Skip to main content

7.6 Generic Functions and Methods

7.6.1 Introduction to Generic Functions

A generic function is a function whose behavior depends on the classes or identities of the arguments supplied to it. A generic function object is associated with a set of methods, a lambda list, a method combination2, and other information.

Like an ordinary function, a generic function takes arguments, performs a series of operations, and perhaps returns useful values. An ordinary function has a single body of code that is always executed when the function is called. A generic function has a set of bodies of code of which a subset is selected for execution. The selected bodies of code and the manner of their combination are determined by the classes or identities of one or more of the arguments to the generic function and by its method combination.

Ordinary functions and generic functions are called with identical syntax.

Generic functions are true functions that can be passed as arguments and used as the first argument to funcall and apply.

A binding of a function name to a generic function can be established in one of several ways. It can be established in the global environment by ensure-generic-function, defmethod (implicitly, due to ensure-generic-function) or defgeneric (also implicitly, due to ensure-generic-function). No standardized mechanism is provided for establishing a binding of a function name to a generic function in the lexical environment.

When a defgeneric form is evaluated, one of three actions is taken (due to ensure-generic-function):

If a generic function of the given name already exists, the existing generic function object is modified. Methods specified by the current defgeneric form are added, and any methods in the existing generic function that were defined by a previous defgeneric form are removed. Methods added by the current defgeneric form might replace methods defined by defmethod, defclass, define-condition, or defstruct. No other methods in the generic function are affected or replaced.

If the given name names an ordinary function, a macro, or a special operator , an error is signaled.

Otherwise a generic function is created with the methods specified by the method definitions in the defgeneric form.

Some operators permit specification of the options of a generic function, such as the type of method combination it uses or its argument precedence order . These operators will be referred to as “operators that specify generic function options.” The only standardized operator in this category is defgeneric.

Some operators define methods for a generic function. These operators will be referred to as method-defining operators; their associated forms are called method-defining forms. The standardized method-defining operators are listed in Figure 7–1.

|

defgeneric defmethod defclass

define-condition defstruct

|

| :- |

Figure 7–1. Standardized Method-Defining Operators

Note that of the standardized method-defining operators only defgeneric can specify generic function options. defgeneric and any implementation-defined operators that can specify generic function options are also referred to as “operators that specify generic function options.”

7.6.2 Introduction to Methods

Methods define the class-specific or identity-specific behavior and operations of a generic function.

A method object is associated with code that implements the method’s behavior, a sequence of parameter specializers that specify when the given method is applicable, a lambda list, and a sequence of qualifiers that are used by the method combination facility to distinguish among methods.

A method object is not a function and cannot be invoked as a function. Various mechanisms in the object system take a method object and invoke its method function, as is the case when a generic function is invoked. When this occurs it is said that the method is invoked or called.

A method-defining form contains the code that is to be run when the arguments to the generic function cause the method that it defines to be invoked. When a method-defining form is evaluated, a method object is created and one of four actions is taken:

If a generic function of the given name already exists and if a method object already exists that agrees with the new one on parameter specializers and qualifiers, the new method object replaces the old one. For a definition of one method agreeing with another on parameter specializers and qualifiers, see Section 7.6.3 (Agreement on Parameter Specializers and Qualifiers).

If a generic function of the given name already exists and if there is no method object that agrees with the new one on parameter specializers and qualifiers, the existing generic function object is modified to contain the new method object.

If the given name names an ordinary function, a macro, or a special operator , an error is signaled.

Otherwise a generic function is created with the method specified by the method-defining form.

If the lambda list of a new method is not congruent with the lambda list of the generic function, an error is signaled. If a method-defining operator that cannot specify generic function options creates a new generic function, a lambda list for that generic function is derived from the lambda list of the method in the method-defining form in such a way as to be congruent with it. For a discussion of congruence, see Section 7.6.4 (Congruent Lambda-lists for all Methods of a Generic Function).

Each method has a specialized lambda list, which determines when that method can be applied. A specialized lambda list is like an ordinary lambda list except that a specialized parameter may occur instead of the name of a required parameter. A specialized parameter is a list (variable-name parameter-specializer-name), where parameter-specializer-name is one of the following:

a symbol

denotes a parameter specializer which is the class named by that symbol.

a class

denotes a parameter specializer which is the class itself.

(eql form)

denotes a parameter specializer which satisfies the type specifier (eql object), where object is the result of evaluating form. The form form is evaluated in the lexical environment in which the method-defining form is evaluated. Note that form is evaluated only once, at the time the method is defined, not each time the generic function is called.

Parameter specializer names are used in macros intended as the user-level interface (defmethod), while parameter specializers are used in the functional interface.

Only required parameters may be specialized, and there must be a parameter specializer for each required parameter. For notational simplicity, if some required parameter in a specialized lambda list in a method-defining form is simply a variable name, its parameter specializer defaults to the class t.

Given a generic function and a set of arguments, an applicable method is a method for that generic function whose parameter specializers are satisfied by their corresponding arguments. The following definition specifies what it means for a method to be applicable and for an argument to satisfy a parameter specializer .

Let hA1, . . . , Ani be the required arguments to a generic function in order. Let hP1, . . . , Pni be the parameter specializers corresponding to the required parameters of the method M in order. The method M is applicable when each Aiis of the type specified by the type specifier Pi. Because every valid parameter specializer is also a valid type specifier , the function typep can be used during method selection to determine whether an argument satisfies a parameter specializer .

A method all of whose parameter specializers are the class t is called a default method; it is always applicable but may be shadowed by a more specific method.

Methods can have qualifiers, which give the method combination procedure a way to distinguish among methods. A method that has one or more qualifiers is called a qualified method. A method with no qualifiers is called an unqualified method. A qualifier is any non-list. The qualifiers defined by the standardized method combination types are symbols.

In this specification, the terms “primary method” and “auxiliary method” are used to partition methods within a method combination type according to their intended use. In standard method combination, primary methods are unqualified methods and auxiliary methods are methods with a single qualifier that is one of :around, :before, or :after. Methods with these qualifiers are called around methods, before methods, and after methods, respectively. When a method combination type is defined using the short form of define-method-combination, primary methods are methods qualified with the name of the type of method combination, and auxiliary methods have the qualifier :around. Thus the terms “primary method” and “auxiliary method” have only a relative definition within a given method combination type.

7.6.3 Agreement on Parameter Specializers and Qualifiers

Two methods are said to agree with each other on parameter specializers and qualifiers if the following conditions hold:

1. Both methods have the same number of required parameters. Suppose the parameter specializers of the two methods are P1,1 . . . P1,n and P2,1 . . . P2,n.

2. For each 1 ≤ i ≤ n, P1,i agrees with P2,i. The parameter specializer P1,i agrees with P2,i if P1,i and P2,i are the same class or if P1,i = (eql object1), P2,i = (eql object2), and (eql object1 object2). Otherwise P1,i and P2,i do not agree.

3. The two lists of qualifiers are the same under equal.

7.6.4 Congruent Lambda

These rules define the congruence of a set of lambda lists, including the lambda list of each method for a given generic function and the lambda list specified for the generic function itself, if given.

1. Each lambda list must have the same number of required parameters.

2. Each lambda list must have the same number of optional parameters. Each method can supply its own default for an optional parameter.

3. If any lambda list mentions &rest or &key, each lambda list must mention one or both of them.

4. If the generic function lambda list mentions &key, each method must accept all of the keyword names mentioned after &key, either by accepting them explicitly, by specifying &allow-other-keys, or by specifying &rest but not &key. Each method can accept additional keyword arguments of its own. The checking of the validity of keyword names is done in the generic function, not in each method. A method is invoked as if the keyword argument pair whose name is :allow-other-keys and whose value is true were supplied, though no such argument pair will be passed.

5. The use of &allow-other-keys need not be consistent across lambda lists. If &allow-other-keys is mentioned in the lambda list of any applicable method or of the generic function, any keyword arguments may be mentioned in the call to the generic function.

6. The use of &aux need not be consistent across methods.

If a method-defining operator that cannot specify generic function options creates a generic function, and if the lambda list for the method mentions keyword arguments, the lambda list of the generic function will mention &key (but no keyword arguments).

7.6.5 Keyword Arguments in Generic Functions and Methods

When a generic function or any of its methods mentions &key in a lambda list, the specific set of keyword arguments accepted by the generic function varies according to the applicable methods. The set of keyword arguments accepted by the generic function for a particular call is the union of the keyword arguments accepted by all applicable methods and the keyword arguments mentioned after &key in the generic function definition, if any. A method that has &rest but not &key does not affect the set of acceptable keyword arguments. If the lambda list of any applicable method or of the generic function definition contains &allow-other-keys, all keyword arguments are accepted by the generic function.

The lambda list congruence rules require that each method accept all of the keyword arguments mentioned after &key in the generic function definition, by accepting them explicitly, by specifying &allow-other-keys, or by specifying &rest but not &key. Each method can accept additional keyword arguments of its own, in addition to the keyword arguments mentioned in the generic function definition.

If a generic function is passed a keyword argument that no applicable method accepts, an error should be signaled; see Section 3.5 (Error Checking in Function Calls).

7.6.5.1 Examples of Keyword Arguments in Generic Functions and Methods

For example, suppose there are two methods defined for width as follows: 
(defmethod width ((c character-class) &key font) ...)
(defmethod width ((p picture-class) &key pixel-size) ...)

Assume that there are no other methods and no generic function definition for width. The evaluation of the following form should signal an error because the keyword argument :pixel-size is not accepted by the applicable method.
(width (make-instance ‘character-class :char #\Q)
:font ’baskerville :pixel-size 10)
The evaluation of the following form should signal an error.
(width (make-instance ‘picture-class :glyph (glyph #\Q))
:font ’baskerville :pixel-size 10)
The evaluation of the following form will not signal an error if the class named character-picture class is a subclass of both picture-class and character-class.
(width (make-instance ‘character-picture-class :char #\Q)
:font ’baskerville :pixel-size 10)

7.6.6 Method Selection and Combination

When a generic function is called with particular arguments, it must determine the code to execute. This code is called the effective method for those arguments. The effective method is a combination of the applicable methods in the generic function that calls some or all of the methods.

If a generic function is called and no methods are applicable, the generic function no-applicable-method is invoked, with the results from that call being used as the results of the call to the original generic function. Calling no-applicable-method takes precedence over checking for acceptable keyword arguments; see Section 7.6.5 (Keyword Arguments in Generic Functions and Methods).

When the effective method has been determined, it is invoked with the same arguments as were passed to the generic function. Whatever values it returns are returned as the values of the generic function.

7.6.6.1 Determining the Effective Method

The effective method is determined by the following three-step procedure:

1. Select the applicable methods.

2. Sort the applicable methods by precedence order, putting the most specific method first.

3. Apply method combination to the sorted list of applicable methods, producing the effective method.

7.6.6.1.1 Selecting the Applicable Methods

This step is described in Section 7.6.2 (Introduction to Methods).

7.6.6.1.2 Sorting the Applicable Methods by Precedence Order

To compare the precedence of two methods, their parameter specializers are examined in order. The default examination order is from left to right, but an alternative order may be specified by the :argument-precedence-order option to defgeneric or to any of the other operators that specify generic function options.

The corresponding parameter specializers from each method are compared. When a pair of parameter specializers agree, the next pair are compared for agreement. If all corresponding parameter specializers agree, the two methods must have different qualifiers; in this case, either method can be selected to precede the other. For information about agreement, see Section 7.6.3 (Agreement on Parameter Specializers and Qualifiers).

If some corresponding parameter specializers do not agree, the first pair of parameter specializers that do not agree determines the precedence. If both parameter specializers are classes, the more specific of the two methods is the method whose parameter specializer appears earlier in the class precedence list of the corresponding argument. Because of the way in which the set of applicable methods is chosen, the parameter specializers are guaranteed to be present in the class precedence list of the class of the argument.

If just one of a pair of corresponding parameter specializers is (eql object), the method with that parameter specializer precedes the other method. If both parameter specializers are eql expressions, the specializers must agree (otherwise the two methods would not both have been applicable to this argument).

The resulting list of applicable methods has the most specific method first and the least specific method last.

7.6.6.1.3 Applying method combination to the sorted list of applicable methods

In the simple case—if standard method combination is used and all applicable methods are primary methods—the effective method is the most specific method. That method can call the next most specific method by using the function call-next-method. The method that call-next-method will call is referred to as the next method. The predicate next-method-p tests whether a next method exists. If call-next-method is called and there is no next most specific method, the generic function no-next-method is invoked.

In general, the effective method is some combination of the applicable methods. It is described by a form that contains calls to some or all of the applicable methods, returns the value or values that will be returned as the value or values of the generic function, and optionally makes some of the methods accessible by means of call-next-method.

The role of each method in the effective method is determined by its qualifiers and the specificity of the method. A qualifier serves to mark a method, and the meaning of a qualifier is determined

by the way that these marks are used by this step of the procedure. If an applicable method has an unrecognized qualifier , this step signals an error and does not include that method in the effective method.

When standard method combination is used together with qualified methods, the effective method is produced as described in Section 7.6.6.2 (Standard Method Combination).

Another type of method combination can be specified by using the :method-combination option of defgeneric or of any of the other operators that specify generic function options. In this way this step of the procedure can be customized.

New types of method combination can be defined by using the define-method-combination macro.

7.6.6.2 Standard Method Combination

Standard method combination is supported by the class standard-generic-function. It is used if no other type of method combination is specified or if the built-in method combination type standard is specified.

Primary methods define the main action of the effective method, while auxiliary methods modify that action in one of three ways. A primary method has no method qualifiers.

An auxiliary method is a method whose qualifier is :before, :after, or :around. Standard method combination allows no more than one qualifier per method; if a method definition specifies more than one qualifier per method, an error is signaled.

A before method has the keyword :before as its only qualifier . A before method specifies code that is to be run before any primary methods.

An after method has the keyword :after as its only qualifier . An after method specifies code that is to be run after primary methods.

An around method has the keyword :around as its only qualifier . An around method specifies code that is to be run instead of other applicable methods, but which might contain explicit code which calls some of those shadowed methods (via call-next-method).

The semantics of standard method combination is as follows:

If there are any around methods, the most specific around method is called. It supplies the value or values of the generic function.

Inside the body of an around method, call-next-method can be used to call the next method. When the next method returns, the around method can execute more code, perhaps based on the returned value or values. The generic function no-next-method is invoked if call-next-method is used and there is no applicable method to call. The function next-method-p may be used to determine whether a next method exists.

If an around method invokes call-next-method, the next most specific around method is called, if one is applicable. If there are no around methods or if call-next-method is called by the least specific around method, the other methods are called as follows:

– All the before methods are called, in most-specific-first order. Their values are ignored. An error is signaled if call-next-method is used in a before method.

– The most specific primary method is called. Inside the body of a primary

method, call-next-method may be used to call the next most specific primary

method. When that method returns, the previous primary method can execute

more code, perhaps based on the returned value or values. The generic function

no-next-method is invoked if call-next-method is used and there are no more

applicable primary methods. The function next-method-p may be used to

determine whether a next method exists. If call-next-method is not used, only

the most specific primary method is called.

– All the after methods are called in most-specific-last order. Their values are

ignored. An error is signaled if call-next-method is used in an after method.

If no around methods were invoked, the most specific primary method supplies the value or values returned by the generic function. The value or values returned by the invocation of call-next-method in the least specific around method are those returned by the most specific primary method.

In standard method combination, if there is an applicable method but no applicable primary method, an error is signaled.

The before methods are run in most-specific-first order while the after methods are run in least-specific-first order. The design rationale for this difference can be illustrated with an example. Suppose class C1 modifies the behavior of its superclass, C2, by adding before methods and after methods. Whether the behavior of the class C2 is defined directly by methods on C2 or is inherited from its superclasses does not affect the relative order of invocation of methods on instances of the class C1. Class C1’s before method runs before all of class C2’s methods. Class C1’s after method runs after all of class C2’s methods.

By contrast, all around methods run before any other methods run. Thus a less specific around method runs before a more specific primary method.

If only primary methods are used and if call-next-method is not used, only the most specific method is invoked; that is, more specific methods shadow more general ones.

7.6.6.3 Declarative Method Combination

The macro define-method-combination defines new forms of method combination. It provides a mechanism for customizing the production of the effective method. The default procedure for producing an effective method is described in Section 7.6.6.1 (Determining the Effective Method).

There are two forms of define-method-combination. The short form is a simple facility while the long form is more powerful and more verbose. The long form resembles defmacro in that the body is an expression that computes a Lisp form; it provides mechanisms for implementing arbitrary control structures within method combination and for arbitrary processing of method qualifiers.

7.6.6.4 Built

The object system provides a set of built-in method combination types. To specify that a generic function is to use one of these method combination types, the name of the method combination type is given as the argument to the :method-combination option to defgeneric or to the :method-combination option to any of the other operators that specify generic function options.

The names of the built-in method combination types are listed in Figure 7–2.

|+ append max nconc progn and list min or standard|

| :- |

Figure 7–2. Built-in Method Combination Types

The semantics of the standard built-in method combination type is described in Section 7.6.6.2 (Standard Method Combination). The other built-in method combination types are called simple built-in method combination types.

The simple built-in method combination types act as though they were defined by the short form of define-method-combination. They recognize two roles for methods:

An around method has the keyword symbol :around as its sole qualifier . The meaning of :around methods is the same as in standard method combination. Use of the functions call-next-method and next-method-p is supported in around methods.

A primary method has the name of the method combination type as its sole qualifier . For example, the built-in method combination type and recognizes methods whose sole qualifier is and; these are primary methods. Use of the functions call-next-method and next-method-p is not supported in primary methods.

The semantics of the simple built-in method combination types is as follows:

If there are any around methods, the most specific around method is called. It supplies the value or values of the generic function.

Inside the body of an around method, the function call-next-method can be used to call the next method. The generic function no-next-method is invoked if call-next-method is used and there is no applicable method to call. The function next-method-p may be used to determine whether a next method exists. When the next method returns, the around method can execute more code, perhaps based on the returned value or values.

If an around method invokes call-next-method, the next most specific around method is called, if one is applicable. If there are no around methods or if call-next-method is called by the least specific around method, a Lisp form derived from the name of the built-in method combination type and from the list of applicable primary methods is evaluated to produce the value of the generic function. Suppose the name of the method combination type is operator and the call to the generic function is of the form

(generic-function a1 . . . an)

Let M1, . . . , Mk be the applicable primary methods in order; then the derived Lisp form is (operator hM1 a1 . . . ani. . .hMk a1 . . . ani)

If the expression hMi a1 . . . ani is evaluated, the method Mi will be applied to the arguments a1 . . . an. For example, if operator is or, the expression hMi a1 . . . ani is evaluated only if hMj a1 . . . ani, 1 ≤ j < i, returned nil.

The default order for the primary methods is :most-specific-first. However, the order can be reversed by supplying :most-specific-last as the second argument to the :method-combination option.

The simple built-in method combination types require exactly one qualifier per method. An error is signaled if there are applicable methods with no qualifiers or with qualifiers that are not supported by the method combination type. An error is signaled if there are applicable around methods and no applicable primary methods.

7.6.7 Inheritance of Methods

A subclass inherits methods in the sense that any method applicable to all instances of a class is also applicable to all instances of any subclass of that class.

The inheritance of methods acts the same way regardless of which of the method-defining operators created the methods.

The inheritance of methods is described in detail in Section 7.6.6 (Method Selection and Combination).