Section 4: Names and Expressions


1     The rules applicable to the different forms of name and expression, and
to their evaluation, are given in this section.


4.1 Names


1     Names can denote declared entities, whether declared explicitly or
implicitly (see 3.1). Names can also denote objects or subprograms designated
by access values; the results of type_conversions or function_calls;
subcomponents and slices of objects and values; protected subprograms, single
entries, entry families, and entries in families of entries. Finally, names
can denote attributes of any of the foregoing.


                                   Syntax

2     name ::= 
           direct_name          | explicit_dereference
         | indexed_component    | slice
         | selected_component   | attribute_reference
         | type_conversion      | function_call
         | character_literal

3     direct_name ::= identifier | operator_symbol

4     prefix ::= name | implicit_dereference

5     explicit_dereference ::= name.all

6     implicit_dereference ::= name

7     Certain forms of name (indexed_components, selected_components, slices,
and attributes) include a prefix that is either itself a name that denotes
some related entity, or an implicit_dereference of an access value that
designates some related entity.


                            Name Resolution Rules

8     The name in a dereference (either an implicit_dereference or an
explicit_dereference) is expected to be of any access type.


                              Static Semantics

9     If the type of the name in a dereference is some access-to-object type
T, then the dereference denotes a view of an object, the nominal subtype of
the view being the designated subtype of T.

10    If the type of the name in a dereference is some access-to-subprogram
type S, then the dereference denotes a view of a subprogram, the profile of
the view being the designated profile of S.


                              Dynamic Semantics

11    The evaluation of a name determines the entity denoted by the name. This
evaluation has no other effect for a name that is a direct_name or a
character_literal.

12    The evaluation of a name that has a prefix includes the evaluation of
the prefix. The evaluation of a prefix consists of the evaluation of the name
or the implicit_dereference. The prefix denotes the entity denoted by the name
or the implicit_dereference.

13    The evaluation of a dereference consists of the evaluation of the name
and the determination of the object or subprogram that is designated by the
value of the name. A check is made that the value of the name is not the null
access value. Constraint_Error is raised if this check fails. The dereference
denotes the object or subprogram designated by the value of the name.


                                  Examples

14    Examples of direct names:

15    Pi        -- the direct name of a number                 (see 3.3.2)
      Limit     -- the direct name of a constant               (see 3.3.1)
      Count     -- the direct name of a scalar variable        (see 3.3.1)
      Board     -- the direct name of an array variable        (see 3.6.1)
      Matrix    -- the direct name of a type                   (see 3.6)
      Random    -- the direct name of a function               (see 6.1)
      Error     -- the direct name of an exception             (see 11.1)

16    Examples of dereferences:

17    Next_Car.all          
      --  explicit dereference denoting the object designated by
                            --  the access variable Next_Car (see 3.10.1)
      Next_Car.Owner        --  selected component with implicit dereference;
                            --  same as Next_Car.all.Owner


4.1.1 Indexed Components


1     An indexed_component denotes either a component of an array or an entry
in a family of entries.


                                   Syntax

2     indexed_component ::= prefix(expression {, expression})


                            Name Resolution Rules

3     The prefix of an indexed_component with a given number of expressions
shall resolve to denote an array (after any implicit dereference) with the
corresponding number of index positions, or shall resolve to denote an entry
family of a task or protected object (in which case there shall be only one
expression).

4     The expected type for each expression is the corresponding index type.


                              Static Semantics

5     When the prefix denotes an array, the indexed_component denotes the
component of the array with the specified index value(s). The nominal subtype
of the indexed_component is the component subtype of the array type.

6     When the prefix denotes an entry family, the indexed_component denotes
the individual entry of the entry family with the specified index value.


                              Dynamic Semantics

7     For the evaluation of an indexed_component, the prefix and the
expressions are evaluated in an arbitrary order. The value of each expression
is converted to the corresponding index type. A check is made that each index
value belongs to the corresponding index range of the array or entry family
denoted by the prefix. Constraint_Error is raised if this check fails.


                                  Examples

8     Examples of indexed components:

9      My_Schedule(Sat)     --  a component of a one-dimensional array               
      (see 3.6.1)
       Page(10)             --  a component of a one-dimensional array               
      (see 3.6)
       Board(M, J + 1)      --  a component of a two-dimensional array               
      (see 3.6.1)
       Page(10)(20)         --  a component of a component                           
      (see 3.6)
       Request(Medium)      --  an entry in a family of entries                      
      (see 9.1)
       Next_Frame(L)(M, N)  --  a component of a function call                       
      (see 6.1)

      NOTES

10    1  Notes on the examples: Distinct notations are used for components of
      multidimensional arrays (such as Board) and arrays of arrays (such as
      Page). The components of an array of arrays are arrays and can therefore
      be indexed. Thus Page(10)(20) denotes the 20th component of Page(10). In
      the last example Next_Frame(L) is a function call returning an access
      value that designates a two-dimensional array.


4.1.2 Slices


1     A slice denotes a one-dimensional array formed by a sequence of
consecutive components of a one-dimensional array. A slice of a variable is a
variable; a slice of a constant is a constant; a slice of a value is a value.


                                   Syntax

2     slice ::= prefix(discrete_range)


                            Name Resolution Rules

3     The prefix of a slice shall resolve to denote a one-dimensional array
(after any implicit dereference).

4     The expected type for the discrete_range of a slice is the index type of
the array type.


                              Static Semantics

5     A slice denotes a one-dimensional array formed by the sequence of
consecutive components of the array denoted by the prefix, corresponding to
the range of values of the index given by the discrete_range.

6     The type of the slice is that of the prefix. Its bounds are those
defined by the discrete_range.


                              Dynamic Semantics

7     For the evaluation of a slice, the prefix and the discrete_range are
evaluated in an arbitrary order. If the slice is not a null slice (a slice
where the discrete_range is a null range), then a check is made that the
bounds of the discrete_range belong to the index range of the array denoted by
the prefix. Constraint_Error is raised if this check fails.

      NOTES

8     2  A slice is not permitted as the prefix of an Access
      attribute_reference, even if the components or the array as a whole are
      aliased. See 3.10.2.

9     3  For a one-dimensional array A, the slice A(N .. N) denotes an array
      that has only one component; its type is the type of A. On the other
      hand, A(N) denotes a component of the array A and has the corresponding
      component type.


                                  Examples

10    Examples of slices:

11      Stars(1 .. 15)        --  a slice of 15 characters                   
      (see 3.6.3)
        Page(10 .. 10 + Size) --  a slice of 1 + Size components             
      (see 3.6)
        Page(L)(A .. B)       --  a slice of the array Page(L)               
      (see 3.6)
        Stars(1 .. 0)         --  a null slice                               
      (see 3.6.3)
        My_Schedule(Weekday)  --  bounds given by subtype                    
      (see 3.6.1 and 3.5.1)
        Stars(5 .. 15)(K)     --  same as Stars(K)                           
      (see 3.6.3)
                              --  provided that K is in 5 .. 15


4.1.3 Selected Components


1     Selected_components are used to denote components (including
discriminants), entries, entry families, and protected subprograms; they are
also used as expanded names as described below.


                                   Syntax

2     selected_component ::= prefix . selector_name

3     selector_name ::= identifier | character_literal | operator_symbol


                            Name Resolution Rules

4     A selected_component is called an expanded name if, according to the
visibility rules, at least one possible interpretation of its prefix denotes a
package or an enclosing named construct (directly, not through a
subprogram_renaming_declaration or generic_renaming_declaration).

5     A selected_component that is not an expanded name shall resolve to
denote one of the following:

6     A component (including a discriminant):

7     The prefix shall resolve to denote an object or value of some non-array
      composite type (after any implicit dereference). The selector_name shall
      resolve to denote a discriminant_specification of the type, or, unless
      the type is a protected type, a component_declaration of the type. The
      selected_component denotes the corresponding component of the object or
      value.

8     A single entry, an entry family, or a protected subprogram:

9     The prefix shall resolve to denote an object or value of some task or
      protected type (after any implicit dereference). The selector_name shall
      resolve to denote an entry_declaration or subprogram_declaration
      occurring (implicitly or explicitly) within the visible part of that
      type. The selected_component denotes the corresponding entry, entry
      family, or protected subprogram.

10    An expanded name shall resolve to denote a declaration that occurs
immediately within a named declarative region, as follows:

11    The prefix shall resolve to denote either a package (including the
      current instance of a generic package, or a rename of a package), or an
      enclosing named construct.

12    The selector_name shall resolve to denote a declaration that occurs
      immediately within the declarative region of the package or enclosing
      construct (the declaration shall be visible at the place of the expanded
      name - see 8.3). The expanded name denotes that declaration.

13    If the prefix does not denote a package, then it shall be a direct_name
      or an expanded name, and it shall resolve to denote a program unit
      (other than a package), the current instance of a type, a
      block_statement, a loop_statement, or an accept_statement (in the case
      of an accept_statement or entry_body, no family index is allowed); the
      expanded name shall occur within the declarative region of this
      construct. Further, if this construct is a callable construct and the
      prefix denotes more than one such enclosing callable construct, then the
      expanded name is ambiguous, independently of the selector_name.


                              Dynamic Semantics

14    The evaluation of a selected_component includes the evaluation of the
prefix.

15    For a selected_component that denotes a component of a variant, a check
is made that the values of the discriminants are such that the value or object
denoted by the prefix has this component. The exception Constraint_Error is
raised if this check fails.


                                  Examples

16    Examples of selected components:

17      Tomorrow.Month     --  a record component                               
      (see 3.8)
        Next_Car.Owner     --  a record component                               
      (see 3.10.1)
        Next_Car.Owner.Age --  a record component                               
      (see 3.10.1)
                           --  the previous two lines involve implicit dereferences
        Writer.Unit        --  a record component (a discriminant)              
      (see 3.8.1)
        Min_Cell(H).Value  --  a record component of the result                 
      (see 6.1)
                           --  of the function call Min_Cell(H)
        Control.Seize      --  an entry of a protected object                   
      (see 9.4)
        Pool(K).Write      --  an entry of the task Pool(K)                     
      (see 9.4)

18    Examples of expanded names:

19      Key_Manager."<"      --  an operator of the visible part of a package          
      (see 7.3.1)
        Dot_Product.Sum      --  a variable declared in a function body                
      (see 6.1)
        Buffer.Pool          --  a variable declared in a protected unit               
      (see 9.11)
        Buffer.Read          --  an entry of a protected unit                          
      (see 9.11)
        Swap.Temp            --  a variable declared in a block statement              
      (see 5.6)
        Standard.Boolean     --  the name of a predefined type                         
      (see A.1)


4.1.4 Attributes


1     An attribute is a characteristic of an entity that can be queried via an
attribute_reference or a range_attribute_reference.


                                   Syntax

2     attribute_reference ::= prefix'attribute_designator

3     attribute_designator ::= 
          identifier[(static_expression)]
        | Access | Delta | Digits

4     range_attribute_reference ::= prefix'range_attribute_designator

5     range_attribute_designator ::= Range[(static_expression)]


                            Name Resolution Rules

6     In an attribute_reference, if the attribute_designator is for an
attribute defined for (at least some) objects of an access type, then the
prefix is never interpreted as an implicit_dereference; otherwise (and for all
range_attribute_references), if the type of the name within the prefix is of
an access type, the prefix is interpreted as an implicit_dereference.
Similarly, if the attribute_designator is for an attribute defined for (at
least some) functions, then the prefix is never interpreted as a parameterless
function_call; otherwise (and for all range_attribute_references), if the
prefix consists of a name that denotes a function, it is interpreted as a
parameterless function_call.

7     The expression, if any, in an attribute_designator or
range_attribute_designator is expected to be of any integer type.


                               Legality Rules

8     The expression, if any, in an attribute_designator or
range_attribute_designator shall be static.


                              Static Semantics

9     An attribute_reference denotes a value, an object, a subprogram, or some
other kind of program entity.

10    A range_attribute_reference X'Range(N) is equivalent to the range
X'First(N) .. X'Last(N), except that the prefix is only evaluated once.
Similarly, X'Range is equivalent to X'First .. X'Last, except that the prefix
is only evaluated once.


                              Dynamic Semantics

11    The evaluation of an attribute_reference (or range_attribute_reference)
consists of the evaluation of the prefix.


                         Implementation Permissions

12/1  An implementation may provide implementation-defined attributes; the
identifier for an implementation-defined attribute shall differ from those of
the language-defined attributes unless supplied for compatibility with a
previous edition of this International Standard.

      NOTES

13    4  Attributes are defined throughout this International Standard, and
      are summarized in Annex K.

14/1  5  In general, the name in a prefix of an attribute_reference (or a
      range_attribute_reference) has to be resolved without using any context.
      However, in the case of the Access attribute, the expected type for the
      prefix has to be a single access type, and if it is an
      access-to-subprogram type (see 3.10.2) then the resolution of the name
      can use the fact that the profile of the callable entity denoted by the
      prefix has to be type conformant with the designated profile of the
      access type.


                                  Examples

15    Examples of attributes:

16    Color'First        -- minimum value of the enumeration type Color              
      (see 3.5.1)
      Rainbow'Base'First -- same as Color'First                                      
      (see 3.5.1)
      Real'Digits        -- precision of the type Real                               
      (see 3.5.7)
      Board'Last(2)      -- upper bound of the second dimension of Board             
      (see 3.6.1)
      Board'Range(1)     -- index range of the first dimension of Board              
      (see 3.6.1)
      Pool(K)'Terminated -- True if task Pool(K) is terminated                       
      (see 9.1)
      Date'Size          -- number of bits for records of type Date                  
      (see 3.8)
      Message'Address    -- address of the record variable Message                   
      (see 3.7.1)


4.2 Literals


1     A literal represents a value literally, that is, by means of notation
suited to its kind. A literal is either a numeric_literal, a
character_literal, the literal null, or a string_literal.


                            Name Resolution Rules

2     The expected type for a literal null shall be a single access type.

3     For a name that consists of a character_literal, either its expected
type shall be a single character type, in which case it is interpreted as a
parameterless function_call that yields the corresponding value of the
character type, or its expected profile shall correspond to a parameterless
function with a character result type, in which case it is interpreted as the
name of the corresponding parameterless function declared as part of the
character type's definition (see 3.5.1). In either case, the character_literal
denotes the enumeration_literal_specification.

4     The expected type for a primary that is a string_literal shall be a
single string type.


                               Legality Rules

5     A character_literal that is a name shall correspond to a
defining_character_literal of the expected type, or of the result type of the
expected profile.

6     For each character of a string_literal with a given expected string
type, there shall be a corresponding defining_character_literal of the
component type of the expected string type.

7     A literal null shall not be of an anonymous access type, since such
types do not have a null value (see 3.10).


                              Static Semantics

8     An integer literal is of type universal_integer. A real literal is of
type universal_real.


                              Dynamic Semantics

9     The evaluation of a numeric literal, or the literal null, yields the
represented value.

10    The evaluation of a string_literal that is a primary yields an array
value containing the value of each character of the sequence of characters of
the string_literal, as defined in 2.6. The bounds of this array value are
determined according to the rules for positional_array_aggregates (see 4.3.3
), except that for a null string literal, the upper bound is the predecessor
of the lower bound.

11    For the evaluation of a string_literal of type T, a check is made that
the value of each character of the string_literal belongs to the component
subtype of T. For the evaluation of a null string literal, a check is made
that its lower bound is greater than the lower bound of the base range of the
index type. The exception Constraint_Error is raised if either of these checks
fails.

      NOTES

12    6  Enumeration literals that are identifiers rather than
      character_literals follow the normal rules for identifiers when used in
      a name (see 4.1 and 4.1.3). Character_literals used as selector_names
      follow the normal rules for expanded names (see 4.1.3).


                                  Examples

13    Examples of literals:

14    3.14159_26536      --  a real literal
      1_345              --  an integer literal
      'A'                --  a character literal
      "Some Text"        --  a string literal 


4.3 Aggregates


1     An aggregate combines component values into a composite value of an
array type, record type, or record extension.


                                   Syntax

2     aggregate ::= record_aggregate | extension_aggregate
       | array_aggregate


                            Name Resolution Rules

3     The expected type for an aggregate shall be a single nonlimited array
type, record type, or record extension.


                               Legality Rules

4     An aggregate shall not be of a class-wide type.


                              Dynamic Semantics

5     For the evaluation of an aggregate, an anonymous object is created and
values for the components or ancestor part are obtained (as described in the
subsequent subclause for each kind of the aggregate) and assigned into the
corresponding components or ancestor part of the anonymous object. Obtaining
the values and the assignments occur in an arbitrary order. The value of the
aggregate is the value of this object.

6     If an aggregate is of a tagged type, a check is made that its value
belongs to the first subtype of the type. Constraint_Error is raised if this
check fails.


4.3.1 Record Aggregates


1     In a record_aggregate, a value is specified for each component of the
record or record extension value, using either a named or a positional
association.


                                   Syntax

2     record_aggregate ::= (record_component_association_list)

3     record_component_association_list ::= 
          record_component_association {, record_component_association}
        | null record

4     record_component_association ::= 
         [ component_choice_list => ] expression

5     component_choice_list ::= 
           component_selector_name {| component_selector_name}
         | others

6     A record_component_association is a named component association if it
      has a component_choice_list; otherwise, it is a positional component
      association. Any positional component associations shall precede any
      named component associations. If there is a named association with a
      component_choice_list of others, it shall come last.

7     In the record_component_association_list for a record_aggregate, if
      there is only one association, it shall be a named association.


                            Name Resolution Rules

8     The expected type for a record_aggregate shall be a single nonlimited
record type or record extension.

9     For the record_component_association_list of a record_aggregate, all
components of the composite value defined by the aggregate are needed; for the
association list of an extension_aggregate, only those components not
determined by the ancestor expression or subtype are needed (see 4.3.2). Each
selector_name in a record_component_association shall denote a needed
component (including possibly a discriminant).

10    The expected type for the expression of a record_component_association
is the type of the associated component(s); the associated component(s) are as
follows:

11    For a positional association, the component (including possibly a
      discriminant) in the corresponding relative position (in the declarative
      region of the type), counting only the needed components;

12    For a named association with one or more component_selector_names, the
      named component(s);

13    For a named association with the reserved word others, all needed
      components that are not associated with some previous association.


                               Legality Rules

14    If the type of a record_aggregate is a record extension, then it shall
be a descendant of a record type, through one or more record extensions (and
no private extensions).

15    If there are no components needed in a given
record_component_association_list, then the reserved words null record shall
appear rather than a list of record_component_associations.

16    Each record_component_association shall have at least one associated
component, and each needed component shall be associated with exactly one
record_component_association. If a record_component_association has two or
more associated components, all of them shall be of the same type.

17    If the components of a variant_part are needed, then the value of a
discriminant that governs the variant_part shall be given by a static
expression.


                              Dynamic Semantics

18    The evaluation of a record_aggregate consists of the evaluation of the
record_component_association_list.

19    For the evaluation of a record_component_association_list, any
per-object constraints (see 3.8) for components specified in the association
list are elaborated and any expressions are evaluated and converted to the
subtype of the associated component. Any constraint elaborations and
expression evaluations (and conversions) occur in an arbitrary order, except
that the expression for a discriminant is evaluated (and converted) prior to
the elaboration of any per-object constraint that depends on it, which in turn
occurs prior to the evaluation and conversion of the expression for the
component with the per-object constraint.

20    The expression of a record_component_association is evaluated (and
converted) once for each associated component.

      NOTES

21    7  For a record_aggregate with positional associations, expressions
      specifying discriminant values appear first since the
      known_discriminant_part is given first in the declaration of the type;
      they have to be in the same order as in the known_discriminant_part.


                                  Examples

22    Example of a record aggregate with positional associations:

23    (4, July, 1776)                                       --  see 3.8 

24    Examples of record aggregates with named associations:

25    (Day => 4, Month => July, Year => 1776)
      (Month => July, Day => 4, Year => 1776)

26    (Disk, Closed, Track => 5, Cylinder => 12)            --  see 3.8.1
      (Unit => Disk, Status => Closed, Cylinder => 9, Track => 1)

27    Example of component association with several choices:

28    (Value => 0, Succ|Pred => new Cell'(0, null, null))   --  see 3.10.1

29     --  The allocator is evaluated twice: Succ and Pred designate different cells

30    Examples of record aggregates for tagged types (see 3.9 and 3.9.1):

31    Expression'(null record)
      Literal'(Value => 0.0)
      Painted_Point'(0.0, Pi/2.0, Paint => Red)


4.3.2 Extension Aggregates


1     An extension_aggregate specifies a value for a type that is a record
extension by specifying a value or subtype for an ancestor of the type,
followed by associations for any components not determined by the
ancestor_part.


                                   Syntax

2     extension_aggregate ::= 
          (ancestor_part with record_component_association_list)

3     ancestor_part ::= expression | subtype_mark


                            Name Resolution Rules

4     The expected type for an extension_aggregate shall be a single
nonlimited type that is a record extension. If the ancestor_part is an
expression, it is expected to be of any nonlimited tagged type.


                               Legality Rules

5     If the ancestor_part is a subtype_mark, it shall denote a specific
tagged subtype. The type of the extension_aggregate shall be derived from the
type of the ancestor_part, through one or more record extensions (and no
private extensions).


                              Static Semantics

6     For the record_component_association_list of an extension_aggregate, the
only components needed are those of the composite value defined by the
aggregate that are not inherited from the type of the ancestor_part, plus any
inherited discriminants if the ancestor_part is a subtype_mark that denotes an
unconstrained subtype.


                              Dynamic Semantics

7     For the evaluation of an extension_aggregate, the record_component_-
association_list is evaluated. If the ancestor_part is an expression, it is
also evaluated; if the ancestor_part is a subtype_mark, the components of the
value of the aggregate not given by the record_component_association_list are
initialized by default as for an object of the ancestor type. Any implicit
initializations or evaluations are performed in an arbitrary order, except
that the expression for a discriminant is evaluated prior to any other
evaluation or initialization that depends on it.

8     If the type of the ancestor_part has discriminants that are not
inherited by the type of the extension_aggregate, then, unless the
ancestor_part is a subtype_mark that denotes an unconstrained subtype, a check
is made that each discriminant of the ancestor has the value specified for a
corresponding discriminant, either in the record_component_association_-
list, or in the derived_type_definition for some ancestor of the type of the
extension_aggregate. Constraint_Error is raised if this check fails.

      NOTES

9     8  If all components of the value of the extension_aggregate are
      determined by the ancestor_part, then the record_component_association_-
      list is required to be simply null record.

10    9  If the ancestor_part is a subtype_mark, then its type can be
      abstract. If its type is controlled, then as the last step of evaluating
      the aggregate, the Initialize procedure of the ancestor type is called,
      unless the Initialize procedure is abstract (see 7.6).


                                  Examples

11    Examples of extension aggregates (for types defined in 3.9.1):

12    Painted_Point'(Point with Red)
      (Point'(P) with Paint => Black)

13    (Expression with Left => 1.2, Right => 3.4)
      Addition'(Binop with null record)
                   -- presuming Binop is of type Binary_Operation


4.3.3 Array Aggregates


1     In an array_aggregate, a value is specified for each component of an
array, either positionally or by its index. For a positional_array_aggregate,
the components are given in increasing-index order, with a final others, if
any, representing any remaining components. For a named_array_aggregate, the
components are identified by the values covered by the discrete_choices.


                                   Syntax

2     array_aggregate ::= 
        positional_array_aggregate | named_array_aggregate

3     positional_array_aggregate ::= 
          (expression, expression {, expression})
        | (expression {, expression}, others => expression)

4     named_array_aggregate ::= 
          (array_component_association {, array_component_association})

5     array_component_association ::= 
          discrete_choice_list => expression

6     An n-dimensional array_aggregate is one that is written as n levels of
nested array_aggregates (or at the bottom level, equivalent string_literals).
For the multidimensional case (n >= 2) the array_aggregates (or equivalent
string_literals) at the n-1 lower levels are called subaggregates of the
enclosing n-dimensional array_aggregate. The expressions of the bottom level
subaggregates (or of the array_aggregate itself if one-dimensional) are called
the array component expressions of the enclosing n-dimensional
array_aggregate.


                            Name Resolution Rules

7     The expected type for an array_aggregate (that is not a subaggregate)
shall be a single nonlimited array type. The component type of this array type
is the expected type for each array component expression of the
array_aggregate.

8     The expected type for each discrete_choice in any discrete_choice_list
of a named_array_aggregate is the type of the corresponding index; the
corresponding index for an array_aggregate that is not a subaggregate is the
first index of its type; for an (n-m)-dimensional subaggregate within an
array_aggregate of an n-dimensional type, the corresponding index is the index
in position m+1.


                               Legality Rules

9     An array_aggregate of an n-dimensional array type shall be written as an
n-dimensional array_aggregate.

10    An others choice is allowed for an array_aggregate only if an applicable
index constraint applies to the array_aggregate. An applicable index
constraint is a constraint provided by certain contexts where an
array_aggregate is permitted that can be used to determine the bounds of the
array value specified by the aggregate. Each of the following contexts (and
none other) defines an applicable index constraint:

11    For an explicit_actual_parameter, an explicit_generic_actual_parameter,
      the expression of a return_statement, the initialization expression in
      an object_declaration, or a default_expression (for a parameter or a
      component), when the nominal subtype of the corresponding formal
      parameter, generic formal parameter, function result, object, or
      component is a constrained array subtype, the applicable index
      constraint is the constraint of the subtype;

12    For the expression of an assignment_statement where the name denotes an
      array variable, the applicable index constraint is the constraint of the
      array variable;

13    For the operand of a qualified_expression whose subtype_mark denotes a
      constrained array subtype, the applicable index constraint is the
      constraint of the subtype;

14    For a component expression in an aggregate, if the component's nominal
      subtype is a constrained array subtype, the applicable index constraint
      is the constraint of the subtype;

15    For a parenthesized expression, the applicable index constraint is that,
      if any, defined for the expression.

16    The applicable index constraint applies to an array_aggregate that
appears in such a context, as well as to any subaggregates thereof. In the
case of an explicit_actual_parameter (or default_expression) for a call on a
generic formal subprogram, no applicable index constraint is defined.

17    The discrete_choice_list of an array_component_association is allowed to
have a discrete_choice that is a nonstatic expression or that is a
discrete_range that defines a nonstatic or null range, only if it is the
single discrete_choice of its discrete_choice_list, and there is only one
array_component_association in the array_aggregate.

18    In a named_array_aggregate with more than one discrete_choice, no two
discrete_choices are allowed to cover the same value (see 3.8.1); if there is
no others choice, the discrete_choices taken together shall exactly cover a
contiguous sequence of values of the corresponding index type.

19    A bottom level subaggregate of a multidimensional array_aggregate of a
given array type is allowed to be a string_literal only if the component type
of the array type is a character type; each character of such a string_literal
shall correspond to a defining_character_literal of the component type.


                              Static Semantics

20    A subaggregate that is a string_literal is equivalent to one that is a
positional_array_aggregate of the same length, with each expression being the
character_literal for the corresponding character of the string_literal.


                              Dynamic Semantics

21    The evaluation of an array_aggregate of a given array type proceeds in
two steps:

22    1.  Any discrete_choices of this aggregate and of its subaggregates are
          evaluated in an arbitrary order, and converted to the corresponding
          index type;

23    2.  The array component expressions of the aggregate are evaluated in an
          arbitrary order and their values are converted to the component
          subtype of the array type; an array component expression is
          evaluated once for each associated component.

24    The bounds of the index range of an array_aggregate (including a
subaggregate) are determined as follows:

25    For an array_aggregate with an others choice, the bounds are those of
      the corresponding index range from the applicable index constraint;

26    For a positional_array_aggregate (or equivalent string_literal) without
      an others choice, the lower bound is that of the corresponding index
      range in the applicable index constraint, if defined, or that of the
      corresponding index subtype, if not; in either case, the upper bound is
      determined from the lower bound and the number of expressions (or the
      length of the string_literal);

27    For a named_array_aggregate without an others choice, the bounds are
      determined by the smallest and largest index values covered by any
      discrete_choice_list.

28    For an array_aggregate, a check is made that the index range defined by
its bounds is compatible with the corresponding index subtype.

29    For an array_aggregate with an others choice, a check is made that no
expression is specified for an index value outside the bounds determined by
the applicable index constraint.

30    For a multidimensional array_aggregate, a check is made that all
subaggregates that correspond to the same index have the same bounds.

31    The exception Constraint_Error is raised if any of the above checks
fail.

      NOTES

32    10  In an array_aggregate, positional notation may only be used with two
      or more expressions; a single expression in parentheses is interpreted
      as a parenthesized_expression. A named_array_aggregate, such as (1 =>
      X), may be used to specify an array with a single component.


                                  Examples

33    Examples of array aggregates with positional associations:

34    (7, 9, 5, 1, 3, 2, 4, 8, 6, 0)
      Table'(5, 8, 4, 1, others => 0)  --  see 3.6 

35    Examples of array aggregates with named associations:

36    (1 .. 5 => (1 .. 8 => 0.0))      --  two-dimensional
      (1 .. N => new Cell)             --  N new cells, in particular for N = 0

37    Table'(2 | 4 | 10 => 1, others => 0)
      Schedule'(Mon .. Fri => True,  others => False)  --  see 3.6
      Schedule'(Wed | Sun  => False, others => True)
      Vector'(1 => 2.5)                                --  single-component vector

38    Examples of two-dimensional array aggregates:

39    -- Three aggregates for the same value of subtype Matrix(1..2,1..3) (see 3.6
      ):

40    ((1.1, 1.2, 1.3), (2.1, 2.2, 2.3))
      (1 => (1.1, 1.2, 1.3), 2 => (2.1, 2.2, 2.3))
      (1 => (1 => 1.1, 2 => 1.2, 3 => 1.3), 2 => (1 => 2.1, 2 => 2.2, 3 => 2.3))

41    Examples of aggregates as initial values:

42    A : Table := (7, 9, 5, 1, 3, 2, 4, 8, 6, 0);        -- A(1)=7, A(10)=0
      B : Table := (2 | 4 | 10 => 1, others => 0);        -- B(1)=0, B(10)=1
      C : constant Matrix := (1 .. 5 => (1 .. 8 => 0.0)); -- C'Last(1)=5, C'Last(2)=8

43    D : Bit_Vector(M .. N) := (M .. N => True);         -- see 3.6
      E : Bit_Vector(M .. N) := (others => True);
      F : String(1 .. 1) := (1 => 'F');  -- a one component aggregate: same as "F"


4.4 Expressions


1     An expression is a formula that defines the computation or retrieval of
a value. In this International Standard, the term ``expression'' refers to a
construct of the syntactic category expression or of any of the other five
syntactic categories defined below.


                                   Syntax

2     expression ::= 
           relation {and relation}  | relation {and then relation}
         | relation {or relation}  | relation {or else relation}
         | relation {xor relation}

3     relation ::= 
           simple_expression [relational_operator simple_expression]
         | simple_expression [not] in range
         | simple_expression [not] in subtype_mark

4     simple_expression ::= [unary_adding_operator] term
       {binary_adding_operator term}

5     term ::= factor {multiplying_operator factor}

6     factor ::= primary [** primary] | abs primary | not primary

7     primary ::= 
         numeric_literal | null | string_literal | aggregate
       | name | qualified_expression | allocator | (expression)


                            Name Resolution Rules

8     A name used as a primary shall resolve to denote an object or a value.


                              Static Semantics

9     Each expression has a type; it specifies the computation or retrieval of
a value of that type.


                              Dynamic Semantics

10    The value of a primary that is a name denoting an object is the value of
the object.


                         Implementation Permissions

11    For the evaluation of a primary that is a name denoting an object of an
unconstrained numeric subtype, if the value of the object is outside the base
range of its type, the implementation may either raise Constraint_Error or
return the value of the object.


                                  Examples

12    Examples of primaries:

13    4.0                --  real literal
      Pi                 --  named number
      (1 .. 10 => 0)     --  array aggregate
      Sum                --  variable
      Integer'Last       --  attribute
      Sine(X)            --  function call
      Color'(Blue)       --  qualified expression
      Real(M*N)          --  conversion
      (Line_Count + 10)  --  parenthesized expression 

14    Examples of expressions:

15    Volume                      -- primary
      not Destroyed               -- factor
      2*Line_Count                -- term  
      -4.0                        -- simple expression
      -4.0 + A                    -- simple expression
      B**2 - 4.0*A*C              -- simple expression
      Password(1 .. 3) = "Bwv"    -- relation
      Count in Small_Int          -- relation
      Count not in Small_Int      -- relation
      Index = 0 or Item_Hit       -- expression
      (Cold and Sunny) or Warm    -- expression (parentheses are required)
      A**(B**C)                   -- expression (parentheses are required)


4.5 Operators and Expression Evaluation


1     The language defines the following six categories of operators (given in
order of increasing precedence). The corresponding operator_symbols, and only
those, can be used as designators 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

8     For 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.

9     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.


                         Implementation Requirements

11    The 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.

12    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

13    For 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.

      NOTES

14    11  The two operands of an expression of the form X op Y, where op is a
      binary operator, are evaluated in an arbitrary order, as for any
      function_call (see 6.4).


                                  Examples

15    Examples of precedence:

16    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 


4.5.1 Logical Operators and Short-circuit Control Forms



                            Name Resolution Rules

1     An expression consisting of two relations 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 relations is that same boolean type.


                              Static Semantics

2     The 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:

3     function "and"(Left, Right : T) return T
      function "or" (Left, Right : T) return T
      function "xor"(Left, Right : T) return T

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

5     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.

6     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

7     The 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.

8     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.

      NOTES

9     12  The conventional meaning of the logical operators is given by the
      following truth table:

    10          A                   B                 (A 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:

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

13    Examples of short-circuit control forms:

14    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_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.

2     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

3     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

4     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

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

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

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

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

9     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

10    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.

11    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.

12    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.

13    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.

14    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.

15    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.

16    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:

17    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;

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

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

21    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:

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

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

24    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.

24.1/1 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.

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

26    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).

27    For the evaluation of a membership test, the simple_expression and the
range (if any) are evaluated in an arbitrary order.

28    A membership test using in yields the result True if:

29    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

30    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.

31    Otherwise the test yields the result False.

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


                         Implementation Requirements

32.1/1 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

33    13  No exception is ever raised by a membership test, by a predefined
      ordering operator, or by a predefined equality operator for an
      elementary type, but an exception can be raised by the evaluation of the
      operands. A predefined equality operator for a composite type can only
      raise an exception if the type has a tagged part whose primitive equals
      operator propagates an exception.

34    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.


                                  Examples

35    Examples of expressions involving relational operators and membership
tests:

36    X /= Y

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

38    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

39    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)
      Archive in Disk_Unit        -- subtype membership test (see 3.8.1)
      Tree.all in Addition'Class  -- class membership test (see 3.9.1)


4.5.3 Binary Adding Operators



                              Static Semantics

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

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

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

4     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

5     For 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:

6     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;

7     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.

8     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.

9     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.

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

      NOTES

11    15  As for all predefined operators on modular types, the binary adding
      operators + and - on modular types include a final reduction modulo the
      modulus if the result is outside the base range of the type.


                                  Examples

12    Examples of expressions involving binary adding operators:

13    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 


4.5.4 Unary Adding Operators



                              Static Semantics

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

2     function "+"(Right : T) return T
      function "-"(Right : T) return T

      NOTES

3     16  For modular integer types, the unary adding operator -, when given a
      nonzero operand, returns the result of subtracting the value of the
      operand from the modulus; for a zero operand, the result is zero.


4.5.5 Multiplying Operators



                              Static Semantics

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

2     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

3     Signed integer multiplication has its conventional meaning.

4     Signed integer division and remainder are defined by the relation:

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

6     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:

7     (-A)/B = -(A/B) = A/(-B)

8     The signed integer modulus operator is defined such that the result of A
mod B 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:

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

10    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).

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

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

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

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

15    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:

16    function "*"(Left, Right : root_real) return root_real
      function "/"(Left, Right : root_real) return root_real

17    function "*"(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

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

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


                               Legality Rules

20    The 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.


                              Dynamic Semantics

21    The 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.

22    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.

      NOTES

23    17  For positive A and B, A/B is the quotient and A rem B is the
      remainder when A is divided by B. The following relations are satisfied
      by the rem operator:

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

25    18  For any signed integer K, the following identity holds:

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

27    The relations between signed integer division, remainder, and modulus
      are illustrated by the following table:

28       A      B   A/B   A rem B  A mod B     A     B    A/B   A rem B   A mod B

29       10     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

30       A      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:

32    I : Integer := 1;
      J : Integer := 2;
      K : Integer := 3;

33    X : Real := 1.0;                      --     see 3.5.7
      Y : Real := 2.0;

34    F : Fraction := 0.25;                 --     see 3.5.9
      G : Fraction := 0.5;

35    Expression            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


4.5.6 Highest Precedence Operators



                              Static Semantics

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

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

3     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:

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

5     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.

6     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.

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

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

9     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):

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

11    The right operand of an exponentiation is the exponent. The expression
X**N with the value of the exponent N positive is equivalent to the expression
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

12    The 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.)

      NOTES

13    19  As implied by the specification given above for exponentiation of an
      integer type, a check is made that the exponent is not negative.
      Constraint_Error is raised if this check fails.


4.6 Type Conversions


1     Explicit type conversions, both value conversions and view conversions,
are allowed between closely related types as defined below. This clause also
defines rules for value and view conversions to a particular subtype of a
type, both explicit ones and those implicit in other constructs.


                                   Syntax

2     type_conversion ::= 
          subtype_mark(expression)
        | subtype_mark(name)

3     The target subtype of a type_conversion is the subtype denoted by the
subtype_mark. The operand of a type_conversion is the expression or name
within the parentheses; its type is the operand type.

4     One type is convertible to a second type if a type_conversion with the
first type as operand type and the second type as target type is legal
according to the rules of this clause. Two types are convertible if each is
convertible to the other.

5/1   A type_conversion whose operand is the name of an object is called a
view conversion if both its target type and operand type are tagged, or if it
appears as an actual parameter of mode out or in out; other type_conversions
are called value conversions.


                            Name Resolution Rules

6     The operand of a type_conversion is expected to be of any type.

7     The operand of a view conversion is interpreted only as a name; the
operand of a value conversion is interpreted as an expression.


                               Legality Rules

8     If the target type is a numeric type, then the operand type shall be a
numeric type.

9     If the target type is an array type, then the operand type shall be an
array type. Further:

10    The types shall have the same dimensionality;

11/1  Corresponding index types shall be convertible;

12/1  The component subtypes shall statically match; and

12.1/1 In a view conversion, the target type and the operand type shall both
      or neither have aliased components.

13    If the target type is a general access type, then the operand type shall
be an access-to-object type. Further:

14    If the target type is an access-to-variable type, then the operand type
      shall be an access-to-variable type;

15    If the target designated type is tagged, then the operand designated
      type shall be convertible to the target designated type;

16    If the target designated type is not tagged, then the designated types
      shall be the same, and either the designated subtypes shall statically
      match or the target designated subtype shall be discriminated and
      unconstrained; and

17    The accessibility level of the operand type shall not be statically
      deeper than that of the target type. 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.

18    If the target type is an access-to-subprogram type, then the operand
type shall be an access-to-subprogram type. Further:

19    The designated profiles shall be subtype-conformant.

20    The accessibility level of the operand type shall not be statically
      deeper than that of the target type. 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. If the operand type is
      declared within a generic body, the target type shall be declared within
      the generic body.

21    If the target type is not included in any of the above four cases, there
shall be a type that is an ancestor of both the target type and the operand
type. Further, if the target type is tagged, then either:

22    The operand type shall be covered by or descended from the target type;
      or

23    The operand type shall be a class-wide type that covers the target type.

24    In a view conversion for an untagged type, the target type shall be
convertible (back) to the operand type.


                              Static Semantics

25    A type_conversion that is a value conversion denotes the value that is
the result of converting the value of the operand to the target subtype.

26    A type_conversion that is a view conversion denotes a view of the object
denoted by the operand. This view is a variable of the target type if the
operand denotes a variable; otherwise it is a constant of the target type.

27    The nominal subtype of a type_conversion is its target subtype.


                              Dynamic Semantics

28    For the evaluation of a type_conversion that is a value conversion, the
operand is evaluated, and then the value of the operand is converted to a
corresponding value of the target type, if any. If there is no value of the
target type that corresponds to the operand value, Constraint_Error is raised;
this can only happen on conversion to a modular type, and only when the
operand value is outside the base range of the modular type. Additional rules
follow:

29    Numeric Type Conversion

    30    If the target and the operand types are both integer types, then the
          result is the value of the target type that corresponds to the same
          mathematical integer as the operand.

    31    If the target type is a decimal fixed point type, then the result is
          truncated (toward 0) if the value of the operand is not a multiple
          of the small of the target type.

    32    If the target type is some other real type, then the result is
          within the accuracy of the target type (see G.2, ``
          Numeric Performance Requirements'', for implementations that support
          the Numerics Annex).

    33    If the target type is an integer type and the operand type is real,
          the result is rounded to the nearest integer (away from zero if
          exactly halfway between two integers).

34    Enumeration Type Conversion

    35    The result is the value of the target type with the same position
          number as that of the operand value.

36    Array Type Conversion

    37    If the target subtype is a constrained array subtype, then a check
          is made that the length of each dimension of the value of the
          operand equals the length of the corresponding dimension of the
          target subtype. The bounds of the result are those of the target
          subtype.

    38    If the target subtype is an unconstrained array subtype, then the
          bounds of the result are obtained by converting each bound of the
          value of the operand to the corresponding index type of the target
          type. For each nonnull index range, a check is made that the bounds
          of the range belong to the corresponding index subtype.

    39    In either array case, the value of each component of the result is
          that of the matching component of the operand value (see 4.5.2).

40    Composite (Non-Array) Type Conversion

    41    The value of each nondiscriminant component of the result is that of
          the matching component of the operand value.

    42    The tag of the result is that of the operand. If the operand type is
          class-wide, a check is made that the tag of the operand identifies a
          (specific) type that is covered by or descended from the target
          type.

    43    For each discriminant of the target type that corresponds to a
          discriminant of the operand type, its value is that of the
          corresponding discriminant of the operand value; if it corresponds
          to more than one discriminant of the operand type, a check is made
          that all these discriminants are equal in the operand value.

    44    For each discriminant of the target type that corresponds to a
          discriminant that is specified by the derived_type_definition for
          some ancestor of the operand type (or if class-wide, some ancestor
          of the specific type identified by the tag of the operand), its
          value in the result is that specified by the
          derived_type_definition.

    45    For each discriminant of the operand type that corresponds to a
          discriminant that is specified by the derived_type_definition for
          some ancestor of the target type, a check is made that in the
          operand value it equals the value specified for it.

    46    For each discriminant of the result, a check is made that its value
          belongs to its subtype.

47    Access Type Conversion

    48    For an access-to-object type, a check is made that the accessibility
          level of the operand type is not deeper than that of the target
          type.

    49    If the target type is an anonymous access type, a check is made that
          the value of the operand is not null; if the target is not an
          anonymous access type, then the result is null if the operand value
          is null.

    50    If the operand value is not null, then the result designates the
          same object (or subprogram) as is designated by the operand value,
          but viewed as being of the target designated subtype (or profile);
          any checks associated with evaluating a conversion to the target
          designated subtype are performed.

51    After conversion of the value to the target type, if the target subtype
is constrained, a check is performed that the value satisfies this constraint.

52    For the evaluation of a view conversion, the operand name is evaluated,
and a new view of the object denoted by the operand is created, whose type is
the target type; if the target type is composite, checks are performed as
above for a value conversion.

53    The properties of this new view are as follows:

54/1  If the target type is composite, the bounds or discriminants (if any) of
      the view are as defined above for a value conversion; each
      nondiscriminant component of the view denotes the matching component of
      the operand object; the subtype of the view is constrained if either the
      target subtype or the operand object is constrained, or if the target
      subtype is indefinite, or if the operand type is a descendant of the
      target type, and has discriminants that were not inherited from the
      target type;

55    If the target type is tagged, then an assignment to the view assigns to
      the corresponding part of the object denoted by the operand; otherwise,
      an assignment to the view assigns to the object, after converting the
      assigned value to the subtype of the object (which might raise
      Constraint_Error);

56    Reading the value of the view yields the result of converting the value
      of the operand object to the target subtype (which might raise
      Constraint_Error), except if the object is of an access type and the
      view conversion is passed as an out parameter; in this latter case, the
      value of the operand object is used to initialize the formal parameter
      without checking against any constraint of the target subtype (see
      6.4.1).

57    If an Accessibility_Check fails, Program_Error is raised. Any other
check associated with a conversion raises Constraint_Error if it fails.

58    Conversion to a type is the same as conversion to an unconstrained
subtype of the type.

      NOTES

59    20  In addition to explicit type_conversions, type conversions are
      performed implicitly in situations where the expected type and the
      actual type of a construct differ, as is permitted by the type
      resolution rules (see 8.6). For example, an integer literal is of the
      type universal_integer, and is implicitly converted when assigned to a
      target of some specific integer type. Similarly, an actual parameter of
      a specific tagged type is implicitly converted when the corresponding
      formal parameter is of a class-wide type.

60    21  Even when the expected and actual types are the same, implicit
      subtype conversions are performed to adjust the array bounds (if any) of
      an operand to match the desired target subtype, or to raise
      Constraint_Error if the (possibly adjusted) value does not satisfy the
      constraints of the target subtype.

61    A ramification of the overload resolution rules is that the operand of
      an (explicit) type_conversion cannot be the literal null, an allocator,
      an aggregate, a string_literal, a character_literal, or an
      attribute_reference for an Access or Unchecked_Access attribute.
      Similarly, such an expression enclosed by parentheses is not allowed. A
      qualified_expression (see 4.7) can be used instead of such a
      type_conversion.

62    22  The constraint of the target subtype has no effect for a
      type_conversion of an elementary type passed as an out parameter. Hence,
      it is recommended that the first subtype be specified as the target to
      minimize confusion (a similar recommendation applies to renaming and
      generic formal in out objects).


                                  Examples

63    Examples of numeric type conversion:

64    Real(2*J)      --  value is converted to floating point
      Integer(1.6)   --  value is 2
      Integer(-0.4)  --  value is 0

65    Example of conversion between derived types:

66    type A_Form is new B_Form;

67    X : A_Form;
      Y : B_Form;

68    X := A_Form(Y);
      Y := B_Form(X);  --  the reverse conversion 

69    Examples of conversions between array types:

70    type Sequence is array (Integer range <>) of Integer;
      subtype Dozen is Sequence(1 .. 12);
      Ledger : array(1 .. 100) of Integer;

71    Sequence(Ledger)            --  bounds are those of Ledger
      Sequence(Ledger(31 .. 42))  --  bounds are 31 and 42
      Dozen(Ledger(31 .. 42))     --  bounds are those of Dozen 


4.7 Qualified Expressions


1     A qualified_expression is used to state explicitly the type, and to
verify the subtype, of an operand that is either an expression or an
aggregate.


                                   Syntax

2     qualified_expression ::= 
         subtype_mark'(expression) | subtype_mark'aggregate


                            Name Resolution Rules

3     The operand (the expression or aggregate) shall resolve to be of the
type determined by the subtype_mark, or a universal type that covers it.


                              Dynamic Semantics

4     The evaluation of a qualified_expression evaluates the operand (and if
of a universal type, converts it to the type determined by the subtype_mark)
and checks that its value belongs to the subtype denoted by the subtype_mark.
The exception Constraint_Error is raised if this check fails.

      NOTES

5     23  When a given context does not uniquely identify an expected type, a
      qualified_expression can be used to do so. In particular, if an
      overloaded name or aggregate is passed to an overloaded subprogram, it
      might be necessary to qualify the operand to resolve its type.


                                  Examples

6     Examples of disambiguating expressions using qualification:

7     type Mask is (Fix, Dec, Exp, Signif);
      type Code is (Fix, Cla, Dec, Tnz, Sub);

8     Print (Mask'(Dec));  --  Dec is of type Mask
      Print (Code'(Dec));  --  Dec is of type Code 

9     for J in Code'(Fix) .. Code'(Dec) loop ... -- qualification needed for either Fix or Dec
      for J in Code range Fix .. Dec loop ...    -- qualification unnecessary
      for J in Code'(Fix) .. Dec loop ...        -- qualification unnecessary for Dec

10    Dozen'(1 | 3 | 5 | 7 => 2, others => 0) -- see 4.6 


4.8 Allocators


1     The evaluation of an allocator creates an object and yields an access
value that designates the object.


                                   Syntax

2     allocator ::= 
         new subtype_indication | new qualified_expression


                            Name Resolution Rules

3/1   The expected type for an allocator shall be a single access-to-object
type with designated type D such that either D covers the type determined by
the subtype_mark of the subtype_indication or qualified_expression, or the
expected type is anonymous and the determined type is D'Class.


                               Legality Rules

4     An initialized allocator is an allocator with a qualified_expression. An
uninitialized allocator is one with a subtype_indication. In the
subtype_indication of an uninitialized allocator, a constraint is permitted
only if the subtype_mark denotes an unconstrained composite subtype; if there
is no constraint, then the subtype_mark shall denote a definite subtype.

5     If the type of the allocator is an access-to-constant type, the
allocator shall be an initialized allocator. If the designated type is
limited, the allocator shall be an uninitialized allocator.


                              Static Semantics

6     If the designated type of the type of the allocator is elementary, then
the subtype of the created object is the designated subtype. If the designated
type is composite, then the created object is always constrained; if the
designated subtype is constrained, then it provides the constraint of the
created object; otherwise, the object is constrained by its initial value
(even if the designated subtype is unconstrained with defaults).


                              Dynamic Semantics

7     For the evaluation of an allocator, the elaboration of the
subtype_indication or the evaluation of the qualified_expression is performed
first. For the evaluation of an initialized allocator, an object of the
designated type is created and the value of the qualified_expression is
converted to the designated subtype and assigned to the object.

8     For the evaluation of an uninitialized allocator:

9     If the designated type is elementary, an object of the designated
      subtype is created and any implicit initial value is assigned;

10/1  If the designated type is composite, an object of the designated type is
      created with tag, if any, determined by the subtype_mark of the
      subtype_indication; any per-object constraints on subcomponents are
      elaborated (see 3.8) and any implicit initial values for the
      subcomponents of the object are obtained as determined by the
      subtype_indication and assigned to the corresponding subcomponents. A
      check is made that the value of the object belongs to the designated
      subtype. Constraint_Error is raised if this check fails. This check and
      the initialization of the object are performed in an arbitrary order.

11    If the created object contains any tasks, they are activated (see 9.2).
Finally, an access value that designates the created object is returned.

      NOTES

12    24  Allocators cannot create objects of an abstract type. See 3.9.3.

13    25  If any part of the created object is controlled, the initialization
      includes calls on corresponding Initialize or Adjust procedures. See
      7.6.

14    26  As explained in 13.11, ``Storage Management'', the storage for an
      object allocated by an allocator comes from a storage pool (possibly
      user defined). The exception Storage_Error is raised by an allocator if
      there is not enough storage. Instances of Unchecked_Deallocation may be
      used to explicitly reclaim storage.

15    27  Implementations are permitted, but not required, to provide garbage
      collection (see 13.11.3).


                                  Examples

16    Examples of allocators:

17    new Cell'(0, null, null)                          -- initialized explicitly, see 3.10.1
      new Cell'(Value => 0, Succ => null, Pred => null) -- initialized explicitly
      new Cell                                          -- not initialized

18    new Matrix(1 .. 10, 1 .. 20)                      -- the bounds only are given
      new Matrix'(1 .. 10 => (1 .. 20 => 0.0))          -- initialized explicitly

19    new Buffer(100)                                   -- the discriminant only is given
      new Buffer'(Size => 80, Pos => 0, Value => (1 .. 80 => 'A')) -- initialized explicitly

20    Expr_Ptr'(new Literal)                  -- allocator for access-to-class-wide type, see 3.9.1
      Expr_Ptr'(new Literal'(Expression with 3.5))      -- initialized explicitly


4.9 Static Expressions and Static Subtypes


1     Certain expressions of a scalar or string type are defined to be static.
Similarly, certain discrete ranges are defined to be static, and certain
scalar and string subtypes are defined to be static subtypes. Static means
determinable at compile time, using the declared properties or values of the
program entities.

2     A static expression is a scalar or string expression that is one of the
following:

3     a numeric_literal;

4     a string_literal of a static string subtype;

5     a name that denotes the declaration of a named number or a static
      constant;

6     a function_call whose function_name or function_prefix statically
      denotes a static function, and whose actual parameters, if any (whether
      given explicitly or by default), are all static expressions;

7     an attribute_reference that denotes a scalar value, and whose prefix
      denotes a static scalar subtype;

8     an attribute_reference whose prefix statically denotes a statically
      constrained array object or array subtype, and whose
      attribute_designator is First, Last, or Length, with an optional
      dimension;

9     a type_conversion whose subtype_mark denotes a static scalar subtype,
      and whose operand is a static expression;

10    a qualified_expression whose subtype_mark denotes a static (scalar or
      string) subtype, and whose operand is a static expression;

11    a membership test whose simple_expression is a static expression, and
      whose range is a static range or whose subtype_mark denotes a static
      (scalar or string) subtype;

12    a short-circuit control form both of whose relations are static
      expressions;

13    a static expression enclosed in parentheses.

14    A name statically denotes an entity if it denotes the entity and:

15    It is a direct_name, expanded name, or character_literal, and it denotes
      a declaration other than a renaming_declaration; or

16    It is an attribute_reference whose prefix statically denotes some
      entity; or

17    It denotes a renaming_declaration with a name that statically denotes
      the renamed entity.

18    A static function is one of the following:

19    a predefined operator whose parameter and result types are all scalar
      types none of which are descendants of formal scalar types;

20    a predefined concatenation operator whose result type is a string type;

21    an enumeration literal;

22    a language-defined attribute that is a function, if the prefix denotes a
      static scalar subtype, and if the parameter and result types are scalar.

23    In any case, a generic formal subprogram is not a static function.

24    A static constant is a constant view declared by a full constant
declaration or an object_renaming_declaration with a static nominal subtype,
having a value defined by a static scalar expression or by a static string
expression whose value has a length not exceeding the maximum length of a
string_literal in the implementation.

25    A static range is a range whose bounds are static expressions, or a
range_attribute_reference that is equivalent to such a range. A static
discrete_range is one that is a static range or is a subtype_indication that
defines a static scalar subtype. The base range of a scalar type is a static
range, unless the type is a descendant of a formal scalar type.

26    A static subtype is either a static scalar subtype or a static string
subtype. A static scalar subtype is an unconstrained scalar subtype whose type
is not a descendant of a formal scalar type, or a constrained scalar subtype
formed by imposing a compatible static constraint on a static scalar subtype.
A static string subtype is an unconstrained string subtype whose index subtype
and component subtype are static (and whose type is not a descendant of a
formal array type), or a constrained string subtype formed by imposing a
compatible static constraint on a static string subtype. In any case, the
subtype of a generic formal object of mode in out, and the result subtype of a
generic formal function, are not static.

27    The different kinds of static constraint are defined as follows:

28    A null constraint is always static;

29    A scalar constraint is static if it has no range_constraint, or one with
      a static range;

30    An index constraint is static if each discrete_range is static, and each
      index subtype of the corresponding array type is static;

31    A discriminant constraint is static if each expression of the constraint
      is static, and the subtype of each discriminant is static.

32    A subtype is statically constrained if it is constrained, and its
constraint is static. An object is statically constrained if its nominal
subtype is statically constrained, or if it is a static string constant.


                               Legality Rules

33    A static expression is evaluated at compile time except when it is part
of the right operand of a static short-circuit control form whose value is
determined by its left operand. This evaluation is performed exactly, without
performing Overflow_Checks. For a static expression that is evaluated:

34    The expression is illegal if its evaluation fails a language-defined
      check other than Overflow_Check.

35    If the expression is not part of a larger static expression, then its
      value shall be within the base range of its expected type. Otherwise,
      the value may be arbitrarily large or small.

36    If the expression is of type universal_real and its expected type is a
      decimal fixed point type, then its value shall be a multiple of the
      small of the decimal type.

37    The last two restrictions above do not apply if the expected type is a
descendant of a formal scalar type (or a corresponding actual type in an
instance).


                         Implementation Requirements

38    For a real static expression that is not part of a larger static
expression, and whose expected type is not a descendant of a formal scalar
type, the implementation shall round or truncate the value (according to the
Machine_Rounds attribute of the expected type) to the nearest machine number
of the expected type; if the value is exactly half-way between two machine
numbers, any rounding shall be performed away from zero. If the expected type
is a descendant of a formal scalar type, no special rounding or truncating is
required - normal accuracy rules apply (see Annex G).

      NOTES

39    28  An expression can be static even if it occurs in a context where
      staticness is not required.

40    29  A static (or run-time) type_conversion from a real type to an
      integer type performs rounding. If the operand value is exactly half-way
      between two integers, the rounding is performed away from zero.


                                  Examples

41    Examples of static expressions:

42    1 + 1       -- 2
      abs(-10)*3  -- 30

43    Kilo : constant := 1000;
      Mega : constant := Kilo*Kilo;   -- 1_000_000
      Long : constant := Float'Digits*2;

44    Half_Pi    : constant := Pi/2;           -- see 3.3.2
      Deg_To_Rad : constant := Half_Pi/90;
      Rad_To_Deg : constant := 1.0/Deg_To_Rad; -- equivalent to 1.0/((3.14159_26536/2)/90)


4.9.1 Statically Matching Constraints and Subtypes



                              Static Semantics

1     A constraint statically matches another constraint if both are null
constraints, both are static and have equal corresponding bounds or
discriminant values, or both are nonstatic and result from the same
elaboration of a constraint of a subtype_indication or the same evaluation of
a range of a discrete_subtype_definition.

2     A subtype statically matches another subtype of the same type if they
have statically matching constraints. Two anonymous access subtypes statically
match if their designated subtypes statically match.

3     Two ranges of the same type statically match if both result from the
same evaluation of a range, or if both are static and have equal corresponding
bounds.

4     A constraint is statically compatible with a scalar subtype if it
statically matches the constraint of the subtype, or if both are static and
the constraint is compatible with the subtype. A constraint is statically
compatible with an access or composite subtype if it statically matches the
constraint of the subtype, or if the subtype is unconstrained. One subtype is
statically compatible with a second subtype if the constraint of the first is
statically compatible with the second subtype.