Ada Reference Manual (Ada 2022) — Legal Information

# 3.4.1 Derivation Classes

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

#### Static Semantics

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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. 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).
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Every type is one of a specific type, a class-wide type, or a universal type. A specific type is one defined by a type_declaration, a formal_type_declaration, or a full type definition embedded in another construct. Class-wide and universal types are implicitly defined, to act as representatives for an entire class of types, as follows:
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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).
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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.
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Universal types
Universal types are defined for (and belong to) the integer, real, fixed point, and access classes, and are referred to in this document as respectively, universal_integer, universal_real, universal_fixed, and universal_access. These are analogous to class-wide types for these language-defined elementary 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).
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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.
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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.
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A class-wide or universal type is said to cover all of the types in its class. In addition, universal_integer covers a type that has a specified Integer_Literal aspect, while universal_real covers a type that has a specified Real_Literal aspect (see 4.2.1). A specific type covers only itself.
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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. If a type T2 is a descendant of a type T1, then T1 is called an ancestor of T2. An ultimate ancestor of a type is an ancestor of that type that is not itself a descendant of any other type. Every untagged type has a unique ultimate ancestor.
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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.
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NOTE 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
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1 + 4 < 7
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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.

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