3.2 Types and Subtypes
Static Semantics
A
type
is characterized by a set of values, and a set of
primitive operations
which implement the fundamental aspects of its semantics.
An
object of a given type is a run-time entity that contains (has)
a value of the type.
Glossary entry: 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: A subtype is a type together
with optional constraints, null exclusions, and predicates, which constrain
the values of the subtype to satisfy certain conditions. The values of
a subtype are a subset of the values of its type.
{
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Types are grouped into
categories
of types.
There exist several
language-defined
categories of types (see NOTES below), reflecting the similarity
of their values and primitive operations.
[Most categories
of types form
classes of types.]
Elementary
types are those whose values are logically indivisible;
composite
types are those whose values are composed of
component values.
Proof: {
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The formal definition of
category and
class is found in
3.4.
Glossary entry: 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: 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: An elementary type does
not have components.
Glossary entry: A composite type may
have components.
Glossary entry: A scalar type is either
a discrete type or a real type.
Glossary entry: An access type has values
that designate aliased objects. Access types correspond to “pointer
types” or “reference types” in some other languages.
Glossary entry: 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: A real type has values
that are approximations of the real numbers. Floating point and fixed
point types are real types.
Glossary entry: 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: An enumeration type is
defined by an enumeration of its values, which may be named by identifiers
or character literals.
Glossary entry: A character type is an
enumeration type whose values include characters.
Glossary entry: A record type is a composite
type consisting of zero or more named components, possibly of different
types.
Glossary entry: A record extension is
a type that extends another type by adding additional components.
Glossary entry: An array type is a composite
type whose components are all of the same type. Components are selected
by indexing.
Glossary entry: 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: 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: 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: A private extension is
a type that extends another type, with the additional properties hidden
from its clients.
Glossary entry: 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.
The elementary types are the
scalar types (
discrete and
real) and the
access
types (whose values provide access to objects or subprograms).
Discrete
types are either
integer types or are defined by enumeration of
their values (
enumeration types).
Real types
are either
floating point types or
fixed point types.
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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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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: {
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The real definitions of the views are in the referenced subclauses.
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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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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.
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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The set of possible values for an object of a given
type can be subjected to a condition that is called a
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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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.
Similarly, the associated
constraint is called the
constraint of the subtype.
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.
Such values
belong to the subtype.
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.
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 nonnull constraint."
However, we changed to this definition since we kept having to special
case composite non-array/nondiscriminated types. It also corresponds
better to the (now obsolescent) attribute 'Constrained.
For scalar types, “constrained”
means “has a nonnull 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).
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:
abstract, incomplete, interface, limited, private,
record.
Discussion: 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.
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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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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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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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
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This subclause now precedes the 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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{
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Reworded most of this subclause 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.
Ada 2005 and 2012 Editions sponsored in part by Ada-Europe
