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 for 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.

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:

its result type is Boolean;

it is declared immediately within the same declaration
list as *D* or any partial or incomplete view of *D*; and

at least one of its operands is an access parameter
with designated type *D*.

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:

When both are of access-to-object types, the designated
types shall be the same or one shall cover the other, and if the designated
types are elementary or array types, then the designated subtypes shall
statically match;

When both are of access-to-subprogram types, the
designated profiles shall be subtype conformant.

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
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 derived type whose parent is an untagged
record type, predefined equality is defined in terms of the primitive
(possibly user-defined) equals operator of the parent type.

For a private type, if its full type is a record
type, 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:

For two composite objects or values of the same
non-array type, matching components are those that correspond to the
same component_declaration
or discriminant_specification;

For two one-dimensional arrays of the same type,
matching components are those (if any) whose index values match in the
following sense: the lower bounds of the index ranges are defined to
match, and the successors of matching indices are defined to match;

For two multidimensional arrays of the same type,
matching components are those whose index values match in successive
index positions.

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 there are no components, the result is defined
to be True;

If there are unmatched components, the result is
defined to be False;

Otherwise, the result is defined in terms of the
primitive equals operator for any matching components that are records,
and the predefined equals for any other matching components.

If the primitive equals operator for an untagged
record type is abstract, then Program_Error is raised at the point of
any (implicit) call to that abstract subprogram.

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).

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:

The membership_choice
is a *choice_*simple_expression,
and the *tested_*simple_expression
is equal to the value of the membership_choice.
If the tested type is a record type or a limited type, the test uses
the primitive equality for the type; otherwise, the test uses predefined
equality.

The membership_choice
is a range
and the value of the *tested_*simple_expression
belongs to the given range.

The membership_choice
is a subtype_mark,
the tested type is scalar, the value of the *tested_*simple_expression
belongs to the range of the named subtype, and the value satisfies the
predicates of the named subtype.

The membership_choice
is a subtype_mark,
the tested type is not scalar, the value of the *tested_*simple_expression
satisfies any constraints of the named subtype, the value satisfies the
predicates of the named subtype, and:

if the type of the *tested_*simple_expression
is class-wide, the value has a tag that identifies a type covered by
the tested type;

if the tested type is an access
type and the named subtype excludes null, the value of the *tested_*simple_expression
is not null;

if the tested type is a general
access-to-object type, the type of the *tested_*simple_expression
is convertible to the tested type and its accessibility level is no deeper
than that of the tested type; further, if the designated type of the
tested type is tagged and the *tested_*simple_expression
is nonnull, the tag of the object designated by the value of the *tested_*simple_expression
is covered by the designated type of the tested type.

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.

NOTES

14 If a composite type has components that
depend on discriminants, two values of this type have matching components
if and only if their discriminants are equal. Two nonnull arrays have
matching components if and only if the length of each dimension is the
same for both.

X /= Y

"" < "A" **and** "A" < "Aa" --* True*

"Aa" < "B"**and** "A" < "A " --* True*

"Aa" < "B"

My_Car = **null** --* True if My_Car has been set to null (see 3.10.1)*

My_Car = Your_Car --* True if we both share the same car*

My_Car.**all** = Your_Car.**all** --* True if the two cars are identical*

My_Car = Your_Car --

My_Car.

N **not** **in** 1 .. 10 --* range membership test*

Today**in** Mon .. Fri --* range membership test*

Today**in** Weekday --* subtype membership test (see 3.5.1)*

Card**in** Clubs | Spades --* list membership test (see 3.5.1)*

Archive**in** Disk_Unit --* subtype membership test (see 3.8.1)*

Tree.**all** **in** Addition'Class --* class membership test (see 3.9.1)*

Today

Today

Card

Archive

Tree.

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