# 4.5 Operators and Expression Evaluation

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[ The language defines the following six categories of operators (given in order of increasing precedence). The corresponding `operator_symbol`

s, and only those, can be used as `designator`

s in declarations of functions for user-defined operators. See 6.6, “Overloading of Operators”.]

#### Syntax

2`logical_operator`

` ::= `

**and** | **or** | **xor**

3`relational_operator`

` ::= `

= | /= | < | <= | > | >=

4`binary_adding_operator`

` ::= `

+ | – | &

5`unary_adding_operator`

` ::= `

+ | –

6`multiplying_operator`

` ::= `

* | / | **mod** | **rem**

7`highest_precedence_operator`

` ::= `

** | **abs** | **not**

#### Static Semantics

8For a sequence of operators of the same precedence level, the operators are associated with their operands in textual order from left to right. Parentheses can be used to impose specific associations.

For each form of type definition, certain of the above operators are *predefined*; that is, they are implicitly declared immediately after the type definition. For each such implicit operator declaration, the parameters are called Left and Right for *binary* operators; the single parameter is called Right for *unary* operators. [An expression of the form X op Y, where op is a binary operator, is equivalent to a `function_call`

of the form "op"(X, Y). An expression of the form op Y, where op is a unary operator, is equivalent to a `function_call`

of the form "op"(Y). The predefined operators and their effects are described in subclauses 4.5.1 through 4.5.6.]

#### Dynamic Semantics

10[ The predefined operations on integer types either yield the mathematically correct result or raise the exception Constraint_Error. For implementations that support the Numerics Annex, the predefined operations on real types yield results whose accuracy is defined in Annex G, or raise the exception Constraint_Error. ]

**To be honest:**Predefined operations on real types can “silently” give wrong results when the Machine_Overflows attribute is false, and the computation overflows.

#### Implementation Requirements

11The implementation of a predefined operator that delivers a result of an integer or fixed point type may raise Constraint_Error only if the result is outside the base range of the result type.

The implementation of a predefined operator that delivers a result of a floating point type may raise Constraint_Error only if the result is outside the safe range of the result type.

#### Implementation Permissions

13For a sequence of predefined operators of the same precedence level (and in the absence of parentheses imposing a specific association), an implementation may impose any association of the operators with operands so long as the result produced is an allowed result for the left-to-right association, but ignoring the potential for failure of language-defined checks in either the left-to-right or chosen order of association.

`function_call`

(see 6.4).#### Examples

15*Examples of precedence:*

```
not Sunny or Warm -- same as (not Sunny) or Warm
X > 4.0 and Y > 0.0 -- same as (X > 4.0) and (Y > 0.0)
17-4.0*A**2 -- same as –(4.0 * (A**2))
abs(1 + A) + B -- same as (abs (1 + A)) + B
Y**(-3) -- parentheses are necessary
A / B * C -- same as (A/B)*C
A + (B + C) -- evaluate B + C before adding it to A
```

#### Wording Changes from Ada 83

## 4.5.1 Logical Operators and Short-circuit Control Forms

#### Name Resolution Rules

1An `expression`

consisting of two `relation`

s connected by **and then** or **or else** (a *short-circuit control form*) shall resolve to be of some boolean type; the expected type for both `relation`

s is that same boolean type.

#### Static Semantics

2The following logical operators are predefined for every boolean type *T*, for every modular type *T*, and for every one-dimensional array type *T* whose component type is a boolean type:

`function "and"(Left, Right : T) return T`

function "or" (Left, Right : T) return T

function "xor"(Left, Right : T) return T

*T*. This applies to the italicized

*T*in many other predefined operators and attributes as well.

*T*means:

*T*, but that isn't the case for constrained array types (where the correct subtype is unconstrained) and for access types with a

`null_exclusion`

(where the correct subtype does not exclude null).*T*is used for defining operators and attributes of the language. The meaning is intended to be as described here.

For boolean types, the predefined logical operators **and**, **or**, and **xor** perform the conventional operations of conjunction, inclusive disjunction, and exclusive disjunction, respectively.

For modular types, the predefined logical operators are defined on a bit-by-bit basis, using the binary representation of the value of the operands to yield a binary representation for the result, where zero represents False and one represents True. If this result is outside the base range of the type, a final subtraction by the modulus is performed to bring the result into the base range of the type.

The logical operators on arrays are performed on a component-by-component basis on matching components (as for equality — see 4.5.2), using the predefined logical operator for the component type. The bounds of the resulting array are those of the left operand.

#### Dynamic Semantics

7The short-circuit control forms **and then** and **or else** deliver the same result as the corresponding predefined **and** and **or** operators for boolean types, except that the left operand is always evaluated first, and the right operand is not evaluated if the value of the left operand determines the result.

For the logical operators on arrays, a check is made that for each component of the left operand there is a matching component of the right operand, and vice versa. Also, a check is made that each component of the result belongs to the component subtype. The exception Constraint_Error is raised if either of the above checks fails.

**and**B) (A

**or**B) (A

**xor**B)

True True True True False

True False False True True

False True False True True

False False False False False

#### Examples

11*Examples of logical operators:*

```
Sunny or Warm
Filter(1 .. 10) and Filter(15 .. 24) -- see 3.6.1
```

13*Examples of short-circuit control forms:*

```
Next_Car.Owner /= null and then Next_Car.Owner.Age > 25 -- see 3.10.1
N = 0 or else A(N) = Hit_Value
```

## 4.5.2 Relational Operators and Membership Tests

1[ The *equality operators* = (equals) and /= (not equals) are predefined for nonlimited types. The other `relational_operator`

s 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.

*every*nonlimited type — see below for the exact rule.

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.]

#### Name Resolution Rules

3/3The *tested type* of a membership test is determined by the `membership_choice`

s of the `membership_choice_list`

. Either all `membership_choice`

s 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.

*tested_*

`simple_expression`

to be of any class-wide type that could be converted to the tested type, not just the one rooted at the tested type. This includes any class-wide type that covers the tested type, along with class-wide interfaces in some cases.`membership_choice_list`

s. Without the rule, A **in**B | 1 would be illegal as B and 1 would have different types (the literal having type

*universal integer*).

#### Legality Rules

4/4For 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_expression`

s 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.

#### Static Semantics

5The 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 following additional equality operators for the *universal_access* type are declared in package Standard for use with anonymous access types:

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

function "/="(Left, Right : universal_access) 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

#### Name Resolution Rules

9.1/2At 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 9.4/2 - at least one of its operands is an access parameter with designated type
*D*.

**null**) would be ambiguous for normal access types.

#### Legality Rules

9.5/2At 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, 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.

#### Dynamic Semantics

10For 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.

*nearly*equal values depends on the accuracy of the implementation (see G.2.1, “Model of Floating Point Arithmetic” for implementations that support the Numerics Annex).

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_reference`

s are equal or unequal.]

`attribute_reference`

for a subprogram to designate a distinct “wrapper” subprogram if necessary to support an indirect call. 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.

`variant_part`

in the extension part and the two values have different `variant`

s present. This is a ramification of the requirement that a discriminant governing such a `variant_part`

has to be a “new” discriminant, and so has to be equal in the two values for the values to be equal. Note that `variant_part`

s in the parent part need not match if the primitive equals operator for the parent type considers them equal.`with Pak1;`

package Pak2 is

type Typ3 is new Pak1.Typ1 with private;

private

type Typ3 is new Pak1.Typ2 with null record;

end Pak2;

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:

- 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`

; 18 - 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.

**To be honest:**For a component with an anonymous access type, “predefined equality” is that defined for the

*universal_access*type (anonymous access types have no equality operators of their own).

*T*, “the primitive equals operator” is the one with two parameters of

*T*which returns Boolean. We're not talking about some random other primitive function named "=".

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 "="].

{*8652/0016*} 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**.

`membership_choice`

s; evaluation stops as soon as an individual choice evaluates to True. 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 record extension, or is limited at the point where the membership test occurs , 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`

. 29/4 - 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; 30.3/4 - 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.

**To be honest:**In some of these cases, the bulleted checks need to pass before any predicate check is executed. Otherwise, a predicate check could be performed on an object of the wrong type. Consider:

`type Root is tagged null record;`

type Ext is new Root with record Data : Integer; end record;

function Is_Even (Param : Ext) return Boolean is

(Param.Data mod 2 = 0);

subtype Even_Ext is Ext

with Dynamic_Predicate => Is_Even (Even_Ext);

function F (X : Root'Class) return Boolean is

(X in Even_Ext);

Flag : Boolean := F (Root'(null record));

Otherwise, the test yields the result False.

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

**To be honest:**

*X*

**not in**

*A*|

*B*|

*C*is intended to be exactly equivalent to

**not**(

*X*

**in**

*A*|

*B*|

*C*), including the order of evaluation of the

*tested_*

`simple_expression`

and `membership_choice`

s. #### Implementation Requirements

32.1/1{*8652/0016*} 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.

*not*meet this requirement.

#### Examples

35*Examples of expressions involving relational operators and membership tests:*

```
X /= Y
37/5A_String = "A" -- True (see 3.3.1)
"" < A_String and A_String < "Aa" -- True
A_String < "Bb" and A_String < "A " -- True
38/3My_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
39/3N 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)
```

#### Extensions to Ada 83

#### Wording Changes from Ada 83

`relation`

"X in S" rather to simply the reserved word **in**or

**not in**.

*the*equality operator, and /= as the inequality operator. The new wording is more consistent with the ISO 10646 name for "=" (equals sign) and provides a category similar to “ordering operator” to refer to both = and /=.

#### Extensions to Ada 95

*universal_access*equality operators are new. They provide equality operations (most importantly, testing against

**null**) for anonymous access types.

#### Wording Changes from Ada 95

*8652/0016*}

**Corrigendum:**Wording was added to clarify that the order of calls (and whether the calls are made at all) on "=" for components is unspecified. Also clarified that "=" must compose properly for language-defined types.

#### Inconsistencies With Ada 2005

#### Incompatibilities With Ada 2005

#### Extensions to Ada 2005

#### Wording Changes from Ada 2005

*universal_access*"=" does not apply if an appropriate operator is declared for a partial or incomplete view of the designated type. Otherwise, adding a partial or incomplete view could make some "=" operators ambiguous.

#### Inconsistencies With Ada 2012

**Corrigendum:**Removed the incompatible rule preventing the declaration of "=" in the private part of a package specification for an untagged record type that completes a private type. Any code that calls the predefined "=" on the private type will now execute the body for the redefined "=" instead for the predefined "=". Eliminating the rule eliminates an unnecessary incompatibility (especially for programs that never call the predefined "="). Moreover, (like the composition of untagged record "=" in Ada 2012) this is more likely to fix bugs than cause them (who defines an "=" with a presumably different result and does not want clients to use it?).

#### Incompatibilities With Ada 2012

- The membership test has one or more
*choice_*`simple_expression`

s; 39.s/5 - The membership test occurs in a place where the tested type is nonlimited;
- The tested type has a limited view with a primitive "=" operator;
- The full type of the tested type is not a record type or a record extension.

#### Wording Changes from Ada 2012

**Corrigendum:**Reworded membership tests to use the syntax items

*tested_*

`simple_expression`

and *choice_*

`simple_expression`

. This was necessary to eliminate wording ambiguities introduced when the grammar was corrected to eliminate syntax ambiguities. (Both of the above are now `simple_expression`

s, so merely talking about a `simple_expression`

is insufficient.)**Corrigendum:**Updated wording of the membership tests to use the new term "satisfies the predicates" (see 3.2.4).

## 4.5.3 Binary Adding Operators

#### Static Semantics

1The binary adding operators + (addition) and – (subtraction) are predefined for every specific numeric type *T* with their conventional meaning. They have the following specifications:

`function "+"(Left, Right : T) return T`

function "-"(Left, Right : T) return T

The concatenation operators & are predefined for every nonlimited, one-dimensional array type *T* with component type *C*. They have the following specifications:

`function "&"(Left : T; Right : T) return T`

function "&"(Left : T; Right : C) return T

function "&"(Left : C; Right : T) return T

function "&"(Left : C; Right : C) return T

#### Dynamic Semantics

5For the evaluation of a concatenation with result type *T*, if both operands are of type *T*, the result of the concatenation is a one-dimensional array whose length is the sum of the lengths of its operands, and whose components comprise the components of the left operand followed by the components of the right operand. If the left operand is a null array, the result of the concatenation is the right operand. Otherwise, the lower bound of the result is determined as follows:

- If the ultimate ancestor of the array type was defined by a
`constrained_array_definition`

, then the lower bound of the result is that of the index subtype;

- If the ultimate ancestor of the array type was defined by an
`unconstrained_array_definition`

, then the lower bound of the result is that of the left operand.

[The upper bound is determined by the lower bound and the length.] A check is made that the upper bound of the result of the concatenation belongs to the range of the index subtype, unless the result is a null array. Constraint_Error is raised if this check fails.

If either operand is of the component type *C*, the result of the concatenation is given by the above rules, using in place of such an operand an array having this operand as its only component (converted to the component subtype) and having the lower bound of the index subtype of the array type as its lower bound.

The result of a concatenation is defined in terms of an assignment to an anonymous object, as for any function call (see 6.5).

#### Examples

12*Examples of expressions involving binary adding operators:*

```
Z + 0.1 -- Z has to be of a real type
14"A" & "BCD" -- concatenation of two string literals
'A' & "BCD" -- concatenation of a character literal and a string literal
'A' & 'A' -- concatenation of two character literals
```

#### Inconsistencies With Ada 83

`X : array(1..10) of Integer;`

begin

X := X(6..10) & X(1..5);

#### Extensions to Ada 83

## 4.5.4 Unary Adding Operators

#### Static Semantics

1The unary adding operators + (identity) and – (negation) are predefined for every specific numeric type *T* with their conventional meaning. They have the following specifications:

`function "+"(Right : T) return T`

function "-"(Right : T) return T

## 4.5.5 Multiplying Operators

#### Static Semantics

1The multiplying operators * (multiplication), / (division), **mod** (modulus), and **rem** (remainder) are predefined for every specific integer type T:

`function "*" (Left, Right : T) return T`

function "/" (Left, Right : T) return T

function "mod"(Left, Right : T) return T

function "rem"(Left, Right : T) return T

Signed integer multiplication has its conventional meaning.

Signed integer division and remainder are defined by the relation:

`A = (A/B)*B + (A rem B)`

where (A **rem** B) has the sign of A and an absolute value less than the absolute value of B. Signed integer division satisfies the identity:

`(-A)/B = -(A/B) = A/(-B)`

The signed integer modulus operator is defined such that the result of A **mod** B is either zero, or has the sign of B and an absolute value less than the absolute value of B; in addition, for some signed integer value N, this result satisfies the relation:

`A = B*N + (A mod B)`

The multiplying operators on modular types are defined in terms of the corresponding signed integer operators[, followed by a reduction modulo the modulus if the result is outside the base range of the type] [(which is only possible for the "*" operator)].

Multiplication and division operators are predefined for every specific floating point type T:

`function "*"(Left, Right : T) return T`

function "/"(Left, Right : T) return T

The following multiplication and division operators, with an operand of the predefined type Integer, are predefined for every specific fixed point type T:

`function "*"(Left : T; Right : Integer) return T`

function "*"(Left : Integer; Right : T) return T

function "/"(Left : T; Right : Integer) return T

[All of the above multiplying operators are usable with an operand of an appropriate universal numeric type.] The following additional multiplying operators for *root_real* are predefined[, and are usable when both operands are of an appropriate universal or root numeric type, and the result is allowed to be of type *root_real*, as in a `number_declaration`

]:

*root_real*substitutes for the fixed or floating point type, and

*root_integer*substitutes for Integer. Only values of the corresponding universal numeric types are implicitly convertible to these root numeric types, so these operators are really restricted to use with operands of a universal type, or the specified root numeric types.

```
function "*"(Left, Right : root_real) return root_real
function "/"(Left, Right : root_real) return root_real
17function "*"(Left : root_real; Right : root_integer) return root_real
function "*"(Left : root_integer; Right : root_real) return root_real
function "/"(Left : root_real; Right : root_integer) return root_real
```

18Multiplication and division between any two fixed point types are provided by the following two predefined operators:

*Universal_fixed*is the universal type for the class of fixed point types, meaning that these operators take operands of any fixed point type (not necessarily the same) and return a result that is implicitly (or explicitly) convertible to any fixed point type.

`function "*"(Left, Right : universal_fixed) return universal_fixed`

function "/"(Left, Right : universal_fixed) return universal_fixed

#### Name Resolution Rules

19.1/2The above two fixed-fixed multiplying operators shall not be used in a context where the expected type for the result is itself *universal_fixed* [— the context has to identify some other numeric type to which the result is to be converted, either explicitly or implicitly]. Unless the predefined universal operator is identified using an expanded name with `prefix`

denoting the package Standard, an explicit conversion is required on the result when using the above fixed-fixed multiplication operator if either operand is of a type having a user-defined primitive multiplication operator such that:

- it is declared immediately within the same declaration list as the type or any partial or incomplete view thereof; and
- both of its formal parameters are of a fixed-point type.

A corresponding requirement applies to the universal fixed-fixed division operator.

*small*of

*universal_fixed*is infinitesimal; no loss of precision is permitted. However, fixed-fixed division is impractical to implement when an exact result is required, and multiplication will sometimes result in unanticipated overflows in such circumstances, so we require an explicit conversion to be inserted in expressions like A * B * C if A, B, and C are each of some fixed point type.

*universal_fixed*.

*Paragraph 20 was deleted.*

#### Dynamic Semantics

21The multiplication and division operators for real types have their conventional meaning. [For floating point types, the accuracy of the result is determined by the precision of the result type. For decimal fixed point types, the result is truncated toward zero if the mathematical result is between two multiples of the *small* of the specific result type (possibly determined by context); for ordinary fixed point types, if the mathematical result is between two multiples of the *small*, it is unspecified which of the two is the result. ]

The exception Constraint_Error is raised by integer division, **rem**, and **mod** if the right operand is zero. [Similarly, for a real type *T* with *T'*Machine_Overflows True, division by zero raises Constraint_Error.]

**rem**B is the remainder when A is divided by B. The following relations are satisfied by the rem operator:

`A rem (-B) = A rem B`

(-A) rem B = -(A rem B)

`A mod B = (A + K*B) mod B`

```
A B A/B A rem B A mod B A B A/B A rem B A mod B
2910 5 2 0 0 -10 5 -2 0 0
11 5 2 1 1 -11 5 -2 -1 4
12 5 2 2 2 -12 5 -2 -2 3
13 5 2 3 3 -13 5 -2 -3 2
14 5 2 4 4 -14 5 -2 -4 1
30A B A/B A rem B A mod B A B A/B A rem B A mod B
10 -5 -2 0 0 -10 -5 2 0 0
11 -5 -2 1 -4 -11 -5 2 -1 -1
12 -5 -2 2 -3 -12 -5 2 -2 -2
13 -5 -2 3 -2 -13 -5 2 -3 -3
14 -5 -2 4 -1 -14 -5 2 -4 -4
```

#### Examples

31*Examples of expressions involving multiplying operators:*

```
I : Integer := 1;
J : Integer := 2;
K : Integer := 3;
33X : Real := 1.0; -- see 3.5.7
Y : Real := 2.0;
34F : Fraction := 0.25; -- see 3.5.9
G : Fraction := 0.5;
35Expression Value Result Type
I*J 2 same as I and J, that is, Integer
K/J 1 same as K and J, that is, Integer
K mod J 1 same as K and J, that is, Integer
X/Y 0.5 same as X and Y, that is, Real
F/2 0.125 same as F, that is, Fraction
3*F 0.75 same as F, that is, Fraction
0.75*G 0.375 universal_fixed, implicitly convertible
to any fixed point type
Fraction(F*G) 0.125 Fraction, as stated by the conversion
Real(J)*Y 4.0 Real, the type of both operands after
conversion of J
```

#### Incompatibilities With Ada 83

#### Extensions to Ada 83

*universal_fixed*is covered by

*universal_real*, so real literals and fixed point operands may be multiplied or divided directly, without any explicit conversions required.

#### Wording Changes from Ada 83

#### Incompatibilities With Ada 95

#### Wording Changes from Ada 2005

*universal_fixed*"*" and "/" does not apply if an appropriate operator is declared for a partial (or incomplete) view of the designated type. Otherwise, adding a partial (or incomplete) view could make some "*" and "/" operators ambiguous.

**mod**operator was corrected so that a result of 0 does not have to have "the sign of B" (which is impossible if B is negative).

## 4.5.6 Highest Precedence Operators

#### Static Semantics

1The highest precedence unary operator **abs** (absolute value) is predefined for every specific numeric type *T*, with the following specification:

`function "abs"(Right : T) return T`

The highest precedence unary operator **not** (logical negation) is predefined for every boolean type *T*, every modular type *T*, and for every one-dimensional array type *T* whose components are of a boolean type, with the following specification:

`function "not"(Right : T) return T`

The result of the operator **not** for a modular type is defined as the difference between the high bound of the base range of the type and the value of the operand. [For a binary modulus, this corresponds to a bit-wise complement of the binary representation of the value of the operand.]

The operator **not** that applies to a one-dimensional array of boolean components yields a one-dimensional boolean array with the same bounds; each component of the result is obtained by logical negation of the corresponding component of the operand (that is, the component that has the same index value). A check is made that each component of the result belongs to the component subtype; the exception Constraint_Error is raised if this check fails.

The highest precedence *exponentiation* operator ** is predefined for every specific integer type *T* with the following specification:

`function "**"(Left : T; Right : Natural) return T`

Exponentiation is also predefined for every specific floating point type as well as *root_real*, with the following specification (where *T* is *root_real* or the floating point type):

`function "**"(Left : T; Right : Integer'Base) return T`

The right operand of an exponentiation is the *exponent*. The value of X**N with the value of the exponent N positive is the same as the value of X*X*...X (with N–1 multiplications) except that the multiplications are associated in an arbitrary order. With N equal to zero, the result is one. With the value of N negative [(only defined for a floating point operand)], the result is the reciprocal of the result using the absolute value of N as the exponent.

#### Implementation Permissions

12The implementation of exponentiation for the case of a negative exponent is allowed to raise Constraint_Error if the intermediate result of the repeated multiplications is outside the safe range of the type, even though the final result (after taking the reciprocal) would not be. (The best machine approximation to the final result in this case would generally be 0.0.)

#### Inconsistencies With Ada 83

*8652/0100*} The definition of "**" allows arbitrary association of the multiplications which make up the result. Ada 83 required left-to-right associations (confirmed by AI83-00137). Thus it is possible that "**" would provide a slightly different (and more potentially accurate) answer in Ada 95 than in the same Ada 83 program.

#### Wording Changes from Ada 83

#### Wording Changes from Ada 2005

## 4.5.7 Conditional Expressions

1/3A `conditional_expression`

selects for evaluation at most one of the enclosed *dependent_*`expression`

s, depending on a decision among the alternatives. One kind of `conditional_expression`

is the `if_expression`

, which selects for evaluation a *dependent_*`expression`

depending on the value of one or more corresponding conditions. The other kind of `conditional_expression`

is the `case_expression`

, which selects for evaluation one of a number of alternative *dependent_*`expression`

s; the chosen alternative is determined by the value of a *selecting_*`expression`

.

#### Language Design Principles

`conditional_expression`

, `if_expression`

s and `case_expression`

s. Whenever possible, we have written the rules in terms of `conditional_expression`

s to avoid duplication.`conditional_expression`

s have been designed as much as possible to work similarly to a parenthesized expression. The intent is that as much as possible, wherever a parenthesized expression would be allowed, a `conditional_expression`

would be allowed, and it should work the same way. #### Syntax

2/3`conditional_expression`

` ::= `

`if_expression`

| `case_expression`

3/3`if_expression`

` ::= `

**if** `condition`

**then** *dependent_*`expression`

{**elsif** `condition`

**then** *dependent_*`expression`

}

[**else** *dependent_*`expression`

]

4/3`condition`

` ::= `

*boolean_*`expression`

5/3`case_expression`

` ::= `

**case** *selecting_*`expression`

**is**

`case_expression_alternative`

{,

`case_expression_alternative`

}

6/3`case_expression_alternative`

` ::= `

**when** `discrete_choice_list`

=>

*dependent_*`expression`

7/3Wherever the Syntax Rules allow an `expression`

, a `conditional_expression`

may be used in place of the `expression`

, so long as it is immediately surrounded by parentheses.

`conditional_expression`

appears only as a primary that is parenthesized. The above rule allows it to additionally be used in other contexts where it would be directly surrounded by parentheses.`A := (if X then Y else Z); -- parentheses required`

A := B + (if X then Y else Z) + C; -- parentheses required

```
P(if X then Y else Z);
P((if X then Y else Z)); -- redundant parentheses
7.f/3P((if X then Y else Z), Some_Other_Param);
P(Some_Other_Param, (if X then Y else Z));
P(Formal => (if X then Y else Z));
```

`P(if X then Y else Z, Some_Other_Param);`

P(Some_Other_Param, if X then Y else Z);

P(Formal => if X then Y else Z);

`conditional_expression`

is not immediately surrounded by parentheses (which means on both sides!).`expression_within_parentheses`

, which would consist of `expression`

s and `conditional_expression`

s. Then, that could be used in all of the syntax which could consist of parens directly around an `expression`

. We did not do that because of the large amount of change required. A complete grammar is given in . `conditional_expression`

s. An `if_expression`

and an `if_statement`

are very similar syntactically, (as are a `case_expression`

and a `case_statement`

) and simple mistakes can appear to change one into the other, potentially causing errors to be moved far away from their actual location. The absence of **end if**to terminate an

`if_expression`

(and **end case**for a

`case_expression`

) also may make error handling harder. #### Name Resolution Rules

8/3If a `conditional_expression`

is expected to be of a type *T*, then each *dependent_*`expression`

of the `conditional_expression`

is expected to be of type *T*. Similarly, if a `conditional_expression`

is expected to be of some class of types, then each *dependent_*`expression`

of the `conditional_expression`

is subject to the same expectation. If a `conditional_expression`

shall resolve to be of a type *T*, then each *dependent_*`expression`

shall resolve to be of type *T*.

The possible types of a `conditional_expression`

are further determined as follows:

- If the
`conditional_expression`

is the operand of a type conversion, the type of the`conditional_expression`

is the target type of the conversion; otherwise,

`T(if C then A else B)`

`(if C then T(A) else T(B))`

- If all of the
*dependent_*`expression`

s are of the same type, the type of the`conditional_expression`

is that type; otherwise, 12/3 - If a
*dependent_*`expression`

is of an elementary type, the type of the`conditional_expression`

shall be covered by that type; otherwise,

`conditional_expression`

. - If the
`conditional_expression`

is expected to be of type*T*or shall resolve to type*T*, then the`conditional_expression`

is of type*T*.

`conditional_expression`

cannot be determined by one of these rules, then Name Resolution has failed for that expression, even if the *dependent_*

`expression`

s would resolve individually. A `condition`

is expected to be of any boolean type.

The expected type for the *selecting_*`expression`

and the `discrete_choice`

s are as for case statements (see 5.4).

#### Legality Rules

16/3All of the *dependent_*`expression`

s shall be convertible (see 4.6) to the type of the `conditional_expression`

.

If the expected type of a `conditional_expression`

is a specific tagged type, all of the *dependent_*`expression`

s of the `conditional_expression`

shall be dynamically tagged, or none shall be dynamically tagged. In this case, the `conditional_expression`

is dynamically tagged if all of the *dependent_*`expression`

s are dynamically tagged, is tag-indeterminate if all of the *dependent_*`expression`

s are tag-indeterminate, and is statically tagged otherwise.

If there is no **else** *dependent_*`expression`

, the `if_expression`

shall be of a boolean type.

All Legality Rules that apply to the `discrete_choice`

s of a `case_statement`

(see 5.4) also apply to the `discrete_choice`

s of a `case_expression`

except within an instance of a generic unit.

```
generic
with function Int_Func return Integer;
package G is
X : Float := (case Int_Func is
when Integer'First .. -1 => -1.0,
when 0 => 0.0,
when Positive => 1.0);
end G;
19.c/3function Nat_Func return Natural is (123);
19.d/3package I is new G (Int_Func => Nat_Func); -- Legal
```

#### Dynamic Semantics

20/3For the evaluation of an `if_expression`

, the `condition`

specified after **if**, and any `condition`

s specified after **elsif**, are evaluated in succession (treating a final **else** as **elsif** True **then**), until one evaluates to True or all `condition`

s are evaluated and yield False. If a `condition`

evaluates to True, the associated *dependent_*`expression`

is evaluated, converted to the type of the `if_expression`

, and the resulting value is the value of the `if_expression`

. Otherwise (when there is no **else** clause), the value of the `if_expression`

is True.

**Else**is required unless the

`if_expression`

has a boolean type, so the last sentence can only apply to `if_expression`

s with a boolean type. For the evaluation of a `case_expression`

, the *selecting_*`expression`

is first evaluated. If the value of the *selecting_*`expression`

is covered by the `discrete_choice_list`

of some `case_expression_alternative`

, then the *dependent_*`expression`

of the `case_expression_alternative`

is evaluated, converted to the type of the `case_expression`

, and the resulting value is the value of the `case_expression`

. Otherwise (the value is not covered by any `discrete_choice_list`

, perhaps due to being outside the base range), Constraint_Error is raised.

#### Examples

22/5*Example of use of an* `if_expression`

*:*

```
Put_Line ("Casey is " &
(if Casey.Sex = M then "Male" else "Female")); -- see 3.10.1
```

24/5*Example of use of a* `case_expression`

*:*

```
function Card_Color (Card : Suit) return Color is -- see 3.5.1
(case Card is
when Clubs | Spades => Black,
when Hearts | Diamonds => Red);
```

#### Extensions to Ada 2005

## 4.5.8 Quantified Expressions

0.1/4Quantified expressions provide a way to write universally and existentially quantified predicates over containers and arrays.

#### Syntax

1/3`quantified_expression`

` ::= `

**for** `quantifier`

`loop_parameter_specification`

=> `predicate`

| **for** `quantifier`

`iterator_specification`

=> `predicate`

2/3`quantifier`

` ::= `

**all** | **some**

3/3`predicate`

` ::= `

*boolean_*`expression`

4/3Wherever the Syntax Rules allow an `expression`

, a `quantified_expression`

may be used in place of the `expression`

, so long as it is immediately surrounded by parentheses.

`quantified_expression`

appears only as a `primary`

that is parenthesized. The above rule allows it to additionally be used in other contexts where it would be directly surrounded by parentheses. This is the same rule that is used for `conditional_expression`

s; see 4.5.7 for a detailed discussion of the meaning and effects of this rule. #### Name Resolution Rules

5/3The expected type of a `quantified_expression`

is any Boolean type. The `predicate`

in a `quantified_expression`

is expected to be of the same type.

#### Dynamic Semantics

6/5For the evaluation of a `quantified_expression`

, the `loop_parameter_specification`

or `iterator_specification`

is first elaborated. The evaluation of a `quantified_expression`

then performs an iteration, and evaluates the `predicate`

for each value conditionally produced by the iteration (see 5.5 and 5.5.2).

The value of the `quantified_expression`

is determined as follows:

- If the
`quantifier`

is**all**, the expression is False if the evaluation of any`predicate`

yields False; evaluation of the`quantified_expression`

stops at that point. Otherwise (every predicate has been evaluated and yielded True), the expression is True. Any exception raised by evaluation of the`predicate`

is propagated.

`expression`

is True if the domain contains no values. - If the
`quantifier`

is**some**, the expression is True if the evaluation of any`predicate`

yields True; evaluation of the`quantified_expression`

stops at that point. Otherwise (every predicate has been evaluated and yielded False), the expression is False. Any exception raised by evaluation of the`predicate`

is propagated.

`expression`

is False if the domain contains no values. #### Examples

10/5*Example of a quantified expression as a postcondition for a sorting routine on an array A with an index subtype T:*

`Post => (A'Length < 2 or else`

(for all I in A'First .. T'Pred(A'Last) => A (I) <= A (T'Succ (I))))

*Example of use of a quantified expression as an assertion that a positive number N is composite (as opposed to prime):*

```
pragma Assert (for some X in 2 .. N when X * X <= N => N mod X = 0);
-- see iterator_filter in 5.5
```

#### Extensions to Ada 2005

#### Wording Changes from Ada 2012

**Corrigendum:**Revised the wording to make it clear that the semantics is short-circuited, and what the result is when there are no values for the loop parameter.

## 4.5.9 Declare Expressions

1/5Declare expressions provide a way to declare local constants and object renamings in an expression context.

#### Syntax

2/5`declare_expression`

` ::= `

**declare** {`declare_item`

}

**begin** *body_*`expression`

3/5`declare_item`

` ::= `

`object_declaration`

| `object_renaming_declaration`

**declare begin**

`expression`

) with no `declare_item`

s, for uniformity with block statements, which also allow a pointless **declare**.

Wherever the Syntax Rules allow an `expression`

, a `declare_expression`

may be used in place of the `expression`

, so long as it is immediately surrounded by parentheses.

`declare_expression`

appears only as a `primary`

that is parenthesized. The above rule allows it to additionally be used in other contexts where it would be directly surrounded by parentheses. This is the same rule that is used for `conditional_expression`

s; see 4.5.7 for a detailed discussion of the meaning and effects of this rule. #### Legality Rules

5/5A `declare_item`

that is an `object_declaration`

shall declare a constant of a nonlimited type.

`declare_item`

. A `declare_item`

that is an `object_renaming_declaration`

(see 8.5.1) shall not rename an object of a limited type if any operative constituent of the *object_*`name`

is a value conversion or is newly constructed (see 4.4).

`aggregate`

, parenthesized expression, `conditional_expression`

, or `declare_expression`

(these are not `name`

s), but any of these can appear inside of a `qualified_expression`

or `type_conversion`

(which are `name`

s and thus can be renamed). The following are not allowed within a `declare_expression`

: a declaration containing the reserved word **aliased**; the `attribute_designator`

Access or Unchecked_Access; or an anonymous access type.

`declare_item`

s, as nested `declare_expression`

s cause complexities or usage warts. We want to keep this feature simple to use, understand, and implement. Thus, we do not allow any of the features that would require accessibility rules. #### Name Resolution Rules

8/5If a `declare_expression`

is expected to be of a type *T*, then the *body_*`expression`

is expected to be of type *T*. Similarly, if a `declare_expression`

is expected to be of some class of types, then the *body_*`expression`

is subject to the same expectation. If a `declare_expression`

shall resolve to be of a type *T*, then the *body_*`expression`

shall resolve to be of type *T*.

The type of a `declare_expression`

is the type of the *body_*`expression`

.

#### Dynamic Semantics

10/5For the evaluation of a `declare_expression`

, the `declare_item`

s are elaborated in order, and then the *body_*`expression`

is evaluated. The value of the `declare_expression`

is that of the *body_*`expression`

.

#### Examples

11/5*Example of use of a declare expression as a replacement postcondition for Ada.Containers.Vectors."&" (see A.18.2):*

`with Post =>`

(declare

Result renames Vectors."&"'Result;

Length : constant Count_Type := Left.Length + Right.Length;

begin

Result.Length = Length and then

not Tampering_With_Elements_Prohibited (Result) and then

not Tampering_With_Cursors_Prohibited (Result) and then

Result.Capacity >= Length)

#### Extensions to Ada 2012

## 4.5.10 Reduction Expressions

1/5Reduction expressions provide a way to map or transform a collection of values into a new set of values, and then summarize the values produced by applying an operation to reduce the set to a single value result. A reduction expression is represented as an `attribute_reference`

of the reduction attributes Reduce or Parallel_Reduce.

#### Syntax

3/5`reduction_attribute_reference`

` ::= `

`value_sequence`

'`reduction_attribute_designator`

| `prefix`

'`reduction_attribute_designator`

4/5`value_sequence`

` ::= `

'[' [**parallel**[(`chunk_specification`

)] [`aspect_specification`

]]

`iterated_element_association`

']'

5/5`reduction_attribute_designator`

` ::= `

*reduction_*`identifier`

(`reduction_specification`

)

6/5`reduction_specification`

` ::= `

*reducer_*`name`

, *initial_value_*`expression`

7/5The `iterated_element_association`

of a `value_sequence`

shall not have a *key_*`expression`

, nor shall it have a `loop_parameter_specification`

that has the reserved word **reverse**.

`loop_parameter_specification`

with the **reverse**reserved word would not be permitted in an array aggregate, so we disallow that here.

The `chunk_specification`

, if any, of a `value_sequence`

shall be an *integer_*`simple_expression`

.

#### Name Resolution Rules

9/5The expected type for a `reduction_attribute_reference`

shall be a single nonlimited type.

In the remainder of this subclause, we will refer to nonlimited subtypes *Value_Type* and *Accum_Type* of a `reduction_attribute_reference`

. These subtypes and interpretations of the `name`

s and `expression`

s of a `reduction_attribute_reference`

are determined by the following rules:

*Accum_Type*represents the result of the reduction (the

*accumulator*type), and

*Value_Type*represents the type of the input values to the reduction.

*Accum_Type*is a subtype of the expected type of the`reduction_attribute_reference`

. 12/5- A
*reducer subprogram*is subtype conformant with one of the following specifications:

```
function Reducer(Accumulator : Accum_Type;
Value : Value_Type) return Accum_Type;
14/5procedure Reducer(Accumulator : in out Accum_Type;
Value : in Value_Type);
```

15/5- The
*reducer_*`name`

of a`reduction_specification`

denotes a reducer subprogram. 16/5 - The expected type of an
*initial_value_*`expression`

of a`reduction_specification`

is that of subtype*Accum_Type*. 17/5 - The expected type of the
`expression`

of the`iterated_element_association`

of a`value_sequence`

is that of subtype*Value_Type*.

#### Legality Rules

18/5If the `reduction_attribute_reference`

has a `value_sequence`

with the reserved word **parallel**, the subtypes *Accum_Type* and *Value_Type* shall statically match.

If the `identifier`

of a `reduction_attribute_designator`

is Parallel_Reduce, the subtypes *Accum_Type* and *Value_Type* shall statically match.

`reduction_attribute_reference`

with a `value_sequence`

that does not have the reserved word **parallel**or has a

`prefix`

and the `identifier`

of the `reduction_attribute_designator`

is Reduce, the subtypes *Accum_Type*and

*Value_Type*can be different because only one logical thread of control is presumed so there is no need to combine multiple results.

#### Static Semantics

20/5A `reduction_attribute_reference`

denotes a value, with its nominal subtype being the subtype of the first parameter of the subprogram denoted by the *reducer_*`name`

.

#### Dynamic Semantics

21/5For the evaluation of a `value_sequence`

, the `iterated_element_association`

, the `chunk_specification`

, and the `aspect_specification`

, if any, are elaborated in an arbitrary order. Next an iteration is performed, and for each value conditionally produced by the iteration (see 5.5 and 5.5.2), the associated `expression`

is evaluated with the loop parameter having this value, which produces a result that is converted to Value_Type and is used to define the next value in the sequence.

If the `value_sequence`

does not have the reserved word **parallel**, it is produced as a single sequence of values by a single logical thread of control. If the reserved word **parallel** is present in the `value_sequence`

, the enclosing `reduction_attribute_reference`

is a parallel construct, and the sequence of values is generated by a parallel iteration (as defined in 5.5, 5.5.1, and 5.5.2), as a set of non-empty, non-overlapping contiguous chunks (*subsequences*) with one logical thread of control (see clause 9) associated with each subsequence. If there is a `chunk_specification`

, it determines the maximum number of chunks, as defined in 5.5; otherwise the maximum number of chunks is implementation defined.

`chunk_specification`

.For a `value_sequence`

V, the following attribute is defined:

V'Reduce(Reducer, Initial_Value)

- This attribute represents a
*reduction expression*, and is in the form of a`reduction_attribute_reference`

. 25/5 - The evaluation of a use of this attribute begins by evaluating the parts of the
`reduction_attribute_designator`

(the*reducer_*`name`

Reducer and the*initial_value_*`expression`

Initial_Value), in an arbitrary order. It then initializes the*accumulator*of the reduction expression to the value of the*initial_value_*`expression`

(the*initial value*). The`value_sequence`

V is then evaluated. 26/5 - If the
`value_sequence`

does not have the reserved word**parallel**, each value of the`value_sequence`

is passed, in order, as the second (Value) parameter to a call on Reducer, with the first (Accumulator) parameter being the prior value of the accumulator, saving the result as the new value of the accumulator. The reduction expression yields the final value of the accumulator. 27/5 - If the reserved word
**parallel**is present in a`value_sequence`

, then the (parallel) reduction expression is a parallel construct and the sequence has been partitioned into one or more subsequences (see above) each with its own separate logical thread of control. 28/5 - Each logical thread of control creates a local accumulator for processing its subsequence. The accumulator for a subsequence is initialized to the first value of the subsequence, and calls on Reducer start with the second value of the subsequence (if any). The result for the subsequence is the final value of its local accumulator.
- After all logical threads of control of a parallel reduction expression have completed, Reducer is called for each subsequence, in the original sequence order, passing the local accumulator for that subsequence as the second (Value) parameter, and the overall accumulator [(initialized above to the initial value)] as the first (Accumulator) parameter, with the result saved back in the overall accumulator. The parallel reduction expression yields the final value of the overall accumulator.
- If the evaluation of the
`value_sequence`

yields an empty sequence of values, the reduction expression yields the initial value. 31/5 - If an exception is propagated by one of the calls on Reducer, that exception is propagated from the reduction expression. If different exceptions are propagated in different logical threads of control, one is chosen arbitrarily to be propagated from the reduction expression as a whole.

`reduction_attribute_reference`

that has a `value_sequence`

without the reserved word **parallel**or a

`prefix`

where the `identifier`

of the `reduction_attribute_designator`

is Reduce (see below), generally the compiler can still choose to execute the reduction in parallel, presuming doing so would not change the results. However sequential execution is necessary if the subtypes of the parameters of Reducer do not statically match, since there is no subprogram identified in the construct that could be used for combining the results in parallel. For a `prefix`

X of an array type[ (after any implicit dereference)], or that denotes an iterable container object (see 5.5.1), the following attributes are defined:

X'Reduce(Reducer, Initial_Value)

- X'Reduce is a reduction expression that yields a result equivalent to replacing the
`prefix`

of the attribute with the`value_sequence`

:

`[for Item of X => Item]`

X'Parallel_Reduce(Reducer, Initial_Value)

- X'Parallel_Reduce is a reduction expression that yields a result equivalent to replacing the attribute
`identifier`

with Reduce and the`prefix`

of the attribute with the`value_sequence`

:

`[parallel for Item of X => Item]`

#### Bounded (Run-Time) Errors

35/5For a parallel reduction expression, it is a bounded error if the reducer subprogram is not associative. That is, for any arbitrary values of subtype *Value_Type* *A*, *B*, *C* and a reducer function *R*, the result of *R* (*A*, *R* (*B*, *C*)) should produce a result equal to *R* (*R* (*A*, *B*), *C*)); it is a bounded error if *R* does not. The possible consequences are Program_Error, or a result that does not match the equivalent sequential reduction expression due to the order of calls on the reducer subprogram being unspecified in the overall reduction. Analogous rules apply in the case of a reduction procedure.

*maximum*number of chunks, the actual number of chunks is unspecified. Similarly, the split of elements has only weak requirements. Thus, to get a consistent and portable result, an associative reducer is required for a parallel reduction. We define this as a Bounded (Run-Time) Errors to provide a stern warning about the required nature of the reducer subprogram and to let compilers detect the problem when possible.

**To be honest:**In this rule, “equal” means semantically equal. We don't care if the bit patterns differ but that the results mean the same thing. In particular, if the primitive equal is user-defined, that equality would be the one used to determine if this rule is violated.

#### Examples

36/5*Example of an expression function that returns its result as a reduction expression:*

`function Factorial(N : Natural) return Natural is`

([for J in 1..N => J]'Reduce("*", 1));

*Example of a reduction expression that computes the Sine of X using a Taylor expansion:*

`function Sine (X : Float; Num_Terms : Positive := 5) return Float is`

([for I in 1..Num_Terms =>

(-1.0)**(I-1) * X**(2*I-1)/Float(Factorial(2*I-1))]'Reduce("+", 0.0));

*Example of a reduction expression that outputs the sum of squares:*

`Put_Line ("Sum of Squares is" &`

Integer'Image([for I in 1 .. 10 => I**2]'Reduce("+", 0)));

*Example of a reduction expression used to compute the value of Pi:*

```
-- See 3.5.7.
function Pi (Number_Of_Steps : Natural := 10_000) return Real is
(1.0 / Real (Number_Of_Steps) *
[for I in 1 .. Number_Of_Steps =>
(4.0 / (1.0 + ((Real (I) - 0.5) *
(1.0 / Real (Number_Of_Steps)))**2))]
'Reduce("+", 0.0));
```

44/5*Example of a reduction expression used to calculate the sum of elements of an array of integers:*

```
A'Reduce("+",0) -- See 4.3.3.
```

46/5*Example of a reduction expression used to determine if all elements in a two-dimensional array of booleans are set to true:*

```
Grid'Reduce("and", True) -- See 3.6.
```

48/5*Example of a reduction expression used to calculate the minimum value of an array of integers in parallel:*

`A'Parallel_Reduce(Integer'Min, Integer'Last)`

*Example of a parallel reduction expression used to calculate the mean of the elements of a two-dimensional array of subtype Matrix (see 3.6) that are greater than 100.0:*

```
type Accumulator is record
Sum : Real; -- See 3.5.7.
Count : Integer;
end record;
52/5function Accumulate (L, R : Accumulator) return Accumulator is
(Sum => L.Sum + R.Sum,
Count => L.Count + R.Count);
53/5function Average_of_Values_Greater_Than_100 (M : Matrix) return Real is
(declare
Acc : constant Accumulator :=
[parallel for Val of M when Val > 100.0 => (Val, 1)]
'Reduce(Accumulate, (Sum => 0, Count => 0));
begin
Acc.Sum / Real(Acc.Count));
```