**Common Lisp the Language, 2nd Edition**

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 *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

where 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 be the set of *C* and its superclasses. Let *R* be

The set *R* may or may not generate a partial ordering, depending on
whether the , ,
are consistent; it is assumed
that they are consistent and that *R* generates a partial ordering.
When the are not consistent, it is said that *R* is inconsistent.

To compute the class precedence list for *C*,
topologically sort the elements of 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.

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