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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. 
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.
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.
The composite types are the record types, record extensions, array types, interface types, task types, and protected types. 
  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. 
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.
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. 
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).
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.
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). 
2  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. 
These language-defined categories are organized like this: 
all types
               other enumeration
               signed integer
               modular integer
            floating point
            fixed point
               ordinary fixed point
               decimal fixed point
            other array
      tagged (including interfaces)
         nonlimited tagged record
         limited tagged
            limited tagged record
            synchronized tagged
               tagged task
               tagged protected
There are other categories, such as “numeric” and “discriminated”, which represent other categorization dimensions, but do not fit into the above strictly hierarchical picture.

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