4.5.2 Relational Operators and Membership Tests

The equality operators = (equals) and /= (not equals) are predefined for nonlimited types. The other relational_operators are the ordering operators < (less than), <= (less than or equal), > (greater than), and >= (greater than or equal). The ordering operators are predefined for scalar types, and for discrete array types, that is, one-dimensional array types whose components are of a discrete type. 

A membership test, using in or not in, determines whether or not a value belongs to any given subtype or range, is equal to any given value, has a tag that identifies a type that is covered by a given type, or is convertible to and has an accessibility level appropriate for a given access type. Membership tests are allowed for all types.

The tested type of a membership test is determined by the membership_choices of the membership_choice_list. Either all membership_choices of the membership_choice_list shall resolve to the same type, which is the tested type; or each membership_choice shall be of an elementary type, and the tested type shall be covered by each of these elementary types.

 If the tested type is tagged, then the tested_simple_expression shall resolve to be of a type that is convertible (see 4.6) to the tested type; if untagged, the expected type of the tested_simple_expression is the tested type. The expected type of a choice_simple_expression in a membership_choice, and of a simple_expression of a range in a membership_choice, is the tested type of the membership operation.

For a membership test, if the tested_simple_expression is of a tagged class-wide type, then the tested type shall be (visibly) tagged. 

 If a membership test includes one or more choice_simple_expressions and the tested type of the membership test is limited, then the tested type of the membership test shall have a visible primitive equality operator; if the tested type of the membership test is nonlimited with a user-defined primitive equality operator that is defined at a point where the type is limited, the tested type shall be a record type or record extension.

The result type of a membership test is the predefined type Boolean.

The equality operators are predefined for every specific type T that is not limited, and not an anonymous access type, with the following specifications:

 The following additional equality operators for the universal_access type are declared in package Standard for use with anonymous access types: 

The ordering operators are predefined for every specific scalar type T, and for every discrete array type T, with the following specifications: 

 At least one of the operands of an equality operator for universal_access shall be of a specific anonymous access type. Unless the predefined equality operator is identified using an expanded name with prefix denoting the package Standard, neither operand shall be of an access-to-object type whose designated type is D or D'Class, where D has a user-defined primitive equality operator such that: 

 At least one of the operands of the equality operators for universal_access shall be of type universal_access, or both shall be of access-to-object types, or both shall be of access-to-subprogram types. Further: 

 If the profile of an explicitly declared primitive equality operator of an untagged record type is type conformant with that of the corresponding predefined equality operator, the declaration shall occur before the type is frozen. In addition, no type shall have been derived from the untagged record type before the declaration of the primitive equality operator. In addition to the places where Legality Rules normally apply (see 12.3), this rule applies also in the private part of an instance of a generic unit. 

For discrete types, the predefined relational operators are defined in terms of corresponding mathematical operations on the position numbers of the values of the operands.

For real types, the predefined relational operators are defined in terms of the corresponding mathematical operations on the values of the operands, subject to the accuracy of the type. 

Two access-to-object values are equal if they designate the same object, or if both are equal to the null value of the access type.

Two access-to-subprogram values are equal if they are the result of the same evaluation of an Access attribute_reference, or if both are equal to the null value of the access type. Two access-to-subprogram values are unequal if they designate different subprograms. It is unspecified whether two access values that designate the same subprogram but are the result of distinct evaluations of Access attribute_references are equal or unequal. 

For a type extension, predefined equality is defined in terms of the primitive (possibly user-defined) equals operator for the parent type and for any components that have a record type in the extension part, and predefined equality for any other components not inherited from the parent type. 

For a private type, if its full type is a record type or a record extension, predefined equality is defined in terms of the primitive equals operator of the full type; otherwise, predefined equality for the private type is that of its full type.

For other composite types, the predefined equality operators (and certain other predefined operations on composite types — see 4.5.1 and 4.6) are defined in terms of the corresponding operation on matching components, defined as follows: 

The analogous definitions apply if the types of the two objects or values are convertible, rather than being the same. 

Given the above definition of matching components, the result of the predefined equals operator for composite types (other than for those composite types covered earlier) is defined as follows: 

  If the primitive equals operator for an untagged record type is abstract, then Program_Error is raised at the point of any call to that abstract subprogram, implicitly as part of an equality operation on an enclosing composite object, or in an instance of a generic with a formal private type where the actual type is a record type with an abstract "=". 

  For any composite type, the order in which "=" is called for components is unspecified. Furthermore, if the result can be determined before calling "=" on some components, it is unspecified whether "=" is called on those components.

The predefined "/=" operator gives the complementary result to the predefined "=" operator. 

For a discrete array type, the predefined ordering operators correspond to lexicographic order using the predefined order relation of the component type: A null array is lexicographically less than any array having at least one component. In the case of nonnull arrays, the left operand is lexicographically less than the right operand if the first component of the left operand is less than that of the right; otherwise, the left operand is lexicographically less than the right operand only if their first components are equal and the tail of the left operand is lexicographically less than that of the right (the tail consists of the remaining components beyond the first and can be null).

  An individual membership test is the membership test of a single membership_choice.

For the evaluation of a membership test using in whose membership_choice_list has a single membership_choice, the tested_simple_expression and the membership_choice are evaluated in an arbitrary order; the result is the result of the individual membership test for the membership_choice.

  For the evaluation of a membership test using in whose membership_choice_list has more than one membership_choice, the tested_simple_expression of the membership test is evaluated first and the result of the operation is equivalent to that of a sequence consisting of an individual membership test on each membership_choice combined with the short-circuit control form or else.

An individual membership test yields the result True if: 

Otherwise, the test yields the result False.

A membership test using not in gives the complementary result to the corresponding membership test using in.

  For all nonlimited types declared in language-defined packages, the "=" and "/=" operators of the type shall behave as if they were the predefined equality operators for the purposes of the equality of composite types and generic formal types.

Examples of expressions involving relational operators and membership tests: