Ada's type system allows the programmer to construct powerful abstractions that represent the real world, and to provide valuable information to the compiler, so that the compiler can find many logic or design errors before they become bugs. It is at the heart of the language, and good Ada programmers learn to use it to great advantage. Four principles govern the type system:
Types are incompatible with one another. However, each type can have any number of subtypes, which are compatible with their base type and may be compatible with one another. See below for examples of subtypes which are incompatible with one another.
There are several predefined types, but most programmers prefer to define their own, application-specific types. Nevertheless, these predefined types are very useful as interfaces between libraries developed independently. The predefined library, obviously, uses these types too.
These types are predefined in the Standard package:
Positivesubtypes of this type.
Character), 16-bit characters (called
Wide_Character), and 32-bit characters (
Characterhas been present since the first version of the language (Ada 83),
Wide_Characterwas added in Ada 95, while the type
Wide_Wide_Characteris available with Ada 2005.
Wide_Wide_Characterrespectively. The standard library contains packages for handling strings in three variants: fixed length (
Ada.Strings.Fixed), with varying length below a certain upper bound (
Ada.Strings.Bounded), and unbounded length (
Ada.Strings.Unbounded). Each of these packages has a
Booleanin Ada is an Enumeration of
Truewith special semantics.
Storage_Offsetand their associated subprograms provide for address arithmetic.
Storage_Offsetwhich cannot be negative, and represents the memory size of a data structure (similar to C's
Storage_Elements without any meaning, useful when doing raw memory access.
Types are organized hierarchically. A type inherits properties from types above it in the hierarchy. For example, all scalar types (integer, enumeration, modular, fixed-point and floating-point types) have operators "<", ">" and arithmetic operators defined for them, and all discrete types can serve as array indexes.
Here is a broad overview of each category of types; please follow the links for detailed explanations. Inside parenthesis there are equivalences in C and Pascal for readers familiar with those languages.
The types of this hierarchy can be classified as follows.
Specific vs. Class-wide
Operations of specific types are non-dispatching, those on class-wide types are dispatching.
New types can be declared by deriving from specific types; primitive operations are inherited by derivation. You cannot derive from class-wide types.
Constrained vs. Unconstrained
type AU is array (I range <>) of ... -- unconstrained type R (X: Discriminant [:= Default]) is ... -- unconstrained
By giving a constraint to an unconstrained subtype, a subtype or object becomes constrained:
subtype RC is R (Value); -- constrained subtype of R OC: R (Value); -- constrained object of anonymous constrained subtype of R OU: R; -- unconstrained object
Declaring an unconstrained object is only possible if a default value is given in the type declaration above. The language does not specify how such objects are allocated. GNAT allocates the maximum size, so that size changes that might occur with discriminant changes present no problem. Another possibility is implicit dynamic allocation on the heap and re-allocation followed by a deallocation when the size changes.
Definite vs. Indefinite
type T (<>) is ... -- indefinite type AU is array (I range <>) of ... -- indefinite type RI (X: Discriminant) is ... -- indefinite
Definite subtypes allow the declaration of objects without initial value, since objects of definite subtypes have constraints that are known at creation-time. Object declarations of indefinite subtypes need an initial value to supply a constraint; they are then constrained by the constraint delivered by the initial value.
OT: T := Expr; -- some initial expression (object, function call, etc.) OA: AU := (3 => 10, 5 => 2, 4 => 4); -- index range is now 3 .. 5 OR: RI := Expr; -- again some initial expression as above
Unconstrained vs. Indefinite
Note that unconstrained subtypes are not necessarily indefinite as can be seen above with RD: it is a definite unconstrained subtype.
The Ada language uses types for one more purpose in addition to classifying data + operations. The type system integrates concurrency (threading, parallelism). Programmers will use types for expressing the concurrent threads of control of their programs.
The core pieces of this part of the type system, the task types and the protected types are explained in greater depth in a section on tasking.
Limiting a type means disallowing assignment. The "concurrency types" described above are always limited. Programmers can define their own types to be limited, too, like this:
You can learn more in the limited types chapter.
You can define a new type with the following syntax:
followed by the description of the type, as explained in detail in each category of type.
Formally, the above declaration creates a type and its first subtype named
T. The type itself, correctly called the "type of T", is anonymous; the RM refers to it as
T (in italics), but often speaks sloppily about the type T. But this is an academic consideration; for most purposes, it is sufficient to think of
T as a type. For scalar types, there is also a base type called
T'Base, which encompasses all values of T.
For signed integer types, the type of T comprises the (complete) set of mathematical integers. The base type is a certain hardware type, symmetric around zero (except for possibly one extra negative value), encompassing all values of T.
As explained above, all types are incompatible; thus:
type Integer_1 is range 1 .. 10; type Integer_2 is range 1 .. 10; A : Integer_1 := 8; B : Integer_2 := A; -- illegal!
is illegal, because
Integer_2 are different and incompatible types. It is this feature which allows the compiler to detect logic errors at compile time, such as adding a file descriptor to a number of bytes, or a length to a weight. The fact that the two types have the same range does not make them compatible: this is name equivalence in action, as opposed to structural equivalence. (Below, we will see how you can convert between incompatible types; there are strict rules for this.)
You can also create new subtypes of a given type, which will be compatible with each other, like this:
type Integer_1 is range 1 .. 10; subtype Integer_2 is Integer_1 range 7 .. 11; -- bad subtype Integer_3 is Integer_1'Base range 7 .. 11; -- OK A : Integer_1 := 8; B : Integer_3 := A; -- OK
The declaration of
Integer_2 is bad because the constraint
7 .. 11 is not compatible with
Integer_1; it raises
Constraint_Error at subtype elaboration time.
Integer_3 are compatible because they are both subtypes of the same type, namely
It is not necessary that the subtype ranges overlap, or be included in one another. The compiler inserts a run-time range check when you assign A to B; if the value of A, at that point, happens to be outside the range of
Integer_3, the program raises
There are a few predefined subtypes which are very useful:
subtype Natural is Integer range 0 .. Integer'Last; subtype Positive is Integer range 1 .. Integer'Last;
A derived type is a new, full-blown type created from an existing one. Like any other type, it is incompatible with its parent; however, it inherits the primitive operations defined for the parent type.
type Integer_1 is range 1 .. 10; type Integer_2 is new Integer_1 range 2 .. 8; A : Integer_1 := 8; B : Integer_2 := A; -- illegal!
Here both types are discrete; it is mandatory that the range of the derived type be included in the range of its parent. Contrast this with subtypes. The reason is that the derived type inherits the primitive operations defined for its parent, and these operations assume the range of the parent type. Here is an illustration of this feature:
procedure Derived_Types is package Pak is type Integer_1 is range 1 .. 10; procedure P (I: in Integer_1); -- primitive operation, assumes 1 .. 10 type Integer_2 is new Integer_1 range 8 .. 10; -- must not break P's assumption -- procedure P (I: in Integer_2); inherited P implicitly defined here end Pak; package body Pak is -- omitted end Pak; use Pak; A: Integer_1 := 4; B: Integer_2 := 9; begin P (B); -- OK, call the inherited operation end Derived_Types;
When we call
P (B), the parameter B is converted to
Integer_1; this conversion of course passes since the set of acceptable values for the derived type (here, 8 .. 10) must be included in that of the parent type (1 .. 10). Then P is called with the converted parameter.
Consider however a variant of the example above:
procedure Derived_Types is package Pak is type Integer_1 is range 1 .. 10; procedure P (I: in Integer_1; J: out Integer_1); type Integer_2 is new Integer_1 range 8 .. 10; end Pak; package body Pak is procedure P (I: in Integer_1; J: out Integer_1) is begin J := I - 1; end P; end Pak; use Pak; A: Integer_1 := 4; X: Integer_1; B: Integer_2 := 8; Y: Integer_2; begin P (A, X); P (B, Y); end Derived_Types;
P (B, Y) is called, both parameters are converted to
Integer_1. Thus the range check on J (7) in the body of P will pass. However on return parameter Y is converted back to
Integer_2 and the range check on Y will of course fail.
With the above in mind, you will see why in the following program Constraint_Error will be called at run time, before
P is even called.
procedure Derived_Types is package Pak is type Integer_1 is range 1 .. 10; procedure P (I: in Integer_1; J: out Integer_1); type Integer_2 is new Integer_1'Base range 8 .. 12; end Pak; package body Pak is procedure P (I: in Integer_1; J: out Integer_1) is begin J := I - 1; end P; end Pak; use Pak; B: Integer_2 := 11; Y: Integer_2; begin P (B, Y); end Derived_Types;
Ada supports various categories of subtypes which have different abilities. Here is an overview in alphabetical order.
A subtype which does not have a name assigned to it. Such a subtype is created with a variable declaration:
X : String (1 .. 10) := (others => ' ');
Here, (1 .. 10) is the constraint. This variable declaration is equivalent to:
In Ada, all types are anonymous and only subtypes may be named. For scalar types, there is a special subtype of the anonymous type, called the base type, which is nameable with the 'Base attribute. The base type comprises all values of the first subtype. Some examples:
The base type
Int'Base is a hardware type selected by the compiler that comprises the values of
Int. Thus it may have the range -27 .. 27-1 or -215 .. 215-1 or any other such type.
Enum'Base is the same as
Short'Base also holds the literal
A subtype of an indefinite subtype that adds constraints. The following example defines a 10 character string sub-type.
You cannot partially constrain an unconstrained subtype:
type My_Array is array (Integer range <>, Integer range <>) of Some_Type; -- subtype Constr is My_Array (1 .. 10, Integer range <>); illegal subtype Constr is My_Array (1 .. 10, -100 .. 200);
Constraints for all indices must be given, the result is necessarily a definite subtype.
A definite subtype is a subtype whose size is known at compile-time. All subtypes which are not indefinite subtypes are, by definition, definite subtypes.
Objects of definite subtypes may be declared without additional constraints.
An indefinite subtype is a subtype whose size is not known at compile-time but is dynamically calculated at run-time. An indefinite subtype does not by itself provide enough information to create an object; an additional constraint or explicit initialization expression is necessary in order to calculate the actual size and therefore create the object.
X : String := "This is a string";
X is an object of the indefinite (sub)type
String. Its constraint is derived implicitly from its initial value.
X may change its value, but not its bounds.
It should be noted that it is not necessary to initialize the object from a literal. You can also use a function. For example:
X : String := Ada.Command_Line.Argument (1);
This statement reads the first command-line argument and assigns it to
A subtype of an indefinite subtype that does not add a constraint only introduces a new name for the original subtype (a kind of renaming under a different notion).
My_String and String are interchangeable.
A subtype which has a name assigned to it. "First subtypes" are created with the keyword
type (remember that types are always anonymous, the name in a type declaration is the name of the first subtype), others with the keyword
subtype. For example:
Count_to_Ten is the first subtype of a suitable integer base type. However, if you would like to use this as an index constraint on
String, the following declaration is illegal:
This is because
Positive as its index, which is a subtype of
Integer (these declarations are taken from package
subtype Positive is Integer range 1 .. Integer'Last; type String is (Positive range <>) of Character;
So you have to use the following declarations:
Ten_Characters is the name of that subtype of
String which is constrained to
Count_To_Ten. You see that posing constraints on types versus subtypes has very different effects.
Any indefinite type is also an unconstrained subtype. However, unconstrainedness and indefiniteness are not the same.
type My_Enum is (A, B, C); type My_Record (Discriminant: My_Enum) is ...; My_Object_A: My_Record (A);
This type is unconstrained and indefinite because you need to give an actual discriminant for object declarations; the object is constrained to this discriminant which may not change.
When however a default is provided for the discriminant, the type is definite yet unconstrained; it allows to define both, constrained and unconstrained objects:
type My_Enum is (A, B, C); type My_Record (Discriminant: My_Enum := A) is ...; My_Object_U: My_Record; -- unconstrained object My_Object_B: My_Record (B); -- constrained to discriminant B like above
Here, My_Object_U is unconstrained; upon declaration, it has the discriminant A (the default) which however may change.
type My_Integer is range -10 .. + 10; subtype My_Positive is My_Integer range + 1 .. + 10; subtype My_Negative is My_Integer range -10 .. - 1;
These subtypes are of course incompatible.
Another example are subtypes of a discriminated record:
type My_Enum is (A, B, C); type My_Record (Discriminant: My_Enum) is ...; subtype My_A_Record is My_Record (A); subtype My_C_Record is My_Record (C);
Also these subtypes are incompatible.
In most cases, the compiler is able to infer the type of an expression; for example:
Here the compiler knows that
A is a value of the type
Enum. But consider:
procedure Bad is type Enum_1 is (A, B, C); procedure P (E : in Enum_1) is... -- omitted type Enum_2 is (A, X, Y, Z); procedure P (E : in Enum_2) is... -- omitted begin P (A); -- illegal: ambiguous end Bad;
The compiler cannot choose between the two versions of
P; both would be equally valid. To remove the ambiguity, you use a qualified expression:
P (Enum_1'(A)); -- OK
As seen in the following example, this syntax is often used when creating new objects. If you try to compile the example, it will fail with a compilation error since the compiler will determine that 256 is not in range of
with Ada.Text_IO; procedure Convert_Evaluate_As is type Byte is mod 2**8; type Byte_Ptr is access Byte; package T_IO renames Ada.Text_IO; package M_IO is new Ada.Text_IO.Modular_IO (Byte); A : constant Byte_Ptr := new Byte'(256); begin T_IO.Put ("A = "); M_IO.Put (Item => A.all, Width => 5, Base => 10); end Convert_Evaluate_As;
You should use qualified expression when getting a string literal's length.
"foo"'Length -- compilation error: prefix of attribute must be a name -- qualify expression to turn it into a name String'("foo" & "bar")'Length -- 6
Data do not always come in the format you need them. You must, then, face the task of converting them. As a true multi-purpose language with a special emphasis on "mission critical", "system programming" and "safety", Ada has several conversion techniques. The most difficult part is choosing the right one, so the following list is sorted in order of utility. You should try the first one first; the last technique is a last resort, to be used if all others fail. There are also a few related techniques that you might choose instead of actually converting the data.
Since the most important aspect is not the result of a successful conversion, but how the system will react to an invalid conversion, all examples also demonstrate faulty conversions.
An explicit type conversion looks much like a function call; it does not use the tick (apostrophe, ') like the qualified expression does.
The compiler first checks that the conversion is legal, and if it is, it inserts a run-time check at the point of the conversion; hence the name checked conversion. If the conversion fails, the program raises Constraint_Error. Most compilers are very smart and optimise away the constraint checks; so, you need not worry about any performance penalty. Some compilers can also warn that a constraint check will always fail (and optimise the check with an unconditional raise).
Explicit type conversions are legal:
(The rules become more complex with class-wide and anonymous access types.)
I: Integer := Integer (10); -- Unnecessary explicit type conversion J: Integer := 10; -- Implicit conversion from universal integer K: Integer := Integer'(10); -- Use the value 10 of type Integer: qualified expression -- (qualification not necessary here).
This example illustrates explicit type conversions:
with Ada.Text_IO; procedure Convert_Checked is type Short is range -128 .. +127; type Byte is mod 256; package T_IO renames Ada.Text_IO; package I_IO is new Ada.Text_IO.Integer_IO (Short); package M_IO is new Ada.Text_IO.Modular_IO (Byte); A : Short := -1; B : Byte; begin B := Byte (A); -- range check will lead to Constraint_Error T_IO.Put ("A = "); I_IO.Put (Item => A, Width => 5, Base => 10); T_IO.Put (", B = "); M_IO.Put (Item => B, Width => 5, Base => 10); end Convert_Checked;
Explicit conversions are possible between any two numeric types: integers, fixed-point and floating-point types. If one of the types involved is a fixed-point or floating-point type, the compiler not only checks for the range constraints (thus the code above will raise Constraint_Error), but also performs any loss of precision necessary.
Example 1: the loss of precision causes the procedure to only ever print "0" or "1", since
P / 100 is an integer and is always zero or one.
with Ada.Text_IO; procedure Naive_Explicit_Conversion is type Proportion is digits 4 range 0.0 .. 1.0; type Percentage is range 0 .. 100; function To_Proportion (P : in Percentage) return Proportion is begin return Proportion (P / 100); end To_Proportion; begin Ada.Text_IO.Put_Line (Proportion'Image (To_Proportion (27))); end Naive_Explicit_Conversion;
Example 2: we use an intermediate floating-point type to guarantee the precision.
with Ada.Text_IO; procedure Explicit_Conversion is type Proportion is digits 4 range 0.0 .. 1.0; type Percentage is range 0 .. 100; function To_Proportion (P : in Percentage) return Proportion is type Prop is digits 4 range 0.0 .. 100.0; begin return Proportion (Prop (P) / 100.0); end To_Proportion; begin Ada.Text_IO.Put_Line (Proportion'Image (To_Proportion (27))); end Explicit_Conversion;
You might ask why you should convert between two subtypes of the same type. An example will illustrate this.
subtype String_10 is String (1 .. 10); X: String := "A line long enough to make the example valid"; Slice: constant String := String_10 (X (11 .. 20));
Slice has bounds 1 and 10, whereas
X (11 .. 20) has bounds 11 and 20.
Type conversions can be used for packing and unpacking of records or arrays.
type Unpacked is record -- any components end record; type Packed is new Unpacked; for Packed use record -- component clauses for some or for all components end record;
P: Packed; U: Unpacked; P := Packed (U); -- packs U U := Unpacked (P); -- unpacks P
The examples above all revolved around conversions between numeric types; it is possible to convert between any two numeric types in this way. But what happens between non-numeric types, e.g. between array types or record types? The answer is two-fold:
Why would you want to derive a record type from another record type? Because of representation clauses. Here we enter the realm of low-level systems programming, which is not for the faint of heart, nor is it useful for desktop applications. So hold on tight, and let's dive in.
Suppose you have a record type which uses the default, efficient representation. Now you want to write this record to a device, which uses a special record format. This special representation is more compact (uses fewer bits), but is grossly inefficient. You want to have a layered programming interface: the upper layer, intended for applications, uses the efficient representation. The lower layer is a device driver that accesses the hardware directly and uses the inefficient representation.
package Device_Driver is type Size_Type is range 0 .. 64; type Register is record A, B : Boolean; Size : Size_Type; end record; procedure Read (R : out Register); procedure Write (R : in Register); end Device_Driver;
The compiler chooses a default, efficient representation for
Register. For example, on a 32-bit machine, it would probably use three 32-bit words, one for A, one for B and one for Size. This efficient representation is good for applications, but at one point we want to convert the entire record to just 8 bits, because that's what our hardware requires.
package body Device_Driver is type Hardware_Register is new Register; -- Derived type. for Hardware_Register use record A at 0 range 0 .. 0; B at 0 range 1 .. 1; Size at 0 range 2 .. 7; end record; function Get return Hardware_Register; -- Body omitted procedure Put (H : in Hardware_Register); -- Body omitted procedure Read (R : out Register) is H : Hardware_Register := Get; begin R := Register (H); -- Explicit conversion. end Read; procedure Write (R : in Register) is begin Put (Hardware_Register (R)); -- Explicit conversion. end Write; end Device_Driver;
In the above example, the package body declares a derived type with the inefficient, but compact representation, and converts to and from it.
This illustrates that type conversions can result in a change of representation.
Within object-oriented programming you have to distinguish between specific types and class-wide types.
With specific types, only conversions to ancestors are possible and, of course, are checked. During the conversion, you do not "drop" any components that are present in the derived type and not in the parent type; these components are still present, you just don't see them anymore. This is called a view conversion.
There are no conversions to derived types (where would you get the further components from?); extension aggregates have to be used instead.
type Parent_Type is tagged null record; type Child_Type is new Parent_Type with null record; Child_Instance : Child_Type; -- View conversion from the child type to the parent type: Parent_View : Parent_Type := Parent_Type (Child_Instance);
Since, in object-oriented programming, an object of child type is an object of the parent type, no run-time check is necessary.
With class-wide types, conversions to ancestor and child types are possible and are checked as well. These conversions are also view conversions, no data is created or lost.
procedure P (Parent_View : Parent_Type'Class) is -- View conversion to the child type: One : Child_Type := Child_Type (Parent_View); -- View conversion to the class-wide child type: Two : Child_Type'Class := Child_Type'Class (Parent_View);
This view conversion involves a run-time check to see if
Parent_View is indeed a view of an object of type
Child_Type. In the second case, the run-time check accepts objects of type
Child_Type but also any type derived from
A renaming declaration does not create any new object and performs no conversion; it only gives a new name to something that already exists. Performance is optimal since the renaming is completely done at compile time. We mention it here because it is a common idiom in object oriented programming to rename the result of a view conversion.
type Parent_Type is tagged record <components>; end record; type Child_Type is new Parent_Type with record <further components>; end record; Child_Instance : Child_Type; Parent_View : Parent_Type'Class renames Parent_Type'Class (Child_Instance);
Parent_View is not a new object, but another name for
Child_Instance viewed as the parent, i.e. only the parent components are visible, the further child components are hidden.
Ada's access type is not just a memory location (a thin pointer). Depending on implementation and the access type used, the access might keep additional information (a fat pointer). For example GNAT keeps two memory addresses for each access to an indefinite object -- one for the data and one for the constraint informations (Size, First, Last).
If you want to convert an access to a simple memory location you can use the package
System.Address_To_Access_Conversions. Note however that an address and a fat pointer cannot be converted reversibly into one another.
The address of an array object is the address of its first component. Thus the bounds get lost in such a conversion.
type My_Array is array (Positive range <>) of Something; A: My_Array (50 .. 100); A'Address = A(A'First)'Address
One of the great criticisms of Pascal was "there is no escape". The reason was that sometimes you have to convert the incompatible. For this purpose, Ada has the generic function Unchecked_Conversion:
generic type Source (<>) is limited private; type Target (<>) is limited private; function Ada.Unchecked_Conversion (S : Source) return Target;
Unchecked_Conversion will bit-copy the source data and reinterpret them under the target type without any checks. It is your chore to make sure that the requirements on unchecked conversion as stated in RM 13.9 (Annotated) are fulfilled; if not, the result is implementation dependent and may even lead to abnormal data. Use the 'Valid attribute after the conversion to check the validity of the data in problematic cases.
A function call to (an instance of)
Unchecked_Conversion will copy the source to the destination. The compiler may also do a conversion in place (every instance has the convention Intrinsic).
Unchecked_Conversion you need to instantiate the generic.
In the example below, you can see how this is done. When run, the example will output
A = -1, B = 255. No error will be reported, but is this the result you expect?
with Ada.Text_IO; with Ada.Unchecked_Conversion; procedure Convert_Unchecked is type Short is range -128 .. +127; type Byte is mod 256; package T_IO renames Ada.Text_IO; package I_IO is new Ada.Text_IO.Integer_IO (Short); package M_IO is new Ada.Text_IO.Modular_IO (Byte); function Convert is new Ada.Unchecked_Conversion (Source => Short, Target => Byte); A : constant Short := -1; B : Byte; begin B := Convert (A); T_IO.Put ("A = "); I_IO.Put (Item => A, Width => 5, Base => 10); T_IO.Put (", B = "); M_IO.Put (Item => B, Width => 5, Base => 10); end Convert_Unchecked;
There is of course a range check in the assignment
B := Convert (A);. Thus if
B were defined as
B: Byte range 0 .. 10;,
Constraint_Error would be raised.
If the copying of the result of
Unchecked_Conversion is too much waste in terms of performance, then you can try overlays, i.e. address mappings. By using overlays, both objects share the same memory location. If you assign a value to one, the other changes as well. The syntax is:
where expression defines the address of the source object.
While overlays might look more elegant than
Unchecked_Conversion, you should be aware that they are even more dangerous and have even greater potential for doing something very wrong. For example if
Source'Size < Target'Size and you assign a value to Target, you might inadvertently write into memory allocated to a different object.
You have to take care also of implicit initializations of objects of the target type, since they would overwrite the actual value of the source object. The Import pragma with convention Ada can be used to prevent this, since it avoids the implicit initialization, RM B.1 (Annotated).
The example below does the same as the example from "Unchecked Conversion".
with Ada.Text_IO; procedure Convert_Address_Mapping is type Short is range -128 .. +127; type Byte is mod 256; package T_IO renames Ada.Text_IO; package I_IO is new Ada.Text_IO.Integer_IO (Short); package M_IO is new Ada.Text_IO.Modular_IO (Byte); A : aliased Short; B : aliased Byte; for B'Address use A'Address; pragma Import (Ada, B); begin A := -1; T_IO.Put ("A = "); I_IO.Put (Item => A, Width => 5, Base => 10); T_IO.Put (", B = "); M_IO.Put (Item => B, Width => 5, Base => 10); end Convert_Address_Mapping;
Just for the record: There is still another method using the Export and Import pragmas. However, since this method completely undermines Ada's visibility and type concepts even more than overlays, it has no place here in this language introduction and is left to experts.
As explained before, a type declaration
declares an anonymous type
T and its first subtype
T (please note the italicization).
T encompasses the complete set of mathematical integers. Static expressions and named numbers make use of this fact.
All numeric integer literals are of type
Universal_Integer. They are converted to the appropriate specific type where needed.
Universal_Integer itself has no operators.
Some examples with static named numbers:
S1: constant := Integer'Last + Integer'Last; -- "+" of Integer S2: constant := Long_Integer'Last + 1; -- "+" of Long_Integer S3: constant := S1 + S2; -- "+" of root_integer S4: constant := Integer'Last + Long_Integer'Last; -- illegal
Static expressions are evaluated at compile-time on the appropriate types with no overflow checks, i.e. mathematically exact (only limited by computer store). The result is then implicitly converted to
The literal 1 in
S2 is of type
Universal_Integer and implicitly converted to
S3 implicitly converts the summands to
root_integer, performs the calculation and converts back to
S4 is illegal because it mixes two different types. You can however write this as
S5: constant := Integer'Pos (Integer'Last) + Long_Integer'Pos (Long_Integer'Last); -- "+" of root_integer
where the Pos attributes convert the values to
Universal_Integer, which are then further implicitly converted to
root_integer, added and the result converted back to
root_integer is the anonymous greatest integer type representable by the hardware. It has the range
System.Min_Integer .. System.Max_Integer. All integer types are rooted at
root_integer, i.e. derived from it.
Universal_Integer can be viewed as
During run-time, computations of course are performed with range checks and overflow checks on the appropriate subtype. Intermediate results may however exceed the range limits. Thus with
I, J, K of the subtype
T above, the following code will return the correct result:
I := 10; J := 8; K := (I + J) - 12; -- I := I + J; -- range check would fail, leading to Constraint_Error
Real literals are of type
Universal_Real, and similar rules as the ones above apply accordingly.
Types can be made from other types. Array types, for example, are made from two types, one for the arrays' index and one for the arrays' components. An array, then, expresses an association, namely that between one value of the index type and a value of the component type.
type Color is (Red, Green, Blue); type Intensity is range 0 .. 255; type Colored_Point is array (Color) of Intensity;
The type Color is the index type and the type Intensity is the component type of the array type Colored_Point. See array.
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