4.3.5.2 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 Spie = {pie, apple, cinnamon, fruit, spice, food, standard-object, t}. The set R = {(pie, apple), (apple, cinnamon), (apple, fruit), (cinnamon, spice),
(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),
(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),
(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),
(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.