class whose subclass appears earliest in $C$'s local precedence order.
\end{itemize}
+\begin{figure}
+ \centering
+ \begin{tikzpicture}[x=7.5mm, y=-14mm, baseline=(current bounding box.east)]
+ \node[lit] at ( 0, 0) (R) {SodObject};
+ \node[lit] at (-3, +1) (A) {A}; \draw[->] (A) -- (R);
+ \node[lit] at (-1, +1) (B) {B}; \draw[->] (B) -- (R);
+ \node[lit] at (+1, +1) (C) {C}; \draw[->] (C) -- (R);
+ \node[lit] at (+3, +1) (D) {D}; \draw[->] (D) -- (R);
+ \node[lit] at (-2, +2) (E) {E}; \draw[->] (E) -- (A);
+ \draw[->] (E) -- (B);
+ \node[lit] at (+2, +2) (F) {F}; \draw[->] (F) -- (A);
+ \draw[->] (F) -- (D);
+ \node[lit] at (-1, +3) (G) {G}; \draw[->] (G) -- (E);
+ \draw[->] (G) -- (C);
+ \node[lit] at (+1, +3) (H) {H}; \draw[->] (H) -- (F);
+ \node[lit] at ( 0, +4) (I) {I}; \draw[->] (I) -- (G);
+ \draw[->] (I) -- (H);
+ \end{tikzpicture}
+ \quad
+ \vrule
+ \quad
+ \begin{minipage}[c]{0.45\hsize}
+ \begin{nprog}
+ class A: SodObject \{ \}\quad\=@/* @|A|, @|SodObject| */ \\
+ class B: SodObject \{ \}\>@/* @|B|, @|SodObject| */ \\
+ class C: SodObject \{ \}\>@/* @|B|, @|SodObject| */ \\
+ class D: SodObject \{ \}\>@/* @|B|, @|SodObject| */ \\+
+ class E: A, B \{ \}\quad\=@/* @|E|, @|A|, @|B|, \dots */ \\
+ class F: A, D \{ \}\>@/* @|F|, @|A|, @|D|, \dots */ \\+
+ class G: E, C \{ \}\>@/* @|G|, @|E|, @|A|,
+ @|B|, @|C|, \dots */ \\
+ class H: F \{ \}\>@/* @|H|, @|F|, @|A|, @|D|, \dots */ \\+
+ class I: G, H \{ \}\>@/* @|I|, @|G|, @|E|, @|H|, @|F|,
+ @|A|, @|B|, @|C|, @|D|, \dots */
+ \end{nprog}
+ \end{minipage}
+
+ \caption{An example class graph and class precedence lists}
+ \label{fig:concepts.classes.cpl-example}
+\end{figure}
+
+\begin{example}
+ Consider the class relationships shown in
+ \xref{fig:concepts.classes.cpl-example}.
+
+ \begin{itemize}
+
+ \item @|SodObject| has no proper superclasses. Its class precedence list
+ is therefore simply $\langle @|SodObject| \rangle$.
+
+ \item In general, if $X$ is a direct subclass only of $Y$, and $Y$'s class
+ precedence list is $\langle Y, \ldots \rangle$, then $X$'s class
+ precedence list is $\langle X, Y, \ldots \rangle$. This explains $A$,
+ $B$, $C$, $D$, and $H$.
+
+ \item $E$'s list is found by merging its local precedence list $\langle E,
+ A, B \rangle$ with the class precedence lists of its direct superclasses,
+ which are $\langle A, @|SodObject| \rangle$ and $\langle B, @|SodObject|
+ \rangle$. Clearly, @|SodObject| must be last, and $E$'s local precedence
+ list orders the rest, giving $\langle E, A, B, @|SodObject|, \rangle$.
+ $F$ is similar.
+
+ \item We determine $G$'s class precedence list by merging the three lists
+ $\langle G, E, C \rangle$, $\langle E, A, B, @|SodObject| \rangle$, and
+ $\langle C, @|SodObject| \rangle$. The class precedence list begins
+ $\langle G, E, \ldots \rangle$, but the individual lists don't order $A$
+ and $C$. Comparing these to $G$'s direct superclasses, we see that $A$
+ is a subclass of $E$, while $C$ is a subclass of -- indeed equal to --
+ $C$; so $A$ must precede $C$, as must $B$, and the final list is $\langle
+ G, E, A, B, C, @|SodObject| \rangle$.
+
+ \item Finally, we determine $I$'s class precedence list by merging $\langle
+ I, G, H \rangle$, $\langle G, E, A, B, C, @|SodObject| \rangle$, and
+ $\langle H, F, A, D, @|SodObject| \rangle$. The list begins $\langle I,
+ G, \ldots \rangle$, and then we must break a tie between $E$ and $H$; but
+ $E$ is a subclass of $G$, so $E$ wins. Next, $H$ and $F$ must precede
+ $A$, since these are ordered by $H$'s class precedence list. Then $B$
+ and $C$ precede $D$, since the former are superclasses of $G$, and the
+ final list is $\langle I, G, E, H, F, A, B, C, D, @|SodObject| \rangle$.
+
+ \end{itemize}
+
+ (This example combines elements from \cite{Barrett:1996:MSL} and
+ \cite{Ducournau:1994:PMM}.)
+\end{example}
+
\subsubsection{Class links and chains}
The definition for a class $C$ may distinguish one of its proper superclasses
as being the \emph{link superclass} for class $C$. Not every class need have
%%%--------------------------------------------------------------------------
\section{Metaclasses} \label{sec:concepts.metaclasses}
+In Sod, every object is an instance of some class, and -- unlike, say,
+\Cplusplus\ -- classes are proper objects. It follows that, in Sod, every
+class~$C$ is itself an instance of some class~$M$, which is called $C$'s
+\emph{metaclass}. Metaclass instances are usually constructed statically, at
+compile time, and marked read-only.
+
+As an added complication, Sod classes, and other metaobjects such as
+messages, methods, slots and so on, also have classes \emph{at translation
+time}. These translation-time metaclasses are not Sod classes; they are CLOS
+classes, implemented in Common Lisp.
+
+
+\subsection{Runtime metaclasses}
+\label{sec:concepts.metaclasses.runtime}
+
+Like other classes, metaclasses can declare messages, and define slots and
+methods. Slots defined by the metaclass are called \emph{class slots}, as
+opposed to \emph{instance slots}. Similarly, messages and methods defined by
+the metaclass are termed \emph{class messages} and \emph{class methods}
+respectively, though these are used much less frequently.
+
+\subsubsection{The braid}
+Every object is an instance of some class. There are only finitely many
+classes.
+
+\begin{figure}
+ \centering
+ \begin{tikzpicture}
+ \node[lit] (obj) {SodObject};
+ \node[lit] (cls) [right=10mm of obj] {SodClass};
+ \draw [->, dashed] (obj) to[bend right] (cls);
+ \draw [->] (cls) to[bend right] (obj);
+ \draw [->, dashed] (cls) to[loop right] (cls);
+ \end{tikzpicture}
+ \qquad
+ \fbox{\ \begin{tikzpicture}
+ \node (subclass) {subclass of};
+ \node (instance) [below=\jot of subclass] {instance of};
+ \draw [->] ($(subclass.west) - (10mm, 0)$) -- ++(8mm, 0);
+ \draw [->, dashed] ($(instance.west) - (10mm, 0)$) -- ++(8mm, 0);
+ \end{tikzpicture}}
+ \caption{The Sod braid} \label{fig:concepts.metaclasses.braid}
+\end{figure}
+
+Consider the directed graph whose nodes are classes, and where there is an
+arc from $C$ to $D$ if and only if $C$ is an instance of $D$. There are only
+finitely many nodes. Every node has an arc leaving it, because every object
+-- and hence every class -- is an instance of some class. Therefore this
+graph must contain at least one cycle.
+
+In Sod, this situation is resolved in the simplest manner possible:
+@|SodClass| is the only predefined metaclass, and it is an instance of
+itself. The only other predefined class is @|SodObject|, which is also an
+instance of @|SodClass|. There is exactly one root class, namely
+@|SodObject|; consequently, @|SodClass| is a direct subclass of @|SodObject|.
+
+\Xref{fig:concepts.metaclasses.braid} shows a diagram of this situation.
+
+\subsubsection{Class slots and initializers}
+Instance initializers were described in \xref{sec:concepts.classes.slots}. A
+class can also define \emph{class initializers}, which provide values for
+slots defined by its metaclass. The initial value for a class slot is
+determined as follows.
+\begin{itemize}
+\item Nonstandard slot classes may be initialized by custom Lisp code. For
+ example, all of the slots defined by @|SodClass| are of this kind. User
+ initializers are not permitted for such slots.
+\item If the class or any of its superclasses defines a class initializer for
+ the slot, then the class initializer defined by the most specific such
+ superclass is used.
+\item Otherwise, if the metaclass or one of its superclasses defines an
+ instance initializer, then the instance initializer defined by he most
+ specific such class is used.
+\item Otherwise there is no initializer, and an error will be reported.
+\end{itemize}
+Initializers for class slots must be constant expressions (for scalar slots)
+or aggregate initializers containing constant expressions.
+
+\subsubsection{Metaclass selection and consistency}
+Sod enforces a \emph{metaclass consistency rule}: if $C$ has metaclass $M$,
+then any subclass $C$ must have a metaclass which is a subclass of $M$.
+
+The definition of a new class can name the new class's metaclass explicitly,
+by defining a @|metaclass| property; the Sod translator will verify that the
+choice of metaclass is acceptable.
+
+If no @|metaclass| property is given, then the translator will select a
+default metaclass as follows. Let $C_1$, $C_2$, \dots, $C_n$ be the direct
+superclasses of the new class, and let $M_1$, $M_2$, \dots, $M_n$ be their
+respective metaclasses (not necessarily distinct). If there exists exactly
+one minimal metaclass $M_i$, i.e., there exists an $i$, with $1 \le i \le n$,
+such that $M_i$ is a subclass of every $M_j$, for $1 \le j \le n$, then $M_i$
+is selected as the new class's metaclass. Otherwise the situation is
+ambiguous and an error will be reported. Usually, the ambiguity can be
+resolved satisfactorily by defining a new class $M^*$ as a direct subclass of
+the minimal $M_j$.
+
+
+\subsection{Translation-time metaobjects}
+\label{sec:concepts.metaclasses.compile-time}
+
+
+
+\fixme{unwritten}
+
%%%--------------------------------------------------------------------------
\section{Compatibility considerations} \label{sec:concepts.compatibility}
~mdw / sod / blobdiff