# 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 a given subtype or range, or has a tag that identifies a type that is covered by a given type. Membership tests are allowed for all types.

## Name Resolution Rules

The tested type of a membership test is the type of the range or the type determined by the subtype_mark. If the tested type is tagged, then the simple_expression shall resolve to be of a type that covers or is covered by the tested type; if untagged, the expected type for the simple_expression is the tested type.

## Legality Rules

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

## Static Semantics

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:

```function "=" (Left, Right : T) return Boolean
function "/=" (Left, Right : T) return Boolean
```

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

```function "<" (Left, Right : T) return Boolean
function "<=" (Left, Right : T) return Boolean
function ">" (Left, Right : T) return Boolean
function ">=" (Left, Right : T) return Boolean
```

## Dynamic Semantics

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 of the parent type and of any tagged components of 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 tagged, predefined equality is defined in terms of the primitive equals operator of the full type; if the full type is untagged, 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 tagged components, and the predefined equals for any matching untagged components.
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, the simple_expression and the range (if any) are evaluated in an arbitrary order.

A membership test using in yields the result True if:

• The tested type is scalar, and the value of the simple_expression belongs to the given range, or the range of the named subtype; or
• The tested type is not scalar, and the value of the simple_expression satisfies any constraints of the named subtype, and, if the type of the simple_expression is class-wide, the value has a tag that identifies a type covered by 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.

## Implementation Requirements

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.