class-name takes a class object and returns its name. The name of an anonymous class is nil.  A symbol can name a class. The function find-class takes a symbol and returns the class that the symbol names. A class has a proper name if the name is a symbol and if the name of the class names that class. That is, a class~C has the proper name~S if S= (class-name C) and C= (find-class S). Notice that it is possible for (find-class S_1) = (find-class S_2) and S_1!= S_2. If C= (find-class S), we say that C is the class named S.

A class C_1 is a direct superclass of a class C_2 if C_2 explicitly designates C_1 as a superclass in its definition. In this case C_2 is a direct subclass of C_1. A class C_n is a superclass of a class C_1 if there exists a series of classes C_2,...,C_{n-1} such that C_{i+1} is a direct superclass of C_i for 1 <= i<n. In this case, C_1 is a subclass of C_n. A class is considered neither a superclass nor a subclass of itself. That is, if C_1 is a superclass of C_2, then C_1 != C_2. The set of classes consisting of some given class C along with all of its superclasses is called ``C and its superclasses.''

Each class has a class precedence list , which is a total ordering on the set of the given class and its superclasses. The total ordering is expressed as a list ordered from most specific to least specific. The class precedence list is used in several ways.  In general, more specific classes can shadow _1 features that would otherwise be inherited from less specific classes. The method selection and combination process uses the class precedence list to order methods from most specific to least specific.

When a class is defined, the order in which its direct superclasses are mentioned in the defining form is important.  Each class has a local precedence order , which is a list consisting of the class followed by its direct superclasses in the order mentioned in the defining form.

A class precedence list is always consistent with the local precedence order of each class in the list. The classes in each local precedence order appear within the class precedence list in the same order. If the local precedence orders are inconsistent with each other, no class precedence list can be constructed, and an error is signaled. The class precedence list and its computation is discussed in Determining the Class Precedence List.

classes are organized into a directed acyclic graph. There are two distinguished classes, named t and standard-object. The class named t has no superclasses. It is a superclass of every class except itself. The class named standard-object is an instance of the class standard-class and is a superclass of every class that is an instance of the class standard-class except itself.

[Reviewer Note by Barmar: This or something like it needs to be said in the introduction.] There is a mapping from the object system class space into the type space.  Many of the standard types specified in this document have a corresponding class that has the same name as the type. Some types do not have a corresponding class. The integration of the type and class systems is discussed in Integrating Types and Classes.

Classes are represented by objects that are themselves instances of classes. The class of the class of an object is termed the metaclass of that object. When no misinterpretation is possible, the term metaclass is used to refer to a class that has instances that are themselves classes. The metaclass determines the form of inheritance used by the classes that are its instances and the representation of the instances of those classes. The object system provides a default metaclass, standard-class, that is appropriate for most programs.

Except where otherwise specified, all classes mentioned in this standard are instances of the class standard-class, all generic functions are instances of the class standard-generic-function, and all methods are instances of the class standard-method.

Standard Metaclasses
....................

The object system provides a number of predefined metaclasses. These include the classes standard-class, built-in-class, and structure-class:

*
     The class standard-class is the default class of classes defined by defclass.

*
     The class built-in-class is the class whose instances are classes that have special implementations with restricted capabilities.  Any class that corresponds to a standard type might be an instance of built-in-class. The predefined type specifiers that are required to have corresponding classes are listed in Figure~4--8. It is implementation-dependent whether each of these classes is implemented as a built-in class.

*
     All classes defined by means of defstruct are instances of the class structure-class.

Defining Classes
----------------

The macro defclass is used to define a new named class.

The definition of a class includes:

*
     The name of the new class. For newly-defined classes this name is a proper name.

*
     The list of the direct superclasses of the new class.

*
     A set of slot specifiers . Each slot specifier includes the name of the slot and zero or more slot options.  A slot option pertains only to a single slot.  If a class definition contains two slot specifiers with the same name, an error is signaled.

*
     A set of class options. Each class option pertains to the class as a whole.

The slot options and class options of the defclass form provide mechanisms for the following:

*
     Supplying a default initial value form for a given slot.

*
     Requesting that methods for generic functions be automatically generated for reading or writing slots.

*
     Controlling whether a given slot is shared by all instances of the class or whether each instance of the class has its own slot.

*
     Supplying a set of initialization arguments and initialization argument defaults to be used in instance creation.

*
     Indicating that the metaclass is to be other than the default.  The :metaclass option is reserved for future use; an implementation can be extended to make use of the :metaclass option.

*
     Indicating the expected type for the value stored in the slot.

*
     Indicating the documentation string for the slot.

Creating Instances of Classes
-----------------------------

The generic function make-instance creates and returns a new instance of a class. The object system provides several mechanisms for specifying how a new instance is to be initialized.  For example, it is possible to specify the initial values for slots in newly created instances either by giving arguments to make-instance or by providing default initial values.  Further initialization activities can be performed by methods written for generic functions that are part of the initialization protocol.  The complete initialization protocol is described in Object Creation and Initialization.

Inheritance
-----------

A class can inherit methods, slots, and some defclass options from its superclasses. Other sections describe the inheritance of methods, the inheritance of slots and slot options, and the inheritance of class options.

Examples of Inheritance
.......................

      (defclass C1 ()
          ((S1 :initform 5.4 :type number)
           (S2 :allocation :class)))

      (defclass C2 (C1)
          ((S1 :initform 5 :type integer)
           (S2 :allocation :instance)
           (S3 :accessor C2-S3)))

Instances of the class C1 have a local slot named S1, whose default initial value is 5.4 and whose value should always be a number. The class C1 also has a shared slot named S2.

There is a local slot named S1 in instances of C2. The default initial value of S1 is 5. The value of S1 should always be of type (and integer number). There are also local slots named S2 and S3 in instances of C2. The class C2 has a method for C2-S3 for reading the value of slot S3; there is also a method for (setf C2-S3) that writes the value of S3.

Inheritance of Class Options
............................

The :default-initargs class option is inherited.  The set of defaulted initialization arguments for a class is the union of the sets of initialization arguments supplied in the :default-initargs class options of the class and its superclasses. When more than one default initial value form is supplied for a given initialization argument, the default initial value form that is used is the one supplied by the class that is most specific according to the class precedence list.

If a given :default-initargs class option specifies an initialization argument of the same name more than once, an error of type program-error is signaled.

Determining the Class Precedence List
-------------------------------------

The defclass form for a class provides a total ordering on that class and its direct superclasses.  This ordering is called the local precedence order .  It is an ordered list of the class and its direct superclasses. The class precedence list for a class C is a total ordering on C and its superclasses that is consistent with the local precedence orders for each of C and its superclasses.

A class precedes its direct superclasses, and a direct superclass precedes all other direct superclasses specified to its right in the superclasses list of the defclass form. For every class C, define
R_C={(C,C_1),(C_1,C_2),...,(C_{n-1},C_n)}
where C_1,...,C_n are the direct superclasses of C in the order in which they are mentioned in the defclass form. These ordered pairs generate the total ordering on the class C and its direct superclasses.

Let S_C be the set of C and its superclasses. Let R be

R=\bigcup_{c\in S_C}R_c
.

[Reviewer Note by Barmar: ``Consistent'' needs to be defined, or maybe we should say ``logically consistent''?]

The set R might or might not generate a partial ordering, depending on whether the R_c, c\in S_C, are consistent; it is assumed that they are consistent and that R generates a partial ordering. When the R_c are not consistent, it is said that R is inconsistent.

To compute the class precedence list for~C, topologically sort the elements of S_C with respect to the partial ordering generated by R.  When the topological sort must select a class from a set of two or more classes, none of which are preceded by other classes with respect to~R, the class selected is chosen deterministically, as described below.

If R is inconsistent, an error is signaled.

Topological Sorting
...................

Topological sorting proceeds by finding a class C in~S_C such that no other class precedes that element according to the elements in~R.  The class C is placed first in the result. Remove C from S_C, and remove all pairs of the form (C,D), D\in S_C, from R. Repeat the process, adding classes with no predecessors to the end of the result.  Stop when no element can be found that has no predecessor.

If S_C is not empty and the process has stopped, the set R is inconsistent. If every class in the finite set of classes is preceded by another, then R contains a loop. That is, there is a chain of classes C_1,...,C_n such that C_i precedes C_{i+1}, 1<= i<n, and C_n precedes C_1.

Sometimes there are several classes from S_C with no predecessors.  In this case select the one that has a direct subclass rightmost in the class precedence list computed so far. (If there is no such candidate class, R does not generate a partial ordering---the R_c, c\in S_C, are inconsistent.)

In more precise terms, let {N_1,...,N_m}, m>= 2, be the classes from S_C with no predecessors.  Let (C_1... C_n), n>= 1, be the class precedence list constructed so far.  C_1 is the most specific class, and C_n is the least specific.  Let 1<= j<= n be the largest number such that there exists an i where 1<= i<= m and N_i is a direct superclass of C_j; N_i is placed next.

The effect of this rule for selecting from a set of classes with no predecessors is that the classes in a simple superclass chain are adjacent in the class precedence list and that classes in each relatively separated subgraph are adjacent in the class precedence list. For example, let T_1 and T_2 be subgraphs whose only element in common is the class J. Suppose that no superclass of J appears in either T_1 or T_2, and that J is in the superclass chain of every class in both T_1 and T_2. Let C_1 be the bottom of T_1; and let C_2 be the bottom of T_2. Suppose C is a class whose direct superclasses are C_1 and C_2 in that order, then the class precedence list for C starts with C and is followed by all classes in T_1 except J. All the classes of T_2 are next. The class J and its superclasses appear last.

Examples of Class Precedence List Determination
...............................................

This example determines a class precedence list for the class pie.  The following classes are defined:

      (defclass pie (apple cinnamon) ())

      (defclass apple (fruit) ())

      (defclass cinnamon (spice) ())

      (defclass fruit (food) ())

      (defclass spice (food) ())

      (defclass food () ())

The set S_{pie}~= {pie, apple, cinnamon, fruit, spice, food, standard-object, t}. The set R~= {(pie, apple), (apple, cinnamon), (apple, fruit), (cinnamon, spice), \break (fruit, food), (spice, food), (food, standard-object), (standard-object, t)}.

The class pie is not preceded by anything, so it comes first; the result so far is (pie).  Remove pie from S and pairs mentioning pie from R to get S~= {apple, cinnamon, fruit, spice, food, standard-object, t} and R~=~{(apple, cinnamon), (apple, fruit), (cinnamon, spice),\break (fruit, food), (spice, food), (food, standard-object), (standard-object, t)}.

The class apple is not preceded by anything, so it is next; the result is (pie apple). Removing apple and the relevant pairs results in S~= {cinnamon, fruit, spice, food, standard-object, t} and R~= {(cinnamon, spice), (fruit, food), (spice, food), (food, standard-object),\break (standard-object, t)}.

The classes cinnamon and fruit are not preceded by anything, so the one with a direct subclass rightmost in the class precedence list computed so far goes next.  The class apple is a direct subclass of fruit, and the class pie is a direct subclass of cinnamon.  Because apple appears to the right of pie in the class precedence list, fruit goes next, and the result so far is (pie apple fruit).  S~= {cinnamon, spice, food, standard-object, t}; R~= {(cinnamon, spice), (spice, food),\break (food, standard-object), (standard-object, t)}.

The class cinnamon is next, giving the result so far as (pie apple fruit cinnamon).  At this point S~= {spice, food, standard-object, t}; R~= {(spice, food), (food, standard-object), (standard-object, t)}.

The classes spice, food, standard-object, and t are added in that order, and the class precedence list is (pie apple fruit cinnamon spice food standard-object t).

It is possible to write a set of class definitions that cannot be ordered.   For example:

      (defclass new-class (fruit apple) ())

      (defclass apple (fruit) ())

The class fruit must precede apple because the local ordering of superclasses must be preserved. The class apple must precede fruit because a class always precedes its own superclasses. When this situation occurs, an error is signaled, as happens here when the system tries to compute the class precedence list of new-class.

The following might appear to be a conflicting set of definitions:

      (defclass pie (apple cinnamon) ())

      (defclass pastry (cinnamon apple) ())

      (defclass apple () ())

      (defclass cinnamon () ())

The class precedence list for pie is (pie apple cinnamon standard-object t).

The class precedence list for pastry is (pastry cinnamon apple standard-object t).

It is not a problem for apple to precede cinnamon in the ordering of the superclasses of pie but not in the ordering for pastry.  However, it is not possible to build a new class that has both pie and pastry as superclasses.

Redefining Classes
------------------

A class that is a direct instance of standard-class can be redefined if the new class is also a direct instance of standard-class. Redefining a class modifies the existing class object to reflect the new class definition; it does not create a new class object for the class. Any method object created by a :reader, :writer, or :accessor option specified by the old defclass form is removed from the corresponding generic function. Methods specified by the new defclass form are added.

When the class C is redefined, changes are propagated to its instances and to instances of any of its subclasses.  Updating such an instance occurs at an implementation-dependent time, but no later than the next time a slot of that instance is read or written.  Updating an instance does not change its identity as defined by the function eq. The updating process may change the slots of that particular instance, but it does not create a new instance.  Whether updating an instance consumes storage is implementation-dependent.

Note that redefining a class may cause slots to be added or deleted.  If a class is redefined in a way that changes the set of local slots accessible in instances, the instances are updated.  It is implementation-dependent whether instances are updated if a class is redefined in a way that does not change the set of local slots accessible in instances.

The value of a slot that is specified as shared both in the old class and in the new class is retained. If such a shared slot was unbound in the old class, it is unbound in the new class. Slots that were local in the old class and that are shared in the new class are initialized.  Newly added shared slots are initialized.

Each newly added shared slot is set to the result of evaluating the captured initialization form for the slot that was specified in the defclass form for the new class. If there was no initialization form, the slot is unbound.

If a class is redefined in such a way that the set of local slots accessible in an instance of the class is changed, a two-step process of updating the instances of the class takes place.  The process may be explicitly started by invoking the generic function make-instances-obsolete.  This two-step process can happen in other circumstances in some implementations. For example, in some implementations this two-step process is triggered if the order of slots in storage is changed.

The first step modifies the structure of the instance by adding new local slots and discarding local slots that are not defined in the new version of the class.  The second step initializes the newly-added local slots and performs any other user-defined actions. These two steps are further specified in the next two sections.

Modifying the Structure of Instances
....................................

[Reviewer Note by Barmar: What about shared slots that are deleted?]

The first step modifies the structure of instances of the redefined class to conform to its new class definition. Local slots specified by the new class definition that are not specified as either local or shared by the old class are added, and slots not specified as either local or shared by the new class definition that are specified as local by the old class are discarded. The names of these added and discarded slots are passed as arguments to update-instance-for-redefined-class as described in the next section.

The values of local slots specified by both the new and old classes are retained. If such a local slot was unbound, it remains unbound.

The value of a slot that is specified as shared in the old class and as local in the new class is retained.  If such a shared slot was unbound, the local slot is unbound.

Initializing Newly Added Local Slots
....................................

The second step initializes the newly added local slots and performs any other user-defined actions.  This step is implemented by the generic function update-instance-for-redefined-class, which is called after completion of the first step of modifying the structure of the instance.

The generic function update-instance-for-redefined-class takes four required arguments: the instance being updated after it has undergone the first step, a list of the names of local slots that were added, a list of the names of local slots that were discarded, and a property list containing the slot names and values of slots that were discarded and had values.  Included among the discarded slots are slots that were local in the old class and that are shared in the new class.

The generic function update-instance-for-redefined-class also takes any number of initialization arguments.  When it is called by the system to update an instance whose class has been redefined, no initialization arguments are provided.

There is a system-supplied primary method for update-instance-for-redefined-class whose parameter specializer for its instance argument is the class standard-object. First this method checks the validity of initialization arguments and signals an error if an initialization argument is supplied that is not declared as valid.  (For more information, see Declaring the Validity of Initialization Arguments.) Then it calls the generic function shared-initialize with the following arguments: the instance, the list of names of the newly added slots, and the initialization arguments it received.

Customizing Class Redefinition
..............................

[Reviewer Note by Barmar: This description is hard to follow.]

Methods for update-instance-for-redefined-class may be defined to specify actions to be taken when an instance is updated. If only after methods for update-instance-for-redefined-class are defined, they will be run after the system-supplied primary method for initialization and therefore will not interfere with the default behavior of update-instance-for-redefined-class.  Because no initialization arguments are passed to update-instance-for-redefined-class when it is called by the system, the initialization forms for slots that are filled by before methods for update-instance-for-redefined-class will not be evaluated by shared-initialize.

Methods for shared-initialize may be defined to customize class redefinition.  For more information, see Shared-Initialize.

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.

Types and Classes Dictionary
============================

nil [Type]
----------

Supertypes::
............

all types

Description::
.............

The type nil contains no objects and so is also called the empty type. The type nil is a subtype of every type. No object is of type nil.

Notes::
.......

The type containing the object nil is the type null, not the type nil.

boolean [Type]
--------------

Supertypes::
............

boolean, symbol, t

Description::
.............

The type boolean contains the symbols t and nil, which represent true and false, respectively.

See Also::
..........

t (constant variable), nil (constant variable), if , not , complement

Notes::
.......

Conditional operations, such as if, permit the use of generalized booleans, not just booleans; any non-nil value, not just t, counts as true for a generalized boolean. However, as a matter of convention, the symbol t is considered the canonical value to use even for a generalized boolean when no better choice presents itself.

function [System Class]
-----------------------

Class Precedence List::
.......................

function, t

Description::
.............

A function is an object that represents code to be executed when an appropriate number of arguments is supplied. A function is produced by the function special form, the function coerce,

or the function compile. A function can be directly invoked by using it as the first argument to funcall, apply, or multiple-value-call.

Compound Type Specifier Kind::
..............................

Specializing.

Compound Type Specifier Syntax::
................................

(function{[arg-typespec [value-typespec]]})

arg-typespec ::=({typespec}* [&optional {typespec}*] [&rest typespec] [&key {(keyword typespec)}*])

Compound Type Specifier Arguments::
...................................

typespec---a type specifier.

value-typespec---a type specifier.

Compound Type Specifier Description::
.....................................

[Editorial Note by KMP: Isn't there some context info about ftype declarations to be merged here?]

[Editorial Note by KMP: This could still use some cleaning up.]

[Editorial Note by Sandra: Still need clarification about what happens if the number of arguments doesn't match the FUNCTION type declaration.]

The list form of the function type-specifier can be used only for declaration and not for discrimination. Every element of this type is a function that accepts arguments of the types specified by the  argj-types and returns values that are members of the types specified by value-type. The &optional, &rest, &key,

and &allow-other-keys

markers can appear in the list of argument types.

The type specifier provided with &rest is the type of each actual argument, not the type of the corresponding variable.

The &key parameters should be supplied as lists of the form (keyword type). The keyword must be a valid keyword-name symbol as must be supplied in the actual arguments of a call.

This is usually a symbol in the KEYWORD package but can be any symbol.

When &key is given in a function type specifier lambda list, the keyword parameters given are exhaustive unless &allow-other-keys is also present. &allow-other-keys is an indication that other keyword arguments might actually be supplied and, if supplied, can be used. For example, the type of the function make-list could be declared as follows:

      (function ((integer 0) &key (:initial-element t)) list)

The value-type can be a values type specifier in order to indicate the types of multiple values.

Consider a declaration of the following form:

      (ftype (function (arg0-type arg1-type ...) val-type) f))

Any form (f arg0 arg1 ...) within the scope of that declaration is equivalent to the following:

      (the val-type (f (the arg0-type arg0) (the arg1-type arg1) ...))

That is, the consequences are undefined if any of the arguments are not of the specified types or the result is not of the specified type. In particular, if any argument is not of the correct type, the result is not guaranteed to be of the specified type.

Thus, an ftype declaration for a function describes calls to the function, not the actual definition of the function.

Consider a declaration of the following form:

      (type (function (arg0-type arg1-type ...) val-type) fn-valued-variable)

This declaration has the interpretation that, within the scope of the declaration, the consequences are unspecified if the value of fn-valued-variable is called with arguments not of the specified types; the value resulting from a valid call will be of type val-type.

As with variable type declarations, nested declarations imply intersections of types, as follows:

*
     Consider the following two declarations of ftype:

           (ftype (function (arg0-type1 arg1-type1 ...) val-type1) f))

     and

           (ftype (function (arg0-type2 arg1-type2 ...) val-type2) f))

     If both these declarations are in effect, then within the shared scope of the declarations, calls to f can be treated as if f were declared as follows:

           (ftype (function ((and arg0-type1 arg0-type2) (and arg1-type1 arg1-type2 ...) ...)
                            (and val-type1 val-type2))
                  f))

     It is permitted to ignore one or all of the ftype declarations in force.

*
     If two (or more) type declarations are in effect for a variable, and they are both function declarations, the declarations combine similarly.

compiled-function [Type]
------------------------

Supertypes::
............

compiled-function, function, t

Description::
.............

Any function may be considered by an implementation to be a a compiled function if it contains no references to macros that must be expanded at run time, and it contains no unresolved references to load time values.  See Compilation Semantics.

Functions whose definitions appear lexically within a file that has been compiled with compile-file and then loaded with load are of type compiled-function.

Functions produced by the compile function are of type compiled-function.

Other functions might also be of type compiled-function.

generic-function [System Class]
-------------------------------

Class Precedence List::
.......................

generic-function, function, t

Description::
.............

A generic function is a function whose behavior depends on the classes or identities of the arguments supplied to it.  A generic function object contains a set of methods, a lambda list, a method combination type, and other information.  The methods define the class-specific behavior and operations of the generic function; a method is said to specialize a generic function. When invoked, a generic function executes a subset of its methods based on the classes or identities of its arguments.

A generic function can be used in the same ways that an ordinary function can be used; specifically, a generic function can be used as an argument to funcall and apply, and can be given a global or a local name.

standard-generic-function [System Class]
----------------------------------------

Class Precedence List::
.......................

standard-generic-function, generic-function, function, t

Description::
.............

The class standard-generic-function is the default class of generic functions established by defmethod, ensure-generic-function, defgeneric,

and defclass forms.

class [System Class]
--------------------

Class Precedence List::
.......................

class,

standard-object,

t

Description::
.............

The type class represents objects that determine the structure and behavior of their instances. Associated with an object of type class is information describing its place in the directed acyclic graph of classes, its slots, and its options.

built-in-class [System Class]
-----------------------------

Class Precedence List::
.......................

built-in-class, class,

standard-object,

t

Description::
.............

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

structure-class [System Class]
------------------------------

Class Precedence List::
.......................

structure-class, class,

standard-object,

t

Description::
.............

All classes defined by means of defstruct are instances of the class structure-class.

standard-class [System Class]
-----------------------------

Class Precedence List::
.......................

standard-class, class,

standard-object,

t

Description::
.............

The class standard-class is the default class of classes defined by defclass.

method [System Class]
---------------------

Class Precedence List::
.......................

method, t

Description::
.............

A method is an object that represents a modular part of the behavior of a generic function.

A method contains code to implement the method's behavior, a sequence of parameter specializers that specify when the given method is applicable, and a sequence of qualifiers that is used by the method combination facility to distinguish among methods.  Each required parameter of each method has an associated parameter specializer, and the method will be invoked only on arguments that satisfy its parameter specializers.

The method combination facility controls the selection of methods, the order in which they are run, and the values that are returned by the generic function.  The object system offers a default method combination type and provides a facility for declaring new types of method combination.

See Also::
..........

Generic Functions and Methods

standard-method [System Class]
------------------------------

Class Precedence List::
.......................

standard-method, method,

standard-object,

t

Description::
.............

The class standard-method is the default class of methods defined by the defmethod and defgeneric forms.

structure-object [Class]
------------------------

Class Precedence List::
.......................

structure-object, t

Description::
.............

The class structure-object is an instance of structure-class and is a superclass of every class that is an instance of structure-class except itself, and is a superclass of every class that is defined by defstruct.

See Also::
..........

defstruct , Sharpsign S, Printing Structures

standard-object [Class]
-----------------------

Class Precedence List::
.......................

standard-object, t

Description::
.............

The class standard-object is an instance of standard-class and is a superclass of every class that is an instance of standard-class except itself.

method-combination [System Class]
---------------------------------

Class Precedence List::
.......................

method-combination, t

Description::
.............

Every method combination object is an indirect instance of the class method-combination. A method combination object represents the information about the method combination being used by a generic function. A method combination object contains information about both the type of method combination and the arguments being used with that type.

t [System Class]
----------------

Class Precedence List::
.......................

t

Description::
.............

The set of all objects. The type t is a supertype of every type, including itself. Every object is of type t.

satisfies [Type Specifier]
--------------------------

Compound Type Specifier Kind::
..............................

Predicating.

Compound Type Specifier Syntax::
................................

(satisfies{predicate-name})

Compound Type Specifier Arguments::
...................................

predicate-name---a symbol.

Compound Type Specifier Description::
.....................................

This denotes the set of all objects that satisfy the predicate predicate-name, which must be a symbol whose global function definition is a one-argument predicate.  A name is required for predicate-name; lambda expressions are not allowed. For example, the type specifier (and integer (satisfies evenp)) denotes the set of all even integers. The form (typep x '(satisfies p)) is equivalent to (if (p x) t nil).

The argument is required. The symbol * can be the argument, but it denotes itself (the symbol *), and does not represent an unspecified value.

The symbol satisfies is not valid as a type specifier.

member [Type Specifier]
-----------------------

Compound Type Specifier Kind::
..............................

Combining.

Compound Type Specifier Syntax::
................................

(member{{object}*})

Compound Type Specifier Arguments::
...................................

object---an object.

Compound Type Specifier Description::
.....................................

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

The type specifiers (member) and nil are equivalent. * can be among the objects, but if so it denotes itself (the symbol *) and does not represent an unspecified value. The symbol member is not valid as a type specifier; and, specifically, it is not an abbreviation for either (member) or (member *).

See Also::
..........

the type eql

not [Type Specifier]
--------------------

Compound Type Specifier Kind::
..............................

Combining.

Compound Type Specifier Syntax::
................................

(not{typespec})

Compound Type Specifier Arguments::
...................................

typespec---a type specifier.

Compound Type Specifier Description::
.....................................

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

The argument is required, and cannot be *.

The symbol not is not valid as a type specifier.

and [Type Specifier]
--------------------

Compound Type Specifier Kind::
..............................

Combining.

Compound Type Specifier Syntax::
................................

(and{{typespec}*})

Compound Type Specifier Arguments::
...................................

typespec---a type specifier.

Compound Type Specifier Description::
.....................................

This denotes the set of all objects of the type determined by the intersection of the typespecs.

* is not permitted as an argument.

The type specifiers (and) and t are equivalent. The symbol and is not valid as a type specifier, and, specifically, it is not an abbreviation for (and).

or [Type Specifier]
-------------------

Compound Type Specifier Kind::
..............................

Combining.

Compound Type Specifier Syntax::
................................

(or{{typespec}*})

Compound Type Specifier Arguments::
...................................

typespec---a type specifier.

Compound Type Specifier Description::
.....................................

This denotes the set of all objects of the type determined by the union of the typespecs. For example, the type list by definition is the same as (or null cons). Also, the value returned by position is an object of type (or null (integer 0 *)); i.e., either nil or a non-negative integer.

* is not permitted as an argument.

The type specifiers (or) and nil are equivalent. The symbol or is not valid as a type specifier; and, specifically, it is not an abbreviation for (or).

values [Type Specifier]
-----------------------

Compound Type Specifier Kind::
..............................

Specializing.

Compound Type Specifier Syntax::
................................

(values{!value-typespec})

[Reviewer Note by Barmar: Missing &key]

value-typespec ::={typespec}* [&optional {typespec}*] [&rest typespec] [&allow-other-keys]

Compound Type Specifier Arguments::
...................................

typespec---a type specifier.

Compound Type Specifier Description::
.....................................

This type specifier can be used only as the value-type in a function type specifier or a the special form.  It is used to specify individual types when multiple values are involved. The &optional and &rest markers can appear in the value-type list; they indicate the parameter list of a function that, when given to multiple-value-call along with the values, would correctly receive those values.

The symbol * may not be among the value-types.

The symbol values is not valid as a type specifier; and, specifically, it is not an abbreviation for (values).

eql [Type Specifier]
--------------------

Compound Type Specifier Kind::
..............................

Combining.

Compound Type Specifier Syntax::
................................

(eql{object})

Compound Type Specifier Arguments::
...................................

object---an object.

Compound Type Specifier Description::
.....................................

Represents the type whose only element is object.

The argument object is required.  The object can be *, but if so it denotes itself (the symbol *) and does not represent an unspecified value. The symbol eql is not valid as an atomic type specifier.

coerce [Function]
-----------------

coerce  object result-type =>  result

Arguments and Values::
......................

object---an object.

result-type---a type specifier.

result---an object, of type result-type except in situations described in Rule of Canonical Representation for Complex Rationals.

Description::
.............

Coerces the object to type result-type.

If object is already of type result-type, the object itself is returned, regardless of whether it would have been possible in general to coerce an object of some other type to result-type.

Otherwise, the object is coerced to type result-type according to the following rules:

sequence

     If the result-type is a recognizable subtype of list, and the object is a sequence, then the result is a list that has the same elements as object.

     If the result-type is a recognizable subtype of vector, and the object is a sequence, then the result is a vector that has the same elements as object. If result-type is a specialized type, the result has an actual array element type that is the result of upgrading the element type part of that specialized type. If no element type is specified, the element type defaults to t. If the implementation cannot determine the element type, an error is signaled.

character
     If the result-type is character and the object is a character designator, the result is the character it denotes.

complex
     If the result-type is complex and the object is a number, then the result is obtained by constructing a complex whose real part is the object and whose imaginary part is the result of coercing an integer zero to the type of the object (using coerce). (If the real part is a rational, however, then the result must be represented as a rational rather than a complex; see Rule of Canonical Representation for Complex Rationals. So, for example, (coerce 3 'complex) is permissible, but will return 3, which is not a complex.)

float
     If the result-type is any of float, short-float, single-float, double-float, long-float, and the object is a

     real,

     then the result is a float of type result-type which is equal in sign and magnitude to the object to whatever degree of representational precision is permitted by that float representation. (If the result-type is float and object is not already a float, then the result is a single float.)

function
     If the result-type is function, and object is any

     function name

     that is fbound but that is globally defined neither as a macro name nor as a special operator, then the result is the functional value of object.

     If the result-type is function, and object is a lambda expression, then the result is a closure of object in the null lexical environment.

t
     Any object can be coerced to an object of type t. In this case, the object is simply returned.

Examples::
..........

      (coerce '(a b c) 'vector) =>  #(A B C)
      (coerce 'a 'character) =>  #\A
      (coerce 4.56 'complex) =>  #C(4.56 0.0)
      (coerce 4.5s0 'complex) =>  #C(4.5s0 0.0s0)
      (coerce 7/2 'complex) =>  7/2
      (coerce 0 'short-float) =>  0.0s0
      (coerce 3.5L0 'float) =>  3.5L0
      (coerce 7/2 'float) =>  3.5
      (coerce (cons 1 2) t) =>  (1 . 2)

All the following forms should signal an error:

      (coerce '(a b c) '(vector * 4))
      (coerce #(a b c) '(vector * 4))
      (coerce '(a b c) '(vector * 2))
      (coerce #(a b c) '(vector * 2))
      (coerce "foo" '(string 2))
      (coerce #(#\a #\b #\c) '(string 2))
      (coerce '(0 1) '(simple-bit-vector 3))

Exceptional Situations::
........................

If a coercion is not possible, an error of type type-error is signaled.

(coerce x 'nil) always signals an error of type type-error.

An error of type error is signaled if the result-type is function but object is a symbol that is not fbound or if the symbol names a macro or a special operator.

An error of type type-error should be signaled if result-type specifies the number of elements and object is of a different length.

See Also::
..........

rational , floor; ffloor; ceiling; fceiling; truncate; ftruncate; round; fround , char-code , char-int

Notes::
.......

Coercions from floats to rationals and from ratios to integers are not provided because of rounding problems.

      (coerce x 't) == (identity x) == x

deftype [Macro]
---------------

deftype  name lambda-list [[{declaration}* | documentation]] {form}* =>  name

Arguments and Values::
......................

name---a symbol.

lambda-list---a deftype lambda list.

declaration---a declare expression; not evaluated.

documentation---a string; not evaluated.

form---a form.

Description::
.............

deftype defines a derived type specifier named name.

The meaning of the new type specifier is given in terms of a function which expands the type specifier into another type specifier, which itself will be expanded if it contains references to another derived type specifier.

The newly defined type specifier may be referenced as a list of the form (name arg_1 arg_2 ...)\/. The number of arguments must be appropriate to the lambda-list. If the new type specifier takes no arguments, or if all of its arguments are optional, the type specifier may be used as an atomic type specifier.

The argument expressions to the type specifier, arg_1 ... arg_n, are not evaluated. Instead, these literal objects become the objects to which corresponding parameters become bound.

The body of the deftype form

(but not the lambda-list)

is

implicitly enclosed in a block named name,

and is evaluated as an implicit progn, returning a new type specifier.

The lexical environment of the body is the one which was current at the time the deftype form was evaluated, augmented by the variables in the lambda-list.

Recursive expansion of the type specifier returned as the expansion must terminate, including the expansion of type specifiers which are nested within the expansion.

The consequences are undefined if the result of fully expanding a type specifier contains any circular structure, except within the objects referred to by member and eql type specifiers.

Documentation is attached to name as a documentation string of kind type.

If a deftype form appears as a top level form, the compiler must ensure that the name is recognized in subsequent type declarations. The programmer must ensure that the body of a deftype form can be evaluated at compile time if the name is referenced in subsequent type declarations. If the expansion of a type specifier is not defined fully at compile time (perhaps because it expands into an unknown type specifier or a satisfies of a named function that isn't defined in the compile-time environment), an implementation may ignore any references to this type in declarations and/or signal a warning.

Examples::
..........

      (defun equidimensional (a)
        (or (< (array-rank a) 2)
            (apply #'= (array-dimensions a)))) =>  EQUIDIMENSIONAL
      (deftype square-matrix (&optional type size)
        `(and (array ,type (,size ,size))
              (satisfies equidimensional))) =>  SQUARE-MATRIX

See Also::
..........

declare, defmacro , documentation; (setf documentation) , Type Specifiers, Syntactic Interaction of Documentation Strings and Declarations

subtypep [Function]
-------------------

subtypep  type-1 type-2 &optional environment =>  subtype-p, valid-p

Arguments and Values::
......................

type-1---a type specifier.

type-2---a type specifier.

environment---an environment object. The default is nil, denoting the null lexical environment and the current global environment.

subtype-p---a generalized boolean.

valid-p---a generalized boolean.

Description::
.............

If type-1 is a recognizable subtype of type-2, the first value is true. Otherwise, the first value is false, indicating that either type-1 is not a subtype of type-2, or else type-1 is a subtype of type-2 but is not a recognizable subtype.

A second value is also returned indicating the `certainty' of the first value.  If this value is true, then the first value is an accurate indication of the subtype relationship. (The second value is always true when the first value is true.)

Figure 4--9 summarizes the possible combinations of values that might result.

  Value 1  Value 2  Meaning
  true     true     type-1 is definitely a subtype of type-2.
  false    true     type-1 is definitely not a subtype of type-2.
  false    false    subtypep could not determine the relationship,
                    so type-1 might or might not be a subtype of type-2.

               Figure 4--9: Result possibilities for subtypep

subtypep is permitted to return the values false and false only when at least one argument involves one of these type specifiers: and, eql, the list form of function, member, not, or, satisfies, or values. (A type specifier `involves' such a symbol if, after being type expanded, it contains that symbol in a position that would call for its meaning as a type specifier to be used.) One consequence of this is that if neither type-1 nor type-2 involves any of these type specifiers, then subtypep is obliged to determine the relationship accurately.  In particular, subtypep returns the values true and true if the arguments are equal and do not involve any of these type specifiers.

subtypep never returns a second value of nil when both type-1 and type-2 involve only the names in Figure~4--2, or names of types defined by defstruct, define-condition, or defclass, or derived types that expand into only those names. While type specifiers listed in Figure~4--2 and names of defclass and defstruct can in some cases be implemented as derived types, subtypep regards them as primitive.

The relationships between types reflected by subtypep are those specific to the particular implementation.  For example, if an implementation supports only a single type of floating-point numbers, in that implementation (subtypep 'float 'long-float) returns the values true and true (since the two types are identical).

For all T1 and T2 other than *, (array T1) and (array T2) are two different type specifiers that always refer to the same sets of things if and only if they refer to arrays of exactly the same specialized representation, i.e., if (upgraded-array-element-type 'T1)  and (upgraded-array-element-type 'T2) return two different type specifiers that always refer to the same sets of objects. This is another way of saying that `(array type-specifier) and `(array ,(upgraded-array-element-type 'type-specifier)) refer to the same set of specialized array representations. For all T1 and T2 other than *, the intersection of (array T1) and (array T2) is the empty set if and only if they refer to arrays of different, distinct specialized representations.

Therefore,

      (subtypep '(array T1) '(array T2)) =>  true

if and only if

      (upgraded-array-element-type 'T1)  and
      (upgraded-array-element-type 'T2)

return two different type specifiers that always refer to the same sets of objects.

For all type-specifiers T1 and T2 other than *,

      (subtypep '(complex T1) '(complex T2)) =>  true, true

if:

1.
     T1 is a subtype of T2, or

2.
     (upgraded-complex-part-type 'T1) and (upgraded-complex-part-type 'T2) return two different type specifiers that always refer to the same sets of objects; in this case, (complex T1) and (complex T2) both refer to the same specialized representation.

The values are false and true otherwise.

The form

      (subtypep '(complex single-float) '(complex float))

must return true in all implementations, but

      (subtypep '(array single-float) '(array float))

returns true only in implementations that do not have a specialized array representation for single floats distinct from that for other floats.

Examples::
..........

      (subtypep 'compiled-function 'function) =>  true, true
      (subtypep 'null 'list) =>  true, true
      (subtypep 'null 'symbol) =>  true, true
      (subtypep 'integer 'string) =>  false, true
      (subtypep '(satisfies dummy) nil) =>  false, implementation-dependent
      (subtypep '(integer 1 3) '(integer 1 4)) =>  true, true
      (subtypep '(integer (0) (0)) 'nil) =>  true, true
      (subtypep 'nil '(integer (0) (0))) =>  true, true
      (subtypep '(integer (0) (0)) '(member)) =>  true, true ;or false, false
      (subtypep '(member) 'nil) =>  true, true ;or false, false
      (subtypep 'nil '(member)) =>  true, true ;or false, false

Let <aet-x> and <aet-y> be two distinct type specifiers that do not always refer to the same sets of objects in a given implementation, but for which make-array, will return an object of the same array type.

Thus, in each case,

       (subtypep (array-element-type (make-array 0 :element-type '<aet-x>))
                 (array-element-type (make-array 0 :element-type '<aet-y>)))
     =>  true, true

       (subtypep (array-element-type (make-array 0 :element-type '<aet-y>))
                 (array-element-type (make-array 0 :element-type '<aet-x>)))
     =>  true, true

If  (array <aet-x>) and (array <aet-y>) are different names for exactly the same set of objects, these names should always refer to the same sets of objects. That implies that the following set of tests are also true:

      (subtypep '(array <aet-x>) '(array <aet-y>)) =>  true, true
      (subtypep '(array <aet-y>) '(array <aet-x>)) =>  true, true

See Also::
..........

Types

Notes::
.......

The small differences between the subtypep specification for the array and complex types are necessary because there is no creation function for complexes which allows the specification of the resultant part type independently of the actual types of the parts.  Thus in the case of the type complex, the actual type of the parts is referred to, although a number can be a member of more than one type. For example, 17 is of type (mod 18) as well as type (mod 256) and type integer; and 2.3f5 is of type single-float as well as type float.

type-of [Function]
------------------

type-of  object =>  typespec

Arguments and Values::
......................

object---an object.

typespec---a type specifier.

Description::
.............

Returns a type specifier, typespec, for a type that has the object as an element. The typespec satisfies the following:

1.
     For any object that is an element of some built-in type:

     a.
          the type returned is a recognizable subtype of that built-in type.

     b.
          the type returned does not involve and, eql, member, not, or, satisfies, or values.

2.
     For all objects, (typep object (type-of object)) returns true. Implicit in this is that type specifiers which are not valid for use with typep, such as the list form of the function type specifier, are never returned by type-of.

3.
     The type returned by type-of is always a recognizable subtype of the class returned by class-of.  That is,

           (subtypep (type-of object) (class-of object)) =>  true, true

4.
     For objects of metaclass structure-class or standard-class,

     and for conditions,

     type-of returns the proper name of the class returned by class-of if it has a proper name, and otherwise returns the class itself. In particular, for objects created by the constructor function of a structure defined with defstruct without a :type option, type-of returns the structure name; and for objects created by make-condition, the typespec is the name of the condition type.

5.
     For each of the types short-float, single-float, double-float, or long-float of which the object is an element, the typespec is a recognizable subtype of that type.

Examples::
..........

      (type-of 'a) =>  SYMBOL
      (type-of '(1 . 2))
     =>  CONS
     OR=> (CONS FIXNUM FIXNUM)
      (type-of #c(0 1))
     =>  COMPLEX
     OR=> (COMPLEX INTEGER)
      (defstruct temp-struct x y z) =>  TEMP-STRUCT
      (type-of (make-temp-struct)) =>  TEMP-STRUCT
      (type-of "abc")
     =>  STRING
     OR=> (STRING 3)
      (subtypep (type-of "abc") 'string) =>  true, true
      (type-of (expt 2 40))
     =>  BIGNUM
     OR=> INTEGER
     OR=> (INTEGER 1099511627776 1099511627776)
     OR=> SYSTEM::TWO-WORD-BIGNUM
     OR=> FIXNUM
      (subtypep (type-of 112312) 'integer) =>  true, true
      (defvar *foo* (make-array 5 :element-type t)) =>  *FOO*
      (class-name (class-of *foo*)) =>  VECTOR
      (type-of *foo*)
     =>  VECTOR
     OR=> (VECTOR T 5)

See Also::
..........

array-element-type , class-of , defstruct , typecase; ctypecase; etypecase , typep , Types

Notes::
.......

Implementors are encouraged to arrange for type-of to return

a portable value.

typep [Function]
----------------

typep  object type-specifier &optional environment =>  generalized-boolean

Arguments and Values::
......................

object---an object.

type-specifier---any type specifier except

values, or a type specifier list whose first element is either function or values.

environment---an environment object. The default is nil, denoting the null lexical environment and the and current global environment.

generalized-boolean---a generalized boolean.

Description::
.............

Returns true if object is of the type specified by type-specifier; otherwise, returns false.

A type-specifier of the form (satisfies fn) is handled by applying the function fn to object.

(typep object '(array type-specifier)), where type-specifier is not *, returns true if and only if object is an array that could be the result of supplying type-specifier as the :element-type argument to make-array. (array *) refers to all arrays regardless of element type, while (array type-specifier) refers only to those arrays that can result from giving type-specifier as the :element-type argument to make-array. A similar interpretation applies to (simple-array type-specifier) and (vector type-specifier). See Array Upgrading.

(typep object '(complex type-specifier)) returns true for all complex numbers that can result from giving numbers of type type-specifier to the function complex, plus all other complex numbers of the same specialized representation. Both the real and the imaginary parts of any such complex number must satisfy:

      (typep realpart 'type-specifier)
      (typep imagpart 'type-specifier)

See the function upgraded-complex-part-type.

Examples::
..........

      (typep 12 'integer) =>  true
      (typep (1+ most-positive-fixnum) 'fixnum) =>  false
      (typep nil t) =>  true
      (typep nil nil) =>  false
      (typep 1 '(mod 2)) =>  true
      (typep #c(1 1) '(complex (eql 1))) =>  true
     ;; To understand this next example, you might need to refer to
     ;; Rule of Canonical Representation for Complex Rationals.
      (typep #c(0 0) '(complex (eql 0))) =>  false

Let A_x and A_y be two type specifiers that denote different types, but for which

      (upgraded-array-element-type 'A{{}_x})

and

      (upgraded-array-element-type 'A{{}_y})

denote the same type.  Notice that

      (typep (make-array 0 :element-type 'A{{}_x}) '(array A{{}_x})) =>  true
      (typep (make-array 0 :element-type 'A{{}_y}) '(array A{{}_y})) =>  true
      (typep (make-array 0 :element-type 'A{{}_x}) '(array A{{}_y})) =>  true
      (typep (make-array 0 :element-type 'A{{}_y}) '(array A{{}_x})) =>  true

Exceptional Situations::
........................

An error of type error is signaled if type-specifier is values, or a type specifier list whose first element is either function or values.

The consequences are undefined if the type-specifier is not a type specifier.

See Also::
..........

type-of , upgraded-array-element-type , upgraded-complex-part-type , Type Specifiers

Notes::
.......

Implementations are encouraged to recognize and optimize the case of (typep x (the class y)), since it does not involve any need for expansion of deftype information at runtime.

type-error [Condition Type]
---------------------------

Class Precedence List::
.......................

type-error, error, serious-condition, condition, t

Description::
.............

The type type-error represents a situation in which an object is not of the expected type.  The ``offending datum'' and ``expected type'' are initialized by the initialization arguments named :datum and :expected-type to make-condition, and are accessed by the functions type-error-datum and type-error-expected-type.

See Also::
..........

type-error-datum; type-error-expected-type , type-error-expected-type

type-error-datum, type-error-expected-type [Function]
-----------------------------------------------------

type-error-datum  condition =>  datum

type-error-expected-type  condition =>  expected-type

Arguments and Values::
......................

condition---a condition of type type-error.

datum---an object.

expected-type---a type specifier.

Description::
.............

type-error-datum returns the offending datum in the situation represented by the condition.

type-error-expected-type returns the expected type of the offending datum in the situation represented by the condition.

Examples::
..........

      (defun fix-digits (condition)
        (check-type condition type-error)
        (let* ((digits '(zero one two three four
                        five six seven eight nine))
              (val (position (type-error-datum condition) digits)))
          (if (and val (subtypep 'fixnum (type-error-expected-type condition)))
              (store-value 7))))

      (defun foo (x)
        (handler-bind ((type-error #'fix-digits))
          (check-type x number)
          (+ x 3)))

      (foo 'seven)
     =>  10

See Also::
..........

type-error, Conditions

simple-type-error [Condition Type]
----------------------------------

Class Precedence List::
.......................

simple-type-error, simple-condition, type-error, error, serious-condition, condition, t

Description::
.............

Conditions of type simple-type-error are like conditions of type type-error, except that they provide an alternate mechanism for specifying how the condition is to be reported; see the type simple-condition.

See Also::
..........

simple-condition,

simple-condition-format-control; simple-condition-format-arguments ,

simple-condition-format-arguments, type-error-datum; type-error-expected-type , type-error-expected-type