4.9 Static Expressions and Static Subtypes
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.]
Discussion: As opposed to more elaborate
data flow analysis, etc.
Language Design Principles
For an expression to be static, it has to be
calculable at compile time.
Only scalar and string expressions are static.
To be static, an expression cannot have any
nonscalar, nonstring subexpressions (though it can have nonscalar constituent
names). A
static scalar expression cannot have any nonscalar subexpressions. There
is one exception — a membership test for a string subtype can be
static, and the result is scalar, even though a subexpression is nonscalar.
The rules for evaluating static expressions
are designed to maximize portability of static calculations.
Reason: {
AI12-0201-1}
We support static string expressions so that, for example, the
aspect_definition
for a Link_Name aspect can contain a concatenation. We don't support
static aggregates (even for string types) or non-string static nonscalar
types; we're trying to keep it cheap and simple (from the implementer's
viewpoint).
Static Semantics
A
static expression is [a scalar or string expression that is] one of the
following:
Ramification: {
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A
numeric_literal
of a numeric type is always a static expression, even if its expected
type is not that of a static subtype. However, if its value is explicitly
converted to, or qualified by, a nonstatic subtype, the resulting expression
is nonstatic. Non-numeric types can have numeric literals if aspect Integer_Literal
or Real_Literal is used; these are never static.
Ramification: That is, the constrained
subtype defined by the index range of the string is static. Note that
elementary values don't generally have subtypes, while composite values
do (since the bounds or discriminants are inherent in the value).
{
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a
name that
denotes a named number, and that is interpreted as a value of a numeric
type;
To be honest: {
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This is referring the resolution of the named number and not the Static
Semantics (for which all named numbers are values of a universal numeric
type). The word “interpreted” is intended to make the distinction.
Ramification: Note that enumeration literals
are covered by the
function_call
case.
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;
Ramification: This includes uses of operators
that are equivalent to
function_calls.
Ramification: Note that this does not
include the case of an attribute that is a function; a reference to such
an attribute is not even an expression. See above for function calls.
An implementation may define the staticness
and other properties of implementation-defined attributes.
Reason: Adding qualification to an expression
shouldn't make it nonstatic, even for strings.
Reason: Clearly, we should allow membership
tests in exactly the same cases where we allow
qualified_expressions.
a short-circuit control form both of whose
relations
are static expressions;
a static expression enclosed in parentheses.
Discussion: Informally,
we talk about a
static value. When we do, we mean a value specified
by a static expression.
Ramification: {
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The language requires a static expression in a
number_declaration,
a numeric type definition, certain representation items, and a number
of other contexts.
A
name statically
denotes an entity if it denotes the entity and:
{
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statically denotes the declaration of an object [(possibly through one
or more renames)];
Proof: Follows from the definition of
statically denotes.
Reason: We disallow components in a
variant_part
so that no discriminant checks are needed to evaluate the
selected_component.
Note that other kinds of discriminant-dependent components do not need
any checks on access (only when they are changed).
{
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is an
indexed_component
whose prefix statically names an object, there is no implicit dereference
of the prefix, the object is statically constrained, and the index expressions
of the object are static and have values that are within the range of
the index constraint.
{
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For an entity other than an object, a
name
statically names an entity if the
name
statically denotes the entity.
A
static function is one of the following:
Ramification: These are the functions
whose calls can be static expressions.
a predefined operator whose parameter and result
types are all scalar types none of which are descendants of formal scalar
types;
{
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a predefined relational operator whose parameters are of a string type
that is not a descendant of a formal array type;
{
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a predefined concatenation operator whose result type is a string type
that is not a descendant of a formal array type;
{
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a shifting or rotating function associated with a modular type declared
in package Interfaces (see
B.2);
an enumeration literal;
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.
In any case, a generic formal subprogram is not a
static function.
{
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{
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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, and which satisfies any
constraint or predicate that applies to the nominal subtype.
Ramification: A deferred constant is
not static; the view introduced by the corresponding full constant declaration
can be static.
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.
{
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{
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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 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, 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. Also, a subtype is not static if any Dynamic_Predicate
specifications apply to it.
Ramification: String subtypes are the
only composite subtypes that can be static.
Reason: The
part about generic formal objects of mode in out is necessary
because the subtype of the formal is not required to have anything to
do with the subtype of the actual. For example:
subtype Int10 is Integer range 1..10;
generic
F : in out Int10;
procedure G;
procedure G is
begin
case F is
when 1..10 => null;
-- Illegal!
end case;
end G;
X : Integer range 1..20;
procedure I is new G(F => X); -- OK.
The
case_statement
is illegal, because the subtype of F is not static, so the choices have
to cover all values of Integer, not just those in the range 1..10. A
similar issue arises for generic formal functions, now that function
calls are object names.
The
different kinds of
static constraint are defined as follows:
A null constraint is always static;
A
scalar constraint is static if it has no
range_constraint,
or one with a static range;
An index constraint is static
if each
discrete_range
is static, and each index subtype of the corresponding array type is
static;
A discriminant constraint is
static if each
expression
of the constraint is static, and the subtype of each discriminant is
static.
{
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In any case, the constraint of the first subtype of a scalar formal type
is neither static nor null.
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
{
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An expression is
statically unevaluated if it is part of:
{
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the right operand of a static short-circuit control form whose value
is determined by its left operand; or
(if N = 0 then Min elsif 10_000/N > Min then 10_000/N else Min)
legal if N and Min are static and N = 0.
{
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A static expression is evaluated at compile time except when it is statically
unevaluated. The compile-time evaluation of a static expression is performed
exactly, without performing Overflow_Checks. For a static expression
that is evaluated:
{
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The expression is illegal if its evaluation fails a language-defined
check other than Overflow_Check. For the purposes of this evaluation,
the assertion policy is assumed to be Check.
Reason: {
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Assertion policies can control whether checks are made, but we don't
want assertion policies to affect legality. For Ada 2012, subtype predicates
are the only checks controlled by the assertion policy that can appear
in static expressions.
{
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If the expression is not part of a larger static expression and the expression
is expected to be of a single specific type, then its value shall be
within the base range of its expected type. Otherwise, the value may
be arbitrarily large or small.
Ramification: {
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If the expression is expected to be of a universal type, or of “any
integer type”, there are no limits on the value of the expression.
{
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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. This restriction does not apply
if the expected type is a descendant of a formal scalar type (or a corresponding
actual type in an instance).
Ramification: This means that a
numeric_literal
for a decimal type cannot have “extra” significant digits.
Reason: {
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The small is not known for a generic formal type, so we have to exclude
formal types from this check.
{
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In addition to the places where Legality Rules normally
apply (see
12.3), the above restrictions also
apply in the private part of an instance of a generic unit.
Discussion: Values outside the base range
are not permitted when crossing from the “static” domain
to the “dynamic” domain. This rule is designed to enhance
portability of programs containing static expressions. Note that this
rule applies to the exact value, not the value after any rounding or
truncation. (See below for the rounding and truncation requirements.)
Short-circuit
control forms are a special case:
N: constant := 0.0;
X: constant Boolean := (N = 0.0) or else (1.0/N > 0.5); -- Static.
The declaration of X is legal, since the divide-by-zero
part of the expression is not evaluated. X is a static constant equal
to True.
{
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The preceding “statically unevaluated” rule allows
X : constant := (if True then 37 else (1 / 0));
but does not allow
function If_Then_Else (Flag : Boolean; X, Y : Integer)
return Integer
is
(
if Flag
then X
else Y)
with Static; --
see 6.8
X :
constant := If_Then_Else (True, 37, 1 / 0);
because evaluation
of a function call includes evaluation of all of its actual parameters.
Implementation Requirements
{
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{
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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 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, the rounding
performed is implementation-defined. If the expected type is a descendant
of a formal type, or if the static expression appears in the body of
an instance of a generic unit and the corresponding expression is nonstatic
in the corresponding generic body, then no special rounding or truncating
is required — normal accuracy rules apply (see
Annex
G).
Implementation defined: Rounding of real
static expressions which are exactly half-way between two machine numbers.
Reason: {
AI95-00268-01}
Discarding extended precision enhances portability by ensuring that the
value of a static constant of a real type is always a machine number
of the type.
When the expected type is a descendant of a
formal floating point type, extended precision (beyond that of the machine
numbers) can be retained when evaluating a static expression, to ease
code sharing for generic instantiations. For similar reasons, normal
(nondeterministic) rounding or truncating rules apply for descendants
of a formal fixed point type.
{
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There is no requirement for exact evaluation or special rounding in an
instance body (unless the expression is static in the generic body).
This eliminates a potential contract issue where the exact value of a
static expression depends on the actual parameters (which could then
affect the legality of other code).
Implementation Note: Note that the implementation
of static expressions has to keep track of plus and minus zero for a
type whose Signed_Zeros attribute is True.
{
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Note that the only machine numbers of a fixed point type are the multiples
of the small, so a static conversion to a fixed-point type, or division
by an integer, must do truncation to a multiple of small. It is not correct
for the implementation to do all static calculations in infinite precision.
Implementation Advice
{
AI95-00268-01}
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 type, the rounding
should be the same as the default rounding for the target system.
Implementation Advice: A real static
expression with a nonformal type that is not part of a larger static
expression should be rounded the same as the target system.
NOTE 1 An expression can be static
even if it occurs in a context where staticness is not required.
Ramification:
For example:
X : Float := Float'(1.0E+400) + 1.0 - Float'(1.0E+400);
The expression is static, which means that the
value of X must be exactly 1.0, independent of the accuracy or range
of the run-time floating point implementation.
NOTE 2 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.
Reason: We specify this for portability.
The reason for not choosing round-to-nearest-even, for example, is that
this method is easier to undo.
Ramification: The attribute Truncation
(see
A.5.3) can be used to perform a (static)
truncation prior to conversion, to prevent rounding.
Implementation Note: The value of the
literal 0E999999999999999999999999999999999999999999999 is zero. The
implementation must take care to evaluate such literals properly.
Examples
Examples of static
expressions:
1 + 1 -- 2
abs(-10)*3 -- 30
Kilo : constant := 1000;
Mega : constant := Kilo*Kilo; -- 1_000_000
Long : constant := Float'Digits*2;
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)Extensions to Ada 83
The rules for static expressions
and static subtypes are generalized to allow more kinds of compile-time-known
expressions to be used where compile-time-known values are required,
as follows:
Membership tests and short-circuit control
forms may appear in a static expression.
The bounds and length of statically constrained
array objects or subtypes are static.
The Range attribute of a statically constrained
array subtype or object gives a static range.
All numeric literals are now static, even
if the expected type is a formal scalar type. This is useful in
case_statements
and
variant_parts,
which both now allow a value of a formal scalar type to control the selection,
to ease conversion of a package into a generic package. Similarly, named
array aggregates are also permitted for array types with an index type
that is a formal scalar type.
The rules for the evaluation of static expressions
are revised to require exact evaluation at compile time, and force a
machine number result when crossing from the static realm to the dynamic
realm, to enhance portability and predictability. Exact evaluation is
not required for descendants of a formal scalar type, to simplify generic
code sharing and to avoid generic contract model problems.
Static expressions
are legal even if an intermediate in the expression goes outside the
base range of the type. Therefore, the following will succeed in Ada
95, whereas it might raise an exception in Ada 83:
type Short_Int is range -32_768 .. 32_767;
I : Short_Int := -32_768;
This might raise an exception in Ada 83 because
"32_768" is out of range, even though "–32_768"
is not. In Ada 95, this will always succeed.
Certain expressions involving string operations
(in particular concatenation and membership tests) are considered static
in Ada 95.
The reason for this change is to simplify the
rule requiring compile-time-known string expressions as the link name
in an interfacing pragma, and to simplify the preelaborability rules.
Incompatibilities With Ada 83
An Ada 83 program that uses
an out-of-range static value is illegal in Ada 95, unless the expression
is part of a larger static expression, or the expression is not evaluated
due to being on the right-hand side of a short-circuit control form.
Wording Changes from Ada 83
The existence of static string expressions necessitated
changing the definition of static subtype to include string subtypes.
Most occurrences of "static subtype" have been changed to "static
scalar subtype", in order to preserve the effect of the Ada 83 rules.
This has the added benefit of clarifying the difference between "static
subtype" and "statically constrained subtype", which has
been a source of confusion. In cases where we allow static string subtypes,
we explicitly use phrases like "static string subtype" or "static
(scalar or string) subtype", in order to clarify the meaning for
those who have gotten used to the Ada 83 terminology.
In Ada 83, an
expression was considered nonstatic if it raised an exception. Thus,
for example:
Bad: constant := 1/0; -- Illegal!
was illegal because 1/0 was not static. In Ada
95, the above example is still illegal, but for a different reason: 1/0
is static, but there's a separate rule forbidding the exception raising.
Inconsistencies With Ada 95
{
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Amendment Correction: Rounding of static real
expressions is implementation-defined in Ada 2005, while it was specified
as away from zero in (original) Ada 95. This could make subtle differences
in programs. However, the original Ada 95 rule required rounding that
(probably) differed from the target processor, thus creating anomalies
where the value of a static expression was required to be different than
the same expression evaluated at run time.
Wording Changes from Ada 95
{
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{
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The Ada 95 wording that defined static subtypes unintentionally failed
to exclude formal derived types that happen to be scalar (these aren't
formal scalar types); and had a parenthetical remark excluding formal
string types - but that was neither necessary nor parenthetical (it didn't
follow from other wording). This issue also applies to the rounding rules
for real static expressions.
{
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Ada 95 didn't clearly define the bounds of a value of a static expression
for universal types and for “any integer/float/fixed type”.
We also make it clear that we do not intend exact evaluation of static
expressions in an instance body if the expressions aren't static in the
generic body.
{
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We clarify that the first subtype of a scalar formal type has a nonstatic,
nonnull constraint.
Wording Changes from Ada 2005
{
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Added wording to prevent subtypes that have dynamic predicates (see
3.2.4)
from being static.
Incompatibilities With Ada 2012
{
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Added a missing exclusion for concatenations of a
string type descended from a formal array type. This could potentially
make some expression non-static; but as that could only matter in a context
where a static string is required (such as the Link_Name aspect), it
is quite unlikely.
{
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Shifting and rotating functions declared in package Interfaces are now
static. This could potentially make some expression illegal that is legal
if nonstatic (as in Ada 2012). While this can happen especially in conditional
code that is not in use, it is quite unlikely given typical uses of shifting
or rotating functions.
Extensions to Ada 2012
{
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Expressions involving string relational operators
or string type conversions now can be static. Additionally, the length
limit on static string constants was removed as being a hazard without
much help to implementations.
Wording Changes from Ada 2012
{
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Expression functions can be static if declared correctly; this is documented
as an extension in
6.8.
{
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Clarified that a target name symbol can statically denote an entity if
the associated
variable_name
statically denotes an entity. This is necessary so that target names
participate in the anti-order-dependence checks of
6.4.1.
{
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Correction: Clarified that constants whose values do not belong
to their nominal subtype are not static. This change potentially would
be incompatible, but this case is considered pathological and will not
be checked by the ACATS.
Wording Changes from Ada 2022
{
AI22-0018-1}
Corrigendum: Removed text about a non-existent
attribute.
Ada 2005 and 2012 Editions sponsored in part by Ada-Europe
