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3.4.1 Derivation Classes

1
In addition to the various language-defined classes of types, types can be grouped into derivation classes

Static Semantics

2/2
{AI95-00251-01} {AI95-00401-01} {derived from (directly or indirectly)} A derived type is derived from its parent type directly; it is derived indirectly from any type from which its parent type is derived. A derived type, interface type, type extension, task type, protected type, or formal derived type is also derived from every ancestor of each of its progenitor types, if any. {derivation class (for a type)} {root type (of a class)} {rooted at a type} The derivation class of types for a type T (also called the class rooted at T) is the set consisting of T (the root type of the class) and all types derived from T (directly or indirectly) plus any associated universal or class-wide types (defined below). 
2.a
Discussion: Note that the definition of “derived from” is a recursive definition. We don't define a root type for all interesting language-defined classes, though presumably we could. 
2.b
To be honest: By the class-wide type “associated” with a type T, we mean the type T'Class. Similarly, the universal type associated with root_integer, root_real, and root_fixed are universal_integer, universal_real, and universal_fixed, respectively. 
3/2
{AI95-00230-01} Every type is either a specific type, a class-wide type, or a universal type. {specific type} A specific type is one defined by a type_declaration, a formal_type_declaration, or a full type definition embedded in another construct a declaration for an object. Class-wide and universal types are implicitly defined, to act as representatives for an entire class of types, as follows: 
3.a
To be honest: The root types root_integer, root_real, and root_fixed are also specific types. They are declared in the specification of package Standard. 
4
{class-wide type} Class-wide types 

Class-wide types are defined for [(and belong to)] each derivation class rooted at a tagged type (see 3.9). Given a subtype S of a tagged type T, S'Class is the subtype_mark for a corresponding subtype of the tagged class-wide type T'Class. Such types are called “class-wide” because when a formal parameter is defined to be of a class-wide type T'Class, an actual parameter of any type in the derivation class rooted at T is acceptable (see 8.6).
5
{first subtype} The set of values for a class-wide type T'Class is the discriminated union of the set of values of each specific type in the derivation class rooted at T (the tag acts as the implicit discriminant — see 3.9). Class-wide types have no primitive subprograms of their own. However, as explained in 3.9.2, operands of a class-wide type T'Class can be used as part of a dispatching call on a primitive subprogram of the type T. The only components [(including discriminants)] of T'Class that are visible are those of T. If S is a first subtype, then S'Class is a first subtype. 
5.a
Reason: We want S'Class to be a first subtype when S is, so that an attribute_definition_clause like “for S'Class'Output use ...;” will be legal. 
6/2
{AI95-00230-01} {universal type} Universal types 

Universal types are defined for [(and belong to)] the integer, real, and fixed point, and access classes, and are referred to in this standard as respectively, universal_integer, universal_real, and universal_fixed, and universal_access. These are analogous to class-wide types for these language-defined elementary numeric classes. As with class-wide types, if a formal parameter is of a universal type, then an actual parameter of any type in the corresponding class is acceptable. In addition, a value of a universal type (including an integer or real numeric_literal, or the literal null) is “universal” in that it is acceptable where some particular type in the class is expected (see 8.6).
7
The set of values of a universal type is the undiscriminated union of the set of values possible for any definable type in the associated class. Like class-wide types, universal types have no primitive subprograms of their own. However, their “universality” allows them to be used as operands with the primitive subprograms of any type in the corresponding class. 
7.a
Discussion: A class-wide type is only class-wide in one direction, from specific to class-wide, whereas a universal type is class-wide (universal) in both directions, from specific to universal and back.
7.b/2
{AI95-00230-01} We considered defining class-wide or perhaps universal types for all derivation classes, not just tagged classes and these four elementary three numeric classes. However, this was felt to overly weaken the strong-typing model in some situations. Tagged types preserve strong type distinctions thanks to the run-time tag. Class-wide or universal types for untagged types would weaken the compile-time type distinctions without providing a compensating run-time-checkable distinction.
7.c
We considered defining standard names for the universal numeric types so they could be used in formal parameter specifications. However, this was felt to impose an undue implementation burden for some implementations. 
7.d
To be honest: Formally, the set of values of a universal type is actually a copy of the undiscriminated union of the values of the types in its class. This is because we want each value to have exactly one type, with explicit or implicit conversion needed to go between types. An alternative, consistent model would be to associate a class, rather than a particular type, with a value, even though any given expression would have a particular type. In that case, implicit type conversions would not generally need to change the value, although an associated subtype conversion might need to. 
8
{root_integer [partial]} {root_real [partial]} The integer and real numeric classes each have a specific root type in addition to their universal type, named respectively root_integer and root_real.
9
{cover (a type)} A class-wide or universal type is said to cover all of the types in its class. A specific type covers only itself.
10/2
 {AI95-00230-01} {AI95-00251-01} {descendant (of a type)} A specific type T2 is defined to be a descendant of a type T1 if T2 is the same as T1, or if T2 is derived (directly or indirectly) from T1. A class-wide type T2'Class is defined to be a descendant of type T1 if T2 is a descendant of T1. Similarly, the numeric universal types are defined to be descendants of the root types of their classes. {ancestor (of a type)} If a type T2 is a descendant of a type T1, then T1 is called an ancestor of T2. {ultimate ancestor (of a type)} {ancestor (ultimate)} An The ultimate ancestor of a type is an the ancestor of that the type that is not itself a descendant of any other type. Every untagged type has a unique ultimate ancestor. 
10.a
Ramification: A specific type is a descendant of itself. Class-wide types are considered descendants of the corresponding specific type, and do not have any descendants of their own.
10.b
A specific type is an ancestor of itself. The root of a derivation class is an ancestor of all types in the class, including any class-wide types in the class. 
10.c
Discussion: The terms root, parent, ancestor, and ultimate ancestor are all related. For example: 
10.d/2
10.e
10.f
10.g
10.h/2
Glossary entry: {Ancestor} An ancestor of a type is the type itself or, in the case of a type derived from other types, its parent type or one of its progenitor types or one of their ancestors. Note that ancestor and descendant are inverse relationships.
10.i/2
Glossary entry: {Descendant} A type is a descendant of itself, its parent and progenitor types, and their ancestors. Note that descendant and ancestor are inverse relationships.
11
{inherited (from an ancestor type)} An inherited component [(including an inherited discriminant)] of a derived type is inherited from a given ancestor of the type if the corresponding component was inherited by each derived type in the chain of derivations going back to the given ancestor.
NOTES
12
20  Because operands of a universal type are acceptable to the predefined operators of any type in their class, ambiguity can result. For universal_integer and universal_real, this potential ambiguity is resolved by giving a preference (see 8.6) to the predefined operators of the corresponding root types (root_integer and root_real, respectively). Hence, in an apparently ambiguous expression like 
13
1 + 4 < 7
14
where each of the literals is of type universal_integer, the predefined operators of root_integer will be preferred over those of other specific integer types, thereby resolving the ambiguity.
14.a
Ramification: Except for this preference, a root numeric type is essentially like any other specific type in the associated numeric class. In particular, the result of a predefined operator of a root numeric type is not “universal” (implicitly convertible) even if both operands were. 

Wording Changes from Ada 95

14.b/2
{AI95-00230-01} Updated the wording to define the universal_access type. This was defined to make null for anonymous access types sensible.
14.c/2
{AI95-00251-01} {AI95-00401-01} The definitions of ancestors and descendants were updated to allow multiple ancestors (necessary to support interfaces).

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