3.2 Types and Subtypes
Static Semantics
1
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.
1.a/2
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 classes.
Most language-defined categories of types are also
classes of types The types of a given
class share a set of primitive operations. Classes
are closed under derivation; that is, if a type is in a class, then all
of its derivatives are in that class.
1.b/3
Glossary entry: A subtype is a type together
with optional constraints, null exclusions, and
predicates a constraint or null exclusion, which constrain constrains
the values of the subtype to satisfy a certain
conditions condition.
The values of a subtype are a subset of the values of its type.
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Types
are grouped into
categories classes
of types
, reflecting the similarity of their values
and primitive operations.
There exist several
language-defined categories classes
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.
2.a/2
Proof: {
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The formal definition of category and class
is found in 3.4.
2.b/2
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.
2.b.1/2
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.
2.c
Glossary entry: An elementary type does
not have components.
2.d/2
Glossary entry: A composite type may
have has components.
2.e
Glossary entry: A scalar type is either
a discrete type or a real type.
2.f
Glossary entry: An access type has values
that designate aliased objects. Access types correspond to “pointer
types” or “reference types” in some other languages.
2.g
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.
2.h
Glossary entry: A real type has values
that are approximations of the real numbers. Floating point and fixed
point types are real types.
2.i
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.
2.j
Glossary entry: An enumeration type is
defined by an enumeration of its values, which may be named by identifiers
or character literals.
2.k
Glossary entry: A character type is an
enumeration type whose values include characters.
2.l
Glossary entry: A record type is a composite
type consisting of zero or more named components, possibly of different
types.
2.m
Glossary entry: A record extension is
a type that extends another type by adding additional components.
2.n
Glossary entry: An array type is a composite
type whose components are all of the same type. Components are selected
by indexing.
2.o/2
Glossary entry: A task type is a composite
type used to represent whose
values are tasks, which are active entities which that
may execute concurrently and which can communicate
via queued task entries with other tasks.
The top-level task of a partition is called the environment task.
2.p/2
Glossary entry: A protected type is a
composite type whose components are accessible
only through one of its protected operations which synchronize protected
from concurrent access by multiple tasks.
2.q/2
Glossary entry: A private type gives
a is a partial view of a type that
reveals only some of its properties. The remaining properties are provided
by the whose full view given
elsewhere. Private types can be used for defining abstractions that hide
unnecessary details is hidden from
their its clients.
2.r/2
Glossary entry: A private extension is
a type that extends another type, with the additional
properties like a record extension, except
that the components of the extension part are hidden from its
clients.
2.s/2
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.
3
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.
A private type or private extension
represents a partial view (see 7.3) of a type,
providing support for data abstraction. A partial view is a composite
type. 4.a/2
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The set of all record types do not form a class
(because tagged record types can have private extensions), though the
set of untagged record types do. In any case, what record types had in
common in Ada 83 (component selection) is now a property of the composite
class, since all composite types (other than array types) can have discriminants.
Similarly, the set of all private types do not form a class (because
tagged private types can have record extensions), though the set of untagged
private types do. Nevertheless, the set of untagged private types is
not particularly “interesting” — more interesting is
the set of all nonlimited types, since that is what a generic formal
(nonlimited) private type matches.
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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].
4.b/2
Proof: The real
definitions of the views are in the referenced clauses.
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Certain composite types (and
partial 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.
6.a
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.
6.b
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).8/2
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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 type of the subtype.
Similarly, the associated constraint is called
the
constraint of the subtype 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.
8.a
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.
8.b
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."
8.c
Ramification: The value subset for a
subtype might be empty, and need not be a proper subset.
8.d/2
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Any name of a
category class
of types (such as “discrete”
, or “real”
, or),
or other category of types (such as “limited”
or “incomplete”) 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.”
8.e
Discussion: We use these corresponding
terms without explicitly defining them, when the meaning is obvious.
9
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).
9.a
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.
9.b
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.
9.c
Class-wide subtypes are always unconstrained.
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Any set of types can be called a “category”
of types, and any 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. 10.a
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.
10.b/2
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 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.10.d/2
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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”. forms a class in
the sense that it is closed under derivation, but the more interesting
class, from the point of generic formal type matching, is the set of
all types, limited and nonlimited, since that is what matches a generic
formal “limited” private type. Note also that a limited type
can “become nonlimited” under certain circumstances, which
makes “limited” somewhat problematic as a class of 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 classes
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
untagged record
tagged
task
protected
tagged (including interfaces)
nonlimited tagged record
limited tagged
limited tagged record
synchronized tagged
tagged task
tagged protected13/2
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There are other categories, such as The
classes “numeric” and “
discriminated nonlimited”
,
which represent other
categorization classification
dimensions
, but and
do not fit into the above strictly hierarchical picture.
13.a.1/2
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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
13.a
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.
13.b
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
13.c/2
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Added a mention of null exclusions when we're talking
about constraints (these are not constraints, but they are similar).13.d/2
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Defined an interface type to be a composite type.13.e/2
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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.13.f/2
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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.13.g/2
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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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