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.
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