-An \emph{object} maintains \emph{state} and exhibits \emph{behaviour}. An
-object's state is maintained in named \emph{slots}, each of which can store a
-C value of an appropriate (scalar or aggregate) type. An object's behaviour
-is stimulated by sending it \emph{messages}. A message has a name, and may
-carry a number of arguments, which are C values; sending a message may result
-in the state of receiving object (or other objects) being changed, and a C
-value being returned to the sender.
-
-Every object is a (direct) instance of some \emph{class}. The class
-determines which slots its instances have, which messages its instances can
-be sent, and which methods are invoked when those messages are received. The
-Sod translator's main job is to read class definitions and convert them into
-appropriate C declarations, tables, and functions. An object cannot
-(usually) change its direct class, and the direct class of an object is not
-affected by, for example, the static type of a pointer to it.
+An \emph{object} maintains \emph{state} and exhibits \emph{behaviour}.
+(Here, we're using the term `object' in the usual sense of `object-oriented
+programming', rather than that of the ISO~C standard. Once we have defined
+an `instance' below, we shall generally prefer that term, so as to prevent
+further confusion between these two uses of the word.)
+
+An object's state is maintained in named \emph{slots}, each of which can
+store a C value of an appropriate (scalar or aggregate) type. An object's
+behaviour is stimulated by sending it \emph{messages}. A message has a name,
+and may carry a number of arguments, which are C values; sending a message
+may result in the state of receiving object (or other objects) being changed,
+and a C value being returned to the sender.
+
+Every object is a \emph{direct instance} of exactly one \emph{class}. The
+class determines which slots its instances have, which messages its instances
+can be sent, and which \emph{methods} are invoked when those messages are
+received. The Sod translator's main job is to read class definitions and
+convert them into appropriate C declarations, tables, and functions. An
+object cannot (usually) change its direct class, and the direct class of an
+object is not affected by, for example, the static type of a pointer to it.
+
+If an object~$x$ is a direct instance of some class~$C$, then we say that $C$
+is \emph{the class of}~$x$. Note that the class of an object is a property
+of the object's value at runtime, and not of C's compile-time type system.
+We shall be careful in distinguishing C's compile-time notion of \emph{type}
+from Sod's run-time notion of \emph{class}.