3.2 Types and Subtypes
Static Semantics
{type}
{primitive operation
[partial]} A
type is characterized
by a set of values, and a set of
primitive operations which implement
the fundamental aspects of its semantics.
{object
[partial]} An
object of a given type
is a run-time entity that contains (has) a value of the type.
Glossary entry: {Type} Each object
has a type. A type has an associated set of values, and a set
of primitive operations which implement the fundamental aspects
of its semantics. Types are grouped into categories. Most language-defined
categories of types are also classes of types.
Glossary entry: {Subtype} A subtype
is a type together with a constraint or null exclusion, which constrains
the values of the subtype to satisfy a certain condition. The values
of a subtype are a subset of the values of its type.
{
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{category (of types)} {class
(of types)} Types are grouped into
categories
of types.
{language-defined class (of
types)} There exist several
language-defined
categories of types (see NOTES below), reflecting the similarity
of their values and primitive operations.
{language-defined
category (of types)} [Most categories
of types form
classes of types.]
{elementary
type} Elementary types are those
whose values are logically indivisible;
{composite
type} {component}
composite types are those whose values are
composed of
component values.
{aggregate:
See also composite type} Proof: {
AI95-00442-01}
The formal definition of
category and
class is found in
3.4.
Glossary entry: {
Class (of types)}
{
closed under derivation}
A class is a set
of types that is closed under derivation, which means that if a given
type is in the class, then all types derived from that type are also
in the class. The set of types of a class share common properties, such
as their primitive operations.
Glossary entry: {Category (of types)}
A category of types is a set of types with one or more common properties,
such as primitive operations. A category of types that is closed under
derivation is also known as a class.
Glossary entry: {Elementary type}
An elementary type does not have components.
Glossary entry: {Composite type}
A composite type may have components.
Glossary entry: {Scalar type}
A scalar type is either a discrete type or a real type.
Glossary entry: {Access type}
An access type has values that designate aliased objects. Access types
correspond to “pointer types” or “reference types”
in some other languages.
Glossary entry: {
Discrete type}
A discrete type is either an integer type or an enumeration type. Discrete
types may be used, for example, in
case_statements
and as array indices.
Glossary entry: {Real type} A
real type has values that are approximations of the real numbers. Floating
point and fixed point types are real types.
Glossary entry: {Integer type}
Integer types comprise the signed integer types and the modular types.
A signed integer type has a base range that includes both positive and
negative numbers, and has operations that may raise an exception when
the result is outside the base range. A modular type has a base range
whose lower bound is zero, and has operations with “wraparound”
semantics. Modular types subsume what are called “unsigned types”
in some other languages.
Glossary entry: {Enumeration type}
An enumeration type is defined by an enumeration of its values, which
may be named by identifiers or character literals.
Glossary entry: {Character type}
A character type is an enumeration type whose values include characters.
Glossary entry: {Record type}
A record type is a composite type consisting of zero or more named components,
possibly of different types.
Glossary entry: {Record extension}
A record extension is a type that extends another type by adding additional
components.
Glossary entry: {Array type} An
array type is a composite type whose components are all of the same type.
Components are selected by indexing.
Glossary entry: {Task type} A
task type is a composite type used to represent active entities which
execute concurrently and which can communicate via queued task entries.
The top-level task of a partition is called the environment task.
Glossary entry: {Protected type}
A protected type is a composite type whose components are accessible
only through one of its protected operations which synchronize concurrent
access by multiple tasks.
Glossary entry: {Private type}
A private type gives a view of a type that reveals only some of its properties.
The remaining properties are provided by the full view given elsewhere.
Private types can be used for defining abstractions that hide unnecessary
details from their clients.
Glossary entry: {Private extension}
A private extension is a type that extends another type, with the additional
properties hidden from its clients.
Glossary entry: {Incomplete type}
An incomplete type gives a view of a type that reveals only some of its
properties. The remaining properties are provided by the full view given
elsewhere. Incomplete types can be used for defining recursive data structures.
{scalar type}
The elementary types are the
scalar types
(
discrete and
real) and the
access types (whose
values provide access to objects or subprograms).
{discrete
type} {enumeration
type} Discrete types are either
integer
types or are defined by enumeration of their values (
enumeration
types).
{real type} Real
types are either
floating point types or
fixed point types.
{
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{
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The composite types are the
record types,
record extensions,
array types,
interface types,
task types, and
protected
types.
{
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{incomplete type} {private
type} {private
extension} There can be multiple views
of a type with varying sets of operations. [An
incomplete type
represents an incomplete view (see
3.10.1)
of a type with a very restricted usage, providing support for recursive
data structures. A
private type or
private extension represents
a partial view (see
7.3) of a type, providing
support for data abstraction. The full view (see
3.2.1)
of a type represents its complete definition.] An incomplete or partial
view is considered a composite type[, even if the full view is not].
Proof: The real definitions of the views
are in the referenced clauses.
{
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{discriminant} Certain
composite types (and views thereof) have special components called
discriminants
whose values affect the presence, constraints, or initialization of other
components. Discriminants can be thought of as parameters of the type.
{
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{subcomponent} The
term
subcomponent 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.
{part
(of an object or value)} Similarly, a
part of an object or value is used to mean the whole object or
value, or any set of its subcomponents. The terms component, subcomponent,
and part are also applied to a type meaning the component, subcomponent,
or part of objects and values of the type.
Discussion: The definition of “part”
here is designed to simplify rules elsewhere. By design, the intuitive
meaning of “part” will convey the correct result to the casual
reader, while this formalistic definition will answer the concern of
the compiler-writer.
We use the term “part” when talking
about the parent part, ancestor part, or extension part of a type extension.
In contexts such as these, the part might represent an empty set of subcomponents
(e.g. in a null record extension, or a nonnull extension of a null record).
We also use “part” when specifying rules such as those that
apply to an object with a “controlled part” meaning that
it applies if the object as a whole is controlled, or any subcomponent
is.
{
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{constraint [partial]} The
set of possible values for an object of a given type can be subjected
to a condition that is called a
constraint {null
constraint} (the case of a
null constraint
that specifies no restriction is also included)[; the rules for which
values satisfy a given kind of constraint are given in
3.5
for
range_constraints,
3.6.1 for
index_constraints,
and
3.7.1 for
discriminant_constraints].
The set of possible values for an object of an access type can also be
subjected to a condition that excludes the null value (see
3.10).
{
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{
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{subtype} A
subtype 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 of the subtype.
{type
(of a subtype)} {subtype
(type of)} Similarly, the associated constraint
is called the
constraint of the subtype.
{constraint
(of a subtype)} {subtype
(constraint of)} The set of values of
a subtype consists of the values of its type that satisfy its constraint
and any exclusion of the null value.
{belong
(to a subtype)} Such values
belong
to the subtype.
{values (belonging to
a subtype)} {subtype
(values belonging to)} Discussion: We make a strong distinction
between a type and its subtypes. In particular, a type is not
a subtype of itself. There is no constraint associated with a type (not
even a null one), and type-related attributes are distinct from subtype-specific
attributes.
Discussion: We no longer use the term
"base type." All types were "base types" anyway in
Ada 83, so the term was redundant, and occasionally confusing. In the
RM95 we say simply "the type of the subtype" instead
of "the base type of the subtype."
Ramification: The value subset for a
subtype might be empty, and need not be a proper subset.
To be honest: {
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Any name of a category of types (such as “discrete”, “real”,
or “limited”) is also used to qualify its subtypes, as well
as its objects, values, declarations, and definitions, such as an “integer
type declaration” or an “integer value.” In addition,
if a term such as “parent subtype” or “index subtype”
is defined, then the corresponding term for the type of the subtype is
“parent type” or “index type.”
Discussion: We use these corresponding
terms without explicitly defining them, when the meaning is obvious.
{constrained}
{unconstrained}
{constrained (subtype)}
{unconstrained (subtype)}
A subtype is called an
unconstrained 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
constrained subtype (since
it has no unconstrained characteristics).
Discussion: In an earlier version of
Ada 9X, "constrained" meant "has a non-null constraint."
However, we changed to this definition since we kept having to special
case composite non-array/non-discriminated types. It also corresponds
better to the (now obsolescent) attribute 'Constrained.
For scalar types, “constrained”
means “has a non-null constraint”. For composite types, in
implementation terms, “constrained” means that the size of
all objects of the subtype is the same, assuming a typical implementation
model.
Class-wide subtypes are always unconstrained.
2 {
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Any set of types can be called a “category” of types, and
any set of types that is closed under derivation (see
3.4)
can be called a “class” of types. However, only certain categories
and classes are used in the description of the rules of the language
— generally those that have their own particular set of primitive
operations (see
3.2.3), or that correspond
to a set of types that are matched by a given kind of generic formal
type (see
12.5).
{language-defined
class [partial]} The following are examples
of “interesting”
language-defined classes: 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. In addition to these classes, the following are examples of
“interesting”
language-defined categories:
{language-defined
categories [partial]} abstract, incomplete,
interface, limited, private, record.
Discussion: {
value}
A
value is a run-time entity with a given type which can be assigned
to an object of an appropriate subtype of the type. {
operation}
An
operation is a program entity that operates
on zero or more operands to produce an effect, or yield a result, or
both.
Ramification: {
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Note that a type's category (and class) depends on the place of the reference
— a private type is composite outside and possibly elementary inside.
It's really the
view that is elementary or composite. Note that
although private types are composite, there are some properties that
depend on the corresponding full view — for example, parameter
passing modes, and the constraint checks that apply in various places.
{
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{
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Every property of types forms a category, but not every property of types
represents a class. For example, the set of all abstract types does not
form a class, because this set is not closed under derivation. Similarly,
the set of all interface types does not form a class.
{
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The set of limited types does not form a class (since nonlimited types
can inherit from limited interfaces), but the set of nonlimited types
does. The set of tagged record types and the set of tagged private types
do not form a class (because each of them can be extended to create a
type of the other category); that implies that the set of record types
and the set of private types also do not form a class (even though untagged
record types and untagged private types do form a class). In all of these
cases, we can talk about the category of the type; for instance, we can
talk about the “category of limited types”..
{
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Normatively, the
language-defined classes are those that are defined
to be inherited on derivation by
3.4; other
properties either aren't interesting or form categories, not classes.
{
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These language-defined categories are organized like this:
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all types
elementary
scalar
discrete
enumeration
character
boolean
other enumeration
integer
signed integer
modular integer
real
floating point
fixed point
ordinary fixed point
decimal fixed point
access
access-to-object
access-to-subprogram
composite
untagged
array
string
other array
record
task
protected
tagged (including interfaces)
nonlimited tagged record
limited tagged
limited tagged record
synchronized tagged
tagged task
tagged protected
{
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{
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There are other categories, such as “numeric” and “discriminated”,
which represent other categorization dimensions, but do not fit into
the above strictly hierarchical picture.
Discussion: {
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{
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Note that this is also true for some categories mentioned in the chart.
The category “task” includes both untagged tasks and tagged
tasks. Similarly for “protected”, “limited”,
and “nonlimited” (note that limited and nonlimited are not
shown for untagged composite types).
Wording Changes from Ada 83
This clause and its subclauses now precede the
clause and subclauses on objects and named numbers, to cut down on the
number of forward references.
We have dropped the term "base type"
in favor of simply "type" (all types in Ada 83 were "base
types" so it wasn't clear when it was appropriate/necessary to say
"base type"). Given a subtype S of a type T, we call T the
"type of the subtype S."
Wording Changes from Ada 95
{
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Added a mention of null exclusions when we're talking about constraints
(these are not constraints, but they are similar).
{
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Defined an interface type to be a composite type.
{
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Revised the wording so that it is clear that an incomplete view is similar
to a partial view in terms of the language.
{
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Added a definition of component of a type, subcomponent of a type, and
part of a type. These are commonly used in the standard, but they were
not previously defined.
{
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Reworded most of this clause to use category rather than class, since
so many interesting properties are not, strictly speaking, classes. Moreover,
there was no normative description of exactly which properties formed
classes, and which did not. The real definition of class, along with
a list of properties, is now in
3.4.
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