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3.5.5 Operations of Discrete Types

Static Semantics

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   For every discrete subtype S, the following attributes are defined:
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   S'Pos
S'Pos denotes a function with the following specification:
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function S'Pos(Arg : S'Base)
  return universal_integer
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This function returns the position number of the value of Arg, as a value of type universal_integer.
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   S'Val
S'Val denotes a function with the following specification:
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function S'Val(Arg : universal_integer)
  return S'Base
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{evaluation (Val) [partial]} {Constraint_Error (raised by failure of run-time check)} This function returns a value of the type of S whose position number equals the value of Arg. {Range_Check [partial]} {check, language-defined (Range_Check)} For the evaluation of a call on S'Val, if there is no value in the base range of its type with the given position number, Constraint_Error is raised.
7.a
Ramification: By the overload resolution rules, a formal parameter of type universal_integer allows an actual parameter of any integer type.
7.b
Reason: We considered allowing S'Val for a signed integer subtype S to return an out-of-range value, but since checks were required for enumeration and modular types anyway, the allowance didn't seem worth the complexity of the rule.

Implementation Advice

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   For the evaluation of a call on S'Pos for an enumeration subtype, if the value of the operand does not correspond to the internal code for any enumeration literal of its type [(perhaps due to an uninitialized variable)], then the implementation should raise Program_Error. {Program_Error (raised by failure of run-time check)} This is particularly important for enumeration types with noncontiguous internal codes specified by an enumeration_representation_clause.
8.a
Reason: We say Program_Error here, rather than Constraint_Error, because the main reason for such values is uninitialized variables, and the normal way to indicate such a use (if detected) is to raise Program_Error. (Other reasons would involve the misuse of low-level features such as Unchecked_Conversion.)
NOTES
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28  Indexing and loop iteration use values of discrete types.
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29  {predefined operations (of a discrete type) [partial]} The predefined operations of a discrete type include the assignment operation, qualification, the membership tests, and the relational operators; for a boolean type they include the short-circuit control forms and the logical operators; for an integer type they include type conversion to and from other numeric types, as well as the binary and unary adding operators - and +, the multiplying operators, the unary operator abs, and the exponentiation operator. The assignment operation is described in 5.2. The other predefined operations are described in Section 4.
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30  As for all types, objects of a discrete type have Size and Address attributes (see 13.3).
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31  For a subtype of a discrete type, the result delivered by the attribute Val might not belong to the subtype; similarly, the actual parameter of the attribute Pos need not belong to the subtype. The following relations are satisfied (in the absence of an exception) by these attributes:
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   S'Val(S'Pos(X)) = X
   S'Pos(S'Val(N)) = N

Examples

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    Examples of attributes of discrete subtypes:
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--  For the types and subtypes declared in subclause 3.5.1 the following hold: 
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--  Color'First   = White,   Color'Last   = Black
--  Rainbow'First = Red,     Rainbow'Last = Blue
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--  Color'Succ(Blue) = Rainbow'Succ(Blue) = Brown
--  Color'Pos(Blue)  = Rainbow'Pos(Blue)  = 4
--  Color'Val(0)     = Rainbow'Val(0)     = White

Extensions to Ada 83

17.a
{extensions to Ada 83} The attributes S'Succ, S'Pred, S'Width, S'Image, and S'Value have been generalized to apply to real types as well (see 3.5, ``Scalar Types'').

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