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<H1> 3.2 Types and Subtypes</H1>
<H4 ALIGN=CENTER>Static Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>1</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1293"></A><A NAME="I1294"></A>A <I>type</I>
is characterized by a set of values, and a set of <I>primitive operations</I>
which implement the fundamental aspects of its semantics. <A NAME="I1295"></A>An
<I>object</I> of a given type is a run-time entity that contains (has)
a value of the type. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>2</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1296"></A>Types are grouped into <I>classes</I>
of types, reflecting the similarity of their values and primitive operations.
<A NAME="I1297"></A>There exist several <I>language-defined classes</I>
of types (see NOTES below). <A NAME="I1298"></A><I>Elementary</I> types
are those whose values are logically indivisible; <A NAME="I1299"></A><A NAME="I1300"></A><I>composite</I>
types are those whose values are composed of <I>component</I> values.
<A NAME="I1301"></A></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>3</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1302"></A>The elementary types are the
<I>scalar</I> types (<I>discrete</I> and <I>real</I>) and the <I>access</I>
types (whose values provide access to objects or subprograms). <A NAME="I1303"></A><A NAME="I1304"></A>Discrete
types are either <I>integer</I> types or are defined by enumeration of
their values (<I>enumeration</I> types). <A NAME="I1305"></A>Real types
are either <I>floating point</I> types or <I>fixed point</I> types.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>4</FONT></DIV>
<DIV Class="Normal"> The composite types are the <I>record</I> types,
<I>record extensions</I>, <I>array</I> types, <I>task</I> types, and
<I>protected</I> types. <A NAME="I1306"></A><A NAME="I1307"></A>A <I>private</I>
type or <I>private extension</I> represents a partial view (see <A HREF="RM-7-3.html">7.3</A>)
of a type, providing support for data abstraction. A partial view is
a composite type. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>5</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1308"></A>Certain composite types (and
partial views thereof) have special components called <I>discriminants</I>
whose values affect the presence, constraints, or initialization of other
components. Discriminants can be thought of as parameters of the type.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>6</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1309"></A>The term <I>subcomponent</I>
is used in this International Standard in place of the term component
to indicate either a component, or a component of another subcomponent.
Where other subcomponents are excluded, the term component is used instead.
<A NAME="I1310"></A>Similarly, a <I>part</I> of an object or value is
used to mean the whole object or value, or any set of its subcomponents.
</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>7</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1311"></A>The set of possible values
for an object of a given type can be subjected to a condition that is
called a <I>constraint</I> <A NAME="I1312"></A>(the case of a <I>null
constraint</I> that specifies no restriction is also included); the rules
for which values satisfy a given kind of constraint are given in <A HREF="RM-3-5.html">3.5</A>
for <FONT FACE="Arial, Helvetica">range_constraint</FONT>s, <A HREF="RM-3-6-1.html">3.6.1</A>
for <FONT FACE="Arial, Helvetica">index_constraint</FONT>s, and <A HREF="RM-3-7-1.html">3.7.1</A>
for <FONT FACE="Arial, Helvetica">discriminant_constraint</FONT>s.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>8</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1313"></A>A <I>subtype</I> of a given
type is a combination of the type, a constraint on values of the type,
and certain attributes specific to the subtype. The given type is called
the type <I>of</I> the subtype. Similarly, the associated constraint
is called the constraint <I>of</I> the subtype. The set of values of
a subtype consists of the values of its type that satisfy its constraint.
<A NAME="I1314"></A>Such values <I>belong</I> to the subtype. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>9</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1315"></A><A NAME="I1316"></A><A NAME="I1317"></A><A NAME="I1318"></A>A
subtype is called an <I>unconstrained</I> subtype if its type has unknown
discriminants, or if its type allows range, index, or discriminant constraints,
but the subtype does not impose such a constraint; otherwise, the subtype
is called a <I>constrained</I> subtype (since it has no unconstrained
characteristics). </DIV>
<DIV Class="NotesHeader"><FONT SIZE=-1>NOTES</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>10</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>2 Any set of types that is
closed under derivation (see <A HREF="RM-3-4.html">3.4</A>) can be called
a ``class'' of types. However, only certain classes are used in the description
of the rules of the language -- generally those that have their own particular
set of primitive operations (see <A HREF="RM-3-2-3.html">3.2.3</A>),
or that correspond to a set of types that are matched by a given kind
of generic formal type (see <A HREF="RM-12-5.html">12.5</A>). <A NAME="I1319"></A>The
following are examples of ``interesting'' <I>language-defined classes</I>:
elementary, scalar, discrete, enumeration, character, boolean, integer,
signed integer, modular, real, floating point, fixed point, ordinary
fixed point, decimal fixed point, numeric, access, access-to-object,
access-to-subprogram, composite, array, string, (untagged) record, tagged,
task, protected, nonlimited. Special syntax is provided to define types
in each of these classes. </FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>11</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>These language-defined classes are organized
like this: </FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>12</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1>all types<BR>
elementary<BR>
scalar<BR>
discrete<BR>
enumeration<BR>
character<BR>
boolean<BR>
other enumeration<BR>
integer<BR>
signed integer<BR>
modular integer<BR>
real<BR>
floating point<BR>
fixed point<BR>
ordinary fixed point<BR>
decimal fixed point<BR>
access<BR>
access-to-object<BR>
access-to-subprogram<BR>
composite<BR>
array<BR>
string<BR>
other array<BR>
untagged record<BR>
tagged<BR>
task<BR>
protected</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>13</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>The classes ``numeric'' and ``nonlimited''
represent other classification dimensions and do not fit into the above
strictly hierarchical picture. </FONT></DIV>
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