Types

Scalar Types

In general terms, scalar types are the most basic types that we can get. As we know, we can classify them as follows:

Category

Discrete

Numeric

Enumeration

Yes

No

Integer

Yes

Yes

Real

No

Yes

Many attributes exist for scalar types. For example, we can use the Image and Value attributes to convert between a given type and a string type. The following table presents the main attributes for scalar types:

Category

Attribute

Returned value

Ranges

First

First value of the discrete subtype's range.

Last

Last value of the discrete subtype's range.

Range

Range of the discrete subtype (corresponds to Subtype'First .. Subtype'Last).

Iterators

Pred

Predecessor of the input value.

Succ

Successor of the input value.

Comparison

Min

Minimum of two values.

Max

Maximum of two values.

String conversion

Image

String representation of the input value.

Value

Value of a subtype based on input string.

We already discussed some of these attributes in the Introduction to Ada course (in the sections about range and related attributes and image attribute). In this section, we'll discuss some aspects that have been left out of the previous course.

In the Ada Reference Manual

Ranges

We've seen that the First and Last attributes can be used with discrete types. Those attributes are also available for real types. Here's an example using the Float type and a subtype of it:

    
    
    
        
with Ada.Text_IO; use Ada.Text_IO;

procedure Show_First_Last_Real is
   subtype Norm is Float range 0.0 .. 1.0;
begin
   Put_Line ("Float'First: " & Float'First'Image);
   Put_Line ("Float'Last:  " & Float'Last'Image);
   Put_Line ("Norm'First:  " & Norm'First'Image);
   Put_Line ("Norm'Last:   " & Norm'Last'Image);
end Show_First_Last_Real;

This program displays the first and last values of both the Float type and the Norm subtype. In the case of the Float type, we see the full range, while for the Norm subtype, we get the values we used in the declaration of the subtype (i.e. 0.0 and 1.0).

Predecessor and Successor

We can use the Pred and Succ attributes to get the predecessor and successor of a specific value. For discrete types, this is simply the next discrete value. For example, Pred (2) is 1 and Succ (2) is 3. Let's look at a complete source-code example:

    
    
    
        
with Ada.Text_IO; use Ada.Text_IO;

procedure Show_Succ_Pred_Discrete is
   type State is (Idle, Started,
                  Processing, Stopped);

   Machine_State : constant State := Started;

   I : constant Integer := 2;
begin
   Put_Line ("State                     : "
             & Machine_State'Image);
   Put_Line ("State'Pred (Machine_State): "
             & State'Pred (Machine_State)'Image);
   Put_Line ("State'Succ (Machine_State): "
             & State'Succ (Machine_State)'Image);
   Put_Line ("----------");

   Put_Line ("I               : "
             & I'Image);
   Put_Line ("Integer'Pred (I): "
             & Integer'Pred (I)'Image);
   Put_Line ("Integer'Succ (I): "
             & Integer'Succ (I)'Image);
end Show_Succ_Pred_Discrete;

In this example, we use the Pred and Succ attributes for a variable of enumeration type (State) and a variable of Integer type.

We can also use the Pred and Succ attributes with real types. In this case, however, the value we get depends on the actual type we're using:

  • for fixed-point types, the value is calculated using the smallest value (Small), which is derived from the declaration of the fixed-point type;

  • for floating-point types, the value used in the calculation depends on representation constraints of the actual target machine.

Let's look at this example with a decimal type (Decimal) and a floating-point type (My_Float):

    
    
    
        
with Ada.Text_IO; use Ada.Text_IO;

procedure Show_Succ_Pred_Real is
   subtype My_Float is
     Float range 0.0 .. 0.5;

   type Decimal is
     delta 0.1 digits 2
     range 0.0 .. 0.5;

   D : Decimal;
   N : My_Float;
begin
   Put_Line ("---- DECIMAL -----");
   Put_Line ("Small: " & Decimal'Small'Image);
   Put_Line ("----- Succ -------");
   D := Decimal'First;
   loop
      Put_Line (D'Image);
      D := Decimal'Succ (D);

      exit when D = Decimal'Last;
   end loop;
   Put_Line ("----- Pred -------");

   D := Decimal'Last;
   loop
      Put_Line (D'Image);
      D := Decimal'Pred (D);

      exit when D = Decimal'First;
   end loop;
   Put_Line ("==================");

   Put_Line ("---- MY_FLOAT ----");
   Put_Line ("----- Succ -------");
   N := My_Float'First;
   for I in 1 .. 5 loop
      Put_Line (N'Image);
      N := My_Float'Succ (N);
   end loop;
   Put_Line ("----- Pred -------");

   for I in 1 .. 5 loop
      Put_Line (N'Image);
      N := My_Float'Pred (N);
   end loop;
end Show_Succ_Pred_Real;

As the output of the program indicates, the smallest value (see Decimal'Small in the example) is used to calculate the previous and next values of Decimal type.

In the case of the My_Float type, the difference between the current and the previous or next values is 1.40130E-45 (or 2-149) on a standard PC.

Scalar To String Conversion

We've seen that we can use the Image and Value attributes to perform conversions between values of a given subtype and a string:

    
    
    
        
with Ada.Text_IO; use Ada.Text_IO;

procedure Show_Image_Value_Attr is
   I : constant Integer := Integer'Value ("42");
begin
   Put_Line (I'Image);
end Show_Image_Value_Attr;

The Image and Value attributes are used for the String type specifically. In addition to them, there are also attributes for different string types — namely Wide_String and Wide_Wide_String. This is the complete list of available attributes:

Conversion type

Attribute

String type

Conversion to string

Image

String

Wide_Image

Wide_String

Wide_Wide_Image

Wide_Wide_String

Conversion to subtype

Value

String

Wide_Value

Wide_String

Wide_Wide_Value

Wide_Wide_String

We discuss more about Wide_String and Wide_Wide_String in another section.

Width attribute

When converting a value to a string by using the Image attribute, we get a string with variable width. We can assess the maximum width of that string for a specific subtype by using the Width attribute. For example, Integer'Width gives us the maximum width returned by the Image attribute when converting a value of Integer type to a string of String type.

This attribute is useful when we're using bounded strings in our code to store the string returned by the Image attribute. For example:

    
    
    
        
with Ada.Text_IO;         use Ada.Text_IO;
with Ada.Strings;         use Ada.Strings;
with Ada.Strings.Bounded;

procedure Show_Width_Attr is
   package B_Str is new
     Ada.Strings.Bounded.Generic_Bounded_Length
       (Max => Integer'Width);
   use B_Str;

   Str_I : Bounded_String;

   I : constant Integer := 42;
   J : constant Integer := 103;
begin
   Str_I := To_Bounded_String (I'Image);
   Put_Line ("Value:         "
             & To_String (Str_I));
   Put_Line ("String Length: "
             & Length (Str_I)'Image);
   Put_Line ("----");

   Str_I := To_Bounded_String (J'Image);
   Put_Line ("Value:         "
             & To_String (Str_I));
   Put_Line ("String Length: "
             & Length (Str_I)'Image);
end Show_Width_Attr;

In this example, we're storing the string returned by Image in the Str_I variable of Bounded_String type.

Similar to the Image and Value attributes, the Width attribute is also available for string types other than String. In fact, we can use:

  • the Wide_Width attribute for strings returned by Wide_Image; and

  • the Wide_Wide_Width attribute for strings returned by Wide_Wide_Image.

Base

The Base attribute gives us the unconstrained underlying hardware representation selected for a given numeric type. As an example, let's say we declared a subtype of the Integer type named One_To_Ten:

    
    
    
        
package My_Integers is

   subtype One_To_Ten is Integer
     range 1 .. 10;

end My_Integers;

If we then use the Base attribute — by writing One_To_Ten'Base —, we're actually referring to the unconstrained underlying hardware representation selected for One_To_Ten. As One_To_Ten is a subtype of the Integer type, this also means that One_To_Ten'Base is equivalent to Integer'Base, i.e. they refer to the same base type. (This base type is the underlying hardware type representing the Integer type — but is not the Integer type itself.)

For further reading...

The Ada standard defines that the minimum range of the Integer type is -2**15 + 1 .. 2**15 - 1. In modern 64-bit systems — where wider types such as Long_Integer are defined — the range is at least -2**31 + 1 .. 2**31 - 1. Therefore, we could think of the Integer type as having the following declaration:

type Integer is
  range -2 ** 31 .. 2 ** 31 - 1;

However, even though Integer is a predefined Ada type, it's actually a subtype of an anonymous type. That anonymous "type" is the hardware's representation for the numeric type as chosen by the compiler based on the requested range (for the signed integer types) or digits of precision (for floating-point types). In other words, these types are actually subtypes of something that does not have a specific name in Ada, and that is not constrained.

In effect,

type Integer is
  range -2 ** 31 .. 2 ** 31 - 1;

is really as if we said this:

subtype Integer is
  Some_Hardware_Type_With_Sufficient_Range
  range -2 ** 31 .. 2 ** 31 - 1;

Since the Some_Hardware_Type_With_Sufficient_Range type is anonymous and we therefore cannot refer to it in the code, we just say that Integer is a type rather than a subtype.

Let's focus on signed integers — as the other numerics work the same way. When we declare a signed integer type, we have to specify the required range, statically. If the compiler cannot find a hardware-defined or supported signed integer type with at least the range requested, the compilation is rejected. For example, in current architectures, the code below most likely won't compile:

    
    
    
        
package Int_Def is

   type Too_Big_To_Fail is
     range -2 ** 255 .. 2 ** 255 - 1;

end Int_Def;

Otherwise, the compiler maps the named Ada type to the hardware "type", presumably choosing the smallest one that supports the requested range. (That's why the range has to be static in the source code, unlike for explicit subtypes.)

The following example shows how the Base attribute affects the bounds of a variable:

    
    
    
        
with Ada.Text_IO; use Ada.Text_IO;
with My_Integers; use My_Integers;

procedure Show_Base is
   C : constant One_To_Ten := One_To_Ten'Last;
begin
   Using_Constrained_Subtype : declare
      V : One_To_Ten := C;
   begin
      Put_Line
        ("Increasing value for One_To_Ten...");

      V := One_To_Ten'Succ (V);
   exception
      when others =>
         Put_Line ("Exception raised!");
   end Using_Constrained_Subtype;

   Using_Base : declare
      V : One_To_Ten'Base := C;
   begin
      Put_Line
      ("Increasing value for One_To_Ten'Base...");

      V := One_To_Ten'Succ (V);
   exception
      when others =>
         Put_Line ("Exception raised!");
   end Using_Base;

   Put_Line ("One_To_Ten'Last: "
             & One_To_Ten'Last'Image);
   Put_Line ("One_To_Ten'Base'Last: "
             & One_To_Ten'Base'Last'Image);
end Show_Base;

In the first block of the example (Using_Constrained_Subtype), we're asking for the next value after the last value of a range — in this case, One_To_Ten'Succ (One_To_Ten'Last). As expected, since the last value of the range doesn't have a successor, a constraint exception is raised.

In the Using_Base block, we're declaring a variable V of One_To_Ten'Base subtype. In this case, the next value exists — because the condition One_To_Ten'Last + 1 <= One_To_Ten'Base'Last is true —, so we can use the Succ attribute without having an exception being raised.

In the following example, we adjust the result of additions and subtractions to avoid constraint errors:

    
    
    
        
package My_Integers is

   subtype One_To_Ten is Integer range 1 .. 10;

   function Sat_Add (V1, V2 : One_To_Ten'Base)
                     return One_To_Ten;

   function Sat_Sub (V1, V2 : One_To_Ten'Base)
                     return One_To_Ten;

end My_Integers;

    
        
--  with Ada.Text_IO; use Ada.Text_IO;

package body My_Integers is

   function Saturate (V : One_To_Ten'Base)
                      return One_To_Ten is
   begin
      --  Put_Line ("SATURATE " & V'Image);

      if V < One_To_Ten'First then
         return One_To_Ten'First;
      elsif V > One_To_Ten'Last then
         return One_To_Ten'Last;
      else
         return V;
      end if;
   end Saturate;

   function Sat_Add (V1, V2 : One_To_Ten'Base)
                     return One_To_Ten is
   begin
      return Saturate (V1 + V2);
   end Sat_Add;

   function Sat_Sub (V1, V2 : One_To_Ten'Base)
                     return One_To_Ten is
   begin
      return Saturate (V1 - V2);
   end Sat_Sub;

end My_Integers;

    
        
with Ada.Text_IO; use Ada.Text_IO;
with My_Integers; use My_Integers;

procedure Show_Base is

   type Display_Saturate_Op is (Add, Sub);

   procedure Display_Saturate
     (V1, V2 : One_To_Ten;
      Op     : Display_Saturate_Op)
   is
      Res : One_To_Ten;
   begin
      case Op is
      when Add =>
         Res := Sat_Add (V1, V2);
      when Sub =>
         Res := Sat_Sub (V1, V2);
      end case;
      Put_Line ("SATURATE " & Op'Image
                & " (" & V1'Image
                & ", " & V2'Image
                & ") = " & Res'Image);
   end Display_Saturate;

begin
   Display_Saturate (1,  1, Add);
   Display_Saturate (10, 8, Add);
   Display_Saturate (1,  8, Sub);
end Show_Base;

In this example, we're using the Base attribute to declare the parameters of the Sat_Add, Sat_Sub and Saturate functions. Note that the parameters of the Display_Saturate procedure are of One_To_Ten type, while the parameters of the Sat_Add, Sat_Sub and Saturate functions are of the (unconstrained) base subtype (One_To_Ten'Base). In those functions, we perform operations using the parameters of unconstrained subtype and adjust the result — in the Saturate function — before returning it as a constrained value of One_To_Ten subtype.

The code in the body of the My_Integers package contains lines that were commented out — to be more precise, a call to Put_Line call in the Saturate function. If you uncomment them, you'll see the value of the input parameter V (of One_To_Ten'Base type) in the runtime output of the program before it's adapted to fit the constraints of the One_To_Ten subtype.

Enumerations

We've introduced enumerations back in the Introduction to Ada course. In this section, we'll discuss a few useful features of enumerations, such as enumeration renaming, enumeration overloading and representation clauses.

In the Ada Reference Manual

Enumerations as functions

If you have used programming language such as C in the past, you're familiar with the concept of enumerations being constants with integer values. In Ada, however, enumerations are not integers. In fact, they're actually parameterless functions! Let's consider this example:

    
    
    
        
package Days is

   type Day is (Mon, Tue, Wed,
                Thu, Fri,
                Sat, Sun);

   --  Essentially, we're declaring
   --  these functions:
   --
   --  function Mon return Day;
   --  function Tue return Day;
   --  function Wed return Day;
   --  function Thu return Day;
   --  function Fri return Day;
   --  function Sat return Day;
   --  function Sun return Day;

end Days;

In the package Days, we're declaring the enumeration type Day. When we do this, we're essentially declaring seven parameterless functions, one for each enumeration. For example, the Mon enumeration corresponds to function Mon return Day. You can see all seven function declarations in the comments of the example above.

Note that this has no direct relation to how an Ada compiler generates machine code for enumeration. Even though enumerations are parameterless functions, a typical Ada compiler doesn't generate function calls for code that deals with enumerations.

Enumeration renaming

The idea that enumerations are parameterless functions can be used when we want to rename enumerations. For example, we could rename the enumerations of the Day type like this:

    
    
    
        
package Enumeration_Example is

   type Day is (Mon, Tue, Wed,
                Thu, Fri,
                Sat, Sun);

   function Monday    return Day renames Mon;
   function Tuesday   return Day renames Tue;
   function Wednesday return Day renames Wed;
   function Thursday  return Day renames Thu;
   function Friday    return Day renames Fri;
   function Saturday  return Day renames Sat;
   function Sunday    return Day renames Sun;

end Enumeration_Example;

Now, we can use both Monday or Mon to refer to Monday of the Day type:

    
    
    
        
with Ada.Text_IO;         use Ada.Text_IO;
with Enumeration_Example; use Enumeration_Example;

procedure Show_Renaming is
   D1 : constant Day := Mon;
   D2 : constant Day := Monday;
begin
   if D1 = D2 then
      Put_Line ("D1 = D2");
      Put_Line (Day'Image (D1)
                & " =  "
                & Day'Image (D2));
   end if;
end Show_Renaming;

When running this application, we can confirm that D1 is equal to D2. Also, even though we've assigned Monday to D2 (instead of Mon), the application displays Mon = Mon, since Monday is just another name to refer to the actual enumeration (Mon).

Hint

If you just want to have a single (renamed) enumeration visible in your application — and make the original enumeration invisible —, you can use a separate package. For example:

    
    
    
        
package Enumeration_Example is

   type Day is (Mon, Tue, Wed,
                Thu, Fri,
                Sat, Sun);

end Enumeration_Example;

    
        
with Enumeration_Example;

package Enumeration_Renaming is

   subtype Day is Enumeration_Example.Day;

   function Monday    return Day renames
     Enumeration_Example.Mon;
   function Tuesday   return Day renames
     Enumeration_Example.Tue;
   function Wednesday return Day renames
     Enumeration_Example.Wed;
   function Thursday  return Day renames
     Enumeration_Example.Thu;
   function Friday    return Day renames
     Enumeration_Example.Fri;
   function Saturday  return Day renames
     Enumeration_Example.Sat;
   function Sunday    return Day renames
     Enumeration_Example.Sun;

end Enumeration_Renaming;

    
        
with Ada.Text_IO; use Ada.Text_IO;

with Enumeration_Renaming;
use  Enumeration_Renaming;

procedure Show_Renaming is
   D1 : constant Day := Monday;
begin
   Put_Line (Day'Image (D1));
end Show_Renaming;

Note that the call to Put_Line still display Mon instead of Monday.

Enumeration overloading

Enumerations can be overloaded. In simple terms, this means that the same name can be used to declare an enumeration of different types. A typical example is the declaration of colors:

    
    
    
        
package Colors is

   type Color is
     (Salmon,
      Firebrick,
      Red,
      Darkred,
      Lime,
      Forestgreen,
      Green,
      Darkgreen,
      Blue,
      Mediumblue,
      Darkblue);

   type Primary_Color is
     (Red,
      Green,
      Blue);

end Colors;

Note that we have Red as an enumeration of type Color and of type Primary_Color. The same applies to Green and Blue. Because Ada is a strongly-typed language, in most cases, the enumeration that we're referring to is clear from the context. For example:

    
    
    
        
with Ada.Text_IO; use Ada.Text_IO;
with Colors;      use Colors;

procedure Red_Colors is
   C1 : constant Color         := Red;
   --  Using Red from Color

   C2 : constant Primary_Color := Red;
   --  Using Red from Primary_Color
begin
   if C1 = Red then
      Put_Line ("C1 = Red");
   end if;
   if C2 = Red then
      Put_Line ("C2 = Red");
   end if;
end Red_Colors;

When assigning Red to C1 and C2, it is clear that, in the first case, we're referring to Red of Color type, while in the second case, we're referring to Red of the Primary_Color type. The same logic applies to comparisons such as the one in if C1 = Red: because the type of C1 is defined (Color), it's clear that the Red enumeration is the one of Color type.

Enumeration subtypes

Note that enumeration overloading is not the same as enumeration subtypes. For example, we could define the following subtype:

    
    
    
        
package Colors.Shades is

   subtype Blue_Shades is
     Colors range Blue .. Darkblue;

end Colors.Shades;

In this case, Blue of Blue_Shades and Blue of Colors are the same enumeration.

Enumeration ambiguities

A situation where enumeration overloading might lead to ambiguities is when we use them in ranges. For example:

    
    
    
        
package Colors is

   type Color is
     (Salmon,
      Firebrick,
      Red,
      Darkred,
      Lime,
      Forestgreen,
      Green,
      Darkgreen,
      Blue,
      Mediumblue,
      Darkblue);

   type Primary_Color is
     (Red,
      Green,
      Blue);

end Colors;

    
        
with Ada.Text_IO; use Ada.Text_IO;
with Colors;      use Colors;

procedure Color_Loop is
begin
   for C in Red .. Blue loop
   --       ^^^^^^^^^^^
   --  ERROR: range is ambiguous!
      Put_Line (Color'Image (C));
   end loop;
end Color_Loop;

Here, it's not clear whether the range in the loop is of Color type or of Primary_Color type. Therefore, we get a compilation error for this code example. The next line in the code example — the one with the call to Put_Line — gives us a hint about the developer's intention to refer to the Color type. In this case, we can use qualification — for example, Color'(Red) — to resolve the ambiguity:

    
    
    
        
with Ada.Text_IO; use Ada.Text_IO;
with Colors;      use Colors;

procedure Color_Loop is
begin
   for C in Color'(Red) .. Color'(Blue) loop
      Put_Line (Color'Image (C));
   end loop;
end Color_Loop;

Note that, in the case of ranges, we can also rewrite the loop by using a range declaration:

    
    
    
        
with Ada.Text_IO; use Ada.Text_IO;
with Colors;      use Colors;

procedure Color_Loop is
begin
   for C in Color range Red .. Blue loop
      Put_Line (Color'Image (C));
   end loop;
end Color_Loop;

Alternatively, Color range Red .. Blue could be used in a subtype declaration, so we could rewrite the example above using a subtype (such as Red_To_Blue) in the loop:

    
    
    
        
with Ada.Text_IO; use Ada.Text_IO;
with Colors;      use Colors;

procedure Color_Loop is
   subtype Red_To_Blue is Color range Red .. Blue;
begin
   for C in Red_To_Blue loop
      Put_Line (Color'Image (C));
   end loop;
end Color_Loop;

Position and Internal Code

As we've said above, a typical Ada compiler doesn't generate function calls for code that deals with enumerations. On the contrary, each enumeration has values associated with it, and the compiler uses those values instead.

Each enumeration has:

  • a position value, which is a natural value indicating the position of the enumeration in the enumeration type; and

  • an internal code, which, by default, in most cases, is the same as the position value.

Also, by default, the value of the first position is zero, the value of the second position is one, and so on. We can see this by listing each enumeration of the Day type and displaying the value of the corresponding position:

    
    
    
        
package Days is

   type Day is (Mon, Tue, Wed,
                Thu, Fri,
                Sat, Sun);

end Days;

    
        
with Ada.Text_IO; use Ada.Text_IO;
with Days;        use Days;

procedure Show_Days is
begin
   for D in Day loop
      Put_Line (Day'Image (D)
                & " position      = "
                & Integer'Image (Day'Pos (D)));
      Put_Line (Day'Image (D)
                & " internal code = "
                & Integer'Image
                    (Day'Enum_Rep (D)));
   end loop;
end Show_Days;

Note that this application also displays the internal code, which, in this case, is equivalent to the position value for all enumerations.

We may, however, change the internal code of an enumeration using a representation clause. We discuss this topic in another section.

Definite and Indefinite Subtypes

Indefinite types were mentioned back in the Introduction to Ada course. In this section, we'll recapitulate and extend on both definite and indefinite types.

Definite types are the basic kind of types we commonly use when programming applications. For example, we can only declare variables of definite types; otherwise, we get a compilation error. Interestingly, however, to be able to explain what definite types are, we need to first discuss indefinite types.

Indefinite types include:

  • unconstrained arrays;

  • record types with unconstrained discriminants without defaults.

Let's see some examples of indefinite types:

    
    
    
        
package Unconstrained_Types is

   type Integer_Array is
     array (Positive range <>) of Integer;

   type Simple_Record (Extended : Boolean) is
   record
      V : Integer;
      case Extended is
         when False =>
            null;
         when True  =>
            V_Float : Float;
      end case;
   end record;

end Unconstrained_Types;

In this example, both Integer_Array and Simple_Record are indefinite types.

As we've just mentioned, we cannot declare variable of indefinite types:

    
    
    
        
with Unconstrained_Types; use Unconstrained_Types;

procedure Using_Unconstrained_Type is

   A : Integer_Array;

   R : Simple_Record;

begin
   null;
end Using_Unconstrained_Type;

As we can see when we try to build this example, the compiler complains about the declaration of A and R because we're trying to use indefinite types to declare variables. The main reason we cannot use indefinite types here is that the compiler needs to know at this point how much memory it should allocate. Therefore, we need to provide the information that is missing. In other words, we need to change the declaration so the type becomes definite. We can do this by either declaring a definite type or providing constraints in the variable declaration. For example:

    
    
    
        
with Unconstrained_Types; use Unconstrained_Types;

procedure Using_Unconstrained_Type is

   subtype Integer_Array_5 is
     Integer_Array (1 .. 5);

   A1 : Integer_Array_5;
   A2 : Integer_Array (1 .. 5);

   subtype Simple_Record_Ext is
     Simple_Record (Extended => True);

   R1 : Simple_Record_Ext;
   R2 : Simple_Record (Extended => True);

begin
   null;
end Using_Unconstrained_Type;

In this example, we declare the Integer_Array_5 subtype, which is definite because we're constraining it to a range from 1 to 5, thereby defining the information that was missing in the indefinite type Integer_Array. Because we now have a definite type, we can use it to declare the A1 variable. Similarly, we can use the indefinite type Integer_Array directly in the declaration of A2 by specifying the previously unknown range.

Similarly, in this example, we declare the Simple_Record_Ext subtype, which is definite because we're initializing the record discriminant Extended. We can therefore use it in the declaration of the R1 variable. Alternatively, we can simply use the indefinite type Simple_Record and specify the information required for the discriminants. This is what we do in the declaration of the R2 variable.

Although we cannot use indefinite types directly in variable declarations, they're very useful to generalize algorithms. For example, we can use them as parameters of a subprogram:

    
    
    
        
with Unconstrained_Types; use Unconstrained_Types;

procedure Show_Integer_Array (A : Integer_Array);

    
        
with Ada.Text_IO; use Ada.Text_IO;

procedure Show_Integer_Array (A : Integer_Array)
is
begin
   for I in A'Range loop
      Put_Line (Positive'Image (I)
                & ": "
                & Integer'Image (A (I)));
   end loop;
   Put_Line ("--------");
end Show_Integer_Array;

    
        
with Unconstrained_Types; use Unconstrained_Types;
with Show_Integer_Array;

procedure Using_Unconstrained_Type is
   A_5  : constant Integer_Array (1 .. 5)  :=
            (1, 2, 3, 4, 5);
   A_10 : constant Integer_Array (1 .. 10) :=
            (1, 2, 3, 4, 5, others => 99);
begin
   Show_Integer_Array (A_5);
   Show_Integer_Array (A_10);
end Using_Unconstrained_Type;

In this particular example, the compiler doesn't know a priori which range is used for the A parameter of Show_Integer_Array. It could be a range from 1 to 5 as used for variable A_5 of the Using_Unconstrained_Type procedure, or it could be a range from 1 to 10 as used for variable A_10, or it could be anything else. Although the parameter A of Show_Integer_Array is unconstrained, both calls to Show_Integer_Array — in Using_Unconstrained_Type procedure — use constrained objects.

Note that we could call the Show_Integer_Array procedure above with another unconstrained parameter. For example:

    
    
    
        
with Unconstrained_Types; use Unconstrained_Types;

procedure Show_Integer_Array_Header
  (AA : Integer_Array;
   HH : String);

    
        
with Ada.Text_IO;         use Ada.Text_IO;
with Show_Integer_Array;

procedure Show_Integer_Array_Header
  (AA : Integer_Array;
   HH : String)
is
begin
   Put_Line (HH);
   Show_Integer_Array (AA);
end Show_Integer_Array_Header;

    
        
with Unconstrained_Types; use Unconstrained_Types;

with Show_Integer_Array_Header;

procedure Using_Unconstrained_Type is
   A_5  : constant Integer_Array (1 .. 5)  :=
            (1, 2, 3, 4, 5);
   A_10 : constant Integer_Array (1 .. 10) :=
            (1, 2, 3, 4, 5, others => 99);
begin
   Show_Integer_Array_Header (A_5,
                              "First example");
   Show_Integer_Array_Header (A_10,
                              "Second example");
end Using_Unconstrained_Type;

In this case, we're calling the Show_Integer_Array procedure with another unconstrained parameter (the AA parameter). However, although we could have a long chain of procedure calls using indefinite types in their parameters, we still use a (definite) object at the beginning of this chain. For example, for the A_5 object, we have this chain:

A_5

    ==> Show_Integer_Array_Header (AA => A_5,
                                   ...);

        ==> Show_Integer_Array (A => AA);

Therefore, at this specific call to Show_Integer_Array, even though A is declared as a parameter of indefinite type, the actual argument is of definite type because A_5 is constrained — and, thus, of definite type.

Note that we can declare variables based on parameters of indefinite type. For example:

    
    
    
        
with Unconstrained_Types; use Unconstrained_Types;

procedure Show_Integer_Array_Plus
  (A : Integer_Array;
   V : Integer);

    
        
with Show_Integer_Array;

procedure Show_Integer_Array_Plus
  (A : Integer_Array;
   V : Integer)
is
   A_Plus : Integer_Array (A'Range);
begin
   for I in A_Plus'Range loop
      A_Plus (I) := A (I) + V;
   end loop;
   Show_Integer_Array (A_Plus);
end Show_Integer_Array_Plus;

    
        
with Unconstrained_Types; use Unconstrained_Types;

with Show_Integer_Array_Plus;

procedure Using_Unconstrained_Type is
   A_5 : constant Integer_Array (1 .. 5) :=
           (1, 2, 3, 4, 5);
begin
   Show_Integer_Array_Plus (A_5, 5);
end Using_Unconstrained_Type;

In the Show_Integer_Array_Plus procedure, we're declaring A_Plus based on the range of A, which is itself of indefinite type. However, since the object passed as an argument to Show_Integer_Array_Plus must have a constraint, A_Plus will also be constrained. For example, in the call to Show_Integer_Array_Plus using A_5 as an argument, the declaration of A_Plus becomes A_Plus : Integer_Array (1 .. 5);. Therefore, it becomes clear that the compiler needs to allocate five elements for A_Plus.

We'll see later how definite and indefinite types apply to formal parameters.

In the Ada Reference Manual

Constrained Attribute

We can use the Constrained attribute to verify whether an object of discriminated type is constrained or not. Let's start our discussion by reusing the Simple_Record type from previous examples. In this version of the Unconstrained_Types package, we're adding a Reset procedure for the discriminated record type:

    
    
    
        
package Unconstrained_Types is

   type Simple_Record
     (Extended : Boolean := False) is
   record
      V : Integer;
      case Extended is
         when False =>
            null;
         when True  =>
            V_Float : Float;
      end case;
   end record;

   procedure Reset (R : in out Simple_Record);

end Unconstrained_Types;

    
        
with Ada.Text_IO; use Ada.Text_IO;

package body Unconstrained_Types is

   procedure Reset (R : in out Simple_Record) is
      Zero_Not_Extended : constant
        Simple_Record := (Extended => False,
                          V        => 0);

      Zero_Extended : constant
        Simple_Record := (Extended => True,
                          V        => 0,
                          V_Float  => 0.0);
   begin
      Put_Line ("---- Reset: R'Constrained => "
                & R'Constrained'Image);

      if not R'Constrained then
         R := Zero_Extended;
      else
         if R.Extended then
            R := Zero_Extended;
         else
            R := Zero_Not_Extended;
         end if;
      end if;
   end Reset;

end Unconstrained_Types;

As the name indicates, the Reset procedure initializes all record components with zero. Note that we use the Constrained attribute to verify whether objects are constrained before assigning to them. For objects that are not constrained, we can simply assign another object to it — as we do with the R := Zero_Extended statement. When an object is constrained, however, the discriminants must match. If we assign an object to R, the discriminant of that object must match the discriminant of R. This is the kind of verification that we do in the else part of that procedure: we check the state of the Extended discriminant before assigning an object to the R parameter.

The Using_Constrained_Attribute procedure below declares two objects of Simple_Record type: R1 and R2. Because the Simple_Record type has a default value for its discriminant, we can declare objects of this type without specifying a value for the discriminant. This is exactly what we do in the declaration of R1. Here, we don't specify any constraints, so that it takes the default value (Extended => False). In the declaration of R2, however, we explicitly set Extended to False:

    
    
    
        
with Ada.Text_IO;         use Ada.Text_IO;

with Unconstrained_Types; use Unconstrained_Types;

procedure Using_Constrained_Attribute is
   R1 : Simple_Record;
   R2 : Simple_Record (Extended => False);

   procedure Show_Rs is
   begin
      Put_Line ("R1'Constrained => "
                & R1'Constrained'Image);
      Put_Line ("R1.Extended => "
                & R1.Extended'Image);
      Put_Line ("--");
      Put_Line ("R2'Constrained => "
                & R2'Constrained'Image);
      Put_Line ("R2.Extended => "
                & R2.Extended'Image);
      Put_Line ("----------------");
   end Show_Rs;
begin
   Show_Rs;

   Reset (R1);
   Reset (R2);
   Put_Line ("----------------");

   Show_Rs;
end Using_Constrained_Attribute;

When we run this code, the user messages from Show_Rs indicate to us that R1 is not constrained, while R2 is constrained. Because we declare R1 without specifying a value for the Extended discriminant, R1 is not constrained. In the declaration of R2, on the other hand, the explicit value for the Extended discriminant makes this object constrained. Note that, for both R1 and R2, the value of Extended is False in the declarations.

As we were just discussing, the Reset procedure includes checks to avoid mismatches in discriminants. When we don't have those checks, we might get exceptions at runtime. We can force this situation by replacing the implementation of the Reset procedure with the following lines:

--  [...]
begin
   Put_Line ("---- Reset: R'Constrained => "
             & R'Constrained'Image);
   R := Zero_Extended;
end Reset;

Running the code now generates a runtime exception:

raised CONSTRAINT_ERROR : unconstrained_types.adb:12 discriminant check failed

This exception is raised during the call to Reset (R2). As see in the code, R2 is constrained. Also, its Extended discriminant is set to False, which means that it doesn't have the V_Float component. Therefore, R2 is not compatible with the constant Zero_Extended object, so we cannot assign Zero_Extended to R2. Also, because R2 is constrained, its Extended discriminant cannot be modified.

The behavior is different for the call to Reset (R1), which works fine. Here, when we pass R1 as an argument to the Reset procedure, its Extended discriminant is False by default. Thus, R1 is also not compatible with the Zero_Extended object. However, because R1 is not constrained, the assignment modifies R1 (by changing the value of the Extended discriminant). Therefore, with the call to Reset, the Extended discriminant of R1 changes from False to True.

In the Ada Reference Manual

Incomplete types

Incomplete types — as the name suggests — are types that have missing information in their declaration. This is a simple example:

type Incomplete;

Because this type declaration is incomplete, we need to provide the missing information at some later point. Consider the incomplete type R in the following example:

    
    
    
        
package Incomplete_Type_Example is

   type R;
   --  Incomplete type declaration!

   type R is record
      I : Integer;
   end record;
   --  type R is now complete!

end Incomplete_Type_Example;

The first declaration of type R is incomplete. However, in the second declaration of R, we specify that R is a record. By providing this missing information, we're completing the type declaration of R.

It's also possible to declare an incomplete type in the private part of a package specification and its complete form in the package body. Let's rewrite the example above accordingly:

    
    
    
        
package Incomplete_Type_Example is

private

   type R;
   --  Incomplete type declaration!

end Incomplete_Type_Example;

    
        
package body Incomplete_Type_Example is

   type R is record
      I : Integer;
   end record;
   --  type R is now complete!

end Incomplete_Type_Example;

A typical application of incomplete types is to create linked lists using access types based on those incomplete types. This kind of type is called a recursive type. For example:

    
    
    
        
package Linked_List_Example is

   type Integer_List;

   type Next is access Integer_List;

   type Integer_List is record
      I : Integer;
      N : Next;
   end record;

end Linked_List_Example;

Here, the N component of Integer_List is essentially giving us access to the next element of Integer_List type. Because the Next type is both referring to the Integer_List type and being used in the declaration of the Integer_List type, we need to start with an incomplete declaration of the Integer_List type and then complete it after the declaration of Next.

Incomplete types are useful to declare mutually dependent types, as we'll see later on. Also, we can also have formal incomplete types, as we'll discuss later.

In the Ada Reference Manual

Type view

Ada distinguishes between the partial and the full view of a type. The full view is a type declaration that contains all the information needed by the compiler. For example, the following declaration of type R represents the full view of this type:

    
    
    
        
package Full_View is

   --  Full view of the R type:
   type R is record
      I : Integer;
   end record;

end Full_View;

As soon as we start applying encapsulation and information hiding — via the private keyword — to a specific type, we are introducing a partial view and making only that view compile-time visible to clients. Doing so requires us to introduce the private part of the package (unless already present). For example:

    
    
    
        
package Partial_Full_Views is

   --  Partial view of the R type:
   type R is private;

private

   --  Full view of the R type:
   type R is record
      I : Integer;
   end record;

end Partial_Full_Views;

As indicated in the example, the type R is private declaration is the partial view of the R type, while the type R is record [...] declaration in the private part of the package is the full view.

Although the partial view doesn't contain the full type declaration, it contains very important information for the users of the package where it's declared. In fact, the partial view of a private type is all that users actually need to know to effectively use this type, while the full view is only needed by the compiler.

In the previous example, the partial view indicates that R is a private type, which means that, even though users cannot directly access any information stored in this type — for example, read the value of the I component of R —, they can use the R type to declare objects. For example:

    
    
    
        
with Partial_Full_Views; use Partial_Full_Views;

procedure Main is
   --  Partial view of R indicates that
   --  R exists as a private type, so we
   --  can declare objects of this type:
   C : R;
begin
   --  But we cannot directly access any
   --  information declared in the full
   --  view of R:
   --
   --  C.I := 42;
   --
   null;
end Main;

In many cases, the restrictions applied to the partial and full views must match. For example, if we declare a limited type in the full view of a private type, its partial view must also be limited:

    
    
    
        
package Limited_Private_Example is

   --  Partial view must be limited,
   --  since the full view is limited.
   type R is limited private;

private

   type R is limited record
      I : Integer;
   end record;

end Limited_Private_Example;

There are, however, situations where the full view may contain additional requirements that aren't mentioned in the partial view. For example, a type may be declared as non-tagged in the partial view, but, at the same time, be tagged in the full view:

    
    
    
        
package Tagged_Full_View_Example is

   --  Partial view using non-tagged type:
   type R is private;

private

   --  Full view using tagged type:
   type R is tagged record
      I : Integer;
   end record;

end Tagged_Full_View_Example;

In this case, from a user's perspective, the R type is non-tagged, so that users cannot use any object-oriented programming features for this type. In the package body of Tagged_Full_View_Example, however, this type is tagged, so that all object-oriented programming features are available for subprograms of the package body that make use of this type. Again, the partial view of the private type contains the most important information for users that want to declare objects of this type.

In the Ada Reference Manual

Non-Record Private Types

Although it's very common to declare private types as record types, this is not the only option. In fact, we could declare any type in the full view — scalars, for example —, so we could declare a "private integer" type:

    
    
    
        
package Private_Integers is

   --  Partial view of private Integer type:
   type Private_Integer is private;

private

   --  Full view of private Integer type:
   type Private_Integer is new Integer;

end Private_Integers;

This code compiles as expected, but isn't very useful. We can improve it by adding operators to it, for example:

    
    
    
        
package Private_Integers is

   --  Partial view of private Integer type:
   type Private_Integer is private;

   function "+" (Left, Right : Private_Integer)
                 return Private_Integer;

private

   --  Full view of private Integer type:
   type Private_Integer is new Integer;

end Private_Integers;

    
        
package body Private_Integers is

   function "+" (Left, Right : Private_Integer)
                 return Private_Integer
   is
      Res : constant Integer :=
              Integer (Left) + Integer (Right);
      --  Note that we're converting Left
      --  and Right to Integer, which calls
      --  the "+" operator of the Integer
      --  type. Writing "Left + Right" would
      --  have called the "+" operator of
      --  Private_Integer, which leads to
      --  recursive calls, as this is the
      --  operator we're currently in.
   begin
      return Private_Integer (Res);
   end "+";

end Private_Integers;

Now, let's use the new operator in a test application:

    
    
    
        
with Private_Integers; use Private_Integers;

procedure Show_Private_Integers is
   A, B : Private_Integer;
begin
   A := A + B;
end Show_Private_Integers;

In this example, we use the + operator as if we were adding two common integer variables of Integer type.

Unconstrained Types

There are, however, some limitations: we cannot use unconstrained types such as arrays or even discriminants for arrays in the same way as we did for scalars. For example, the following declarations won't work:

    
    
    
        
package Private_Arrays is

   type Private_Unconstrained_Array is private;

   type Private_Constrained_Array
     (L : Positive) is private;

private

   type Integer_Array is
     array (Positive range <>) of Integer;

   type Private_Unconstrained_Array is
     array (Positive range <>) of Integer;

   type Private_Constrained_Array
     (L : Positive) is
       array (1 .. 2) of Integer;

   --  NOTE: using an array type fails as well:
   --
   --  type Private_Constrained_Array
   --    (L : Positive) is
   --      Integer_Array (1 .. L);

end Private_Arrays;

Completing the private type with an unconstrained array type in the full view is not allowed because clients could expect, according to their view, to declare objects of the type. But doing so would not be allowed according to the full view. So this is another case of the partial view having to present clients with a sufficiently true view of the type's capabilities.

One solution is to rewrite the declaration of Private_Constrained_Array using a record type:

    
    
    
        
package Private_Arrays is

   type Private_Constrained_Array
     (L : Positive) is private;

private

   type Integer_Array is
     array (Positive range <>) of Integer;

   type Private_Constrained_Array
     (L : Positive) is
   record
      Arr : Integer_Array  (1 .. 2);
   end record;

end Private_Arrays;

    
        
with Private_Arrays; use Private_Arrays;

procedure Declare_Private_Array is
  Arr : Private_Constrained_Array (5);
begin
  null;
end Declare_Private_Array;

Now, the code compiles fine — but we had to use a record type in the full view to make it work.

Another solution is to make the private type indefinite. In this case, the client's partial view would be consistent with a completion as an indefinite type in the private part:

    
    
    
        
package Private_Arrays is

   type Private_Constrained_Array (<>) is
     private;

   function Init
     (L : Positive)
      return Private_Constrained_Array;

private

   type Private_Constrained_Array is
     array (Positive range <>) of Integer;

end Private_Arrays;

    
        
package body Private_Arrays is

   function Init
     (L : Positive)
      return Private_Constrained_Array
   is
      PCA : Private_Constrained_Array (1 .. L);
   begin
      return PCA;
   end Init;

end Private_Arrays;

    
        
with Private_Arrays; use Private_Arrays;

procedure Declare_Private_Array is
  Arr : Private_Constrained_Array := Init (5);
begin
  null;
end Declare_Private_Array;

The bounds for the object's declaration come from the required initial value when an object is declared. In this case, we initialize the object with a call to the Init function.

Type conversion

An important operation when dealing with objects of different types is type conversion, which we already discussed in the Introduction to Ada course. In fact, we can convert an object Obj_X of an operand type X to a similar, closely related target type Y by simply indicating the target type: Y (Obj_X). In this section, we discuss type conversions for different kinds of types.

Ada distinguishes between two kinds of conversion: value conversion and view conversion. The main difference is the way how the operand (argument) of the conversion is evaluated:

  • in a value conversion, the operand is evaluated as an expression;

  • in a view conversion, the operand is evaluated as a name.

In other words, we cannot use expressions such as 2 * A in a view conversion, but only A. In a value conversion, we could use both forms.

In the Ada Reference Manual

Value conversion

Value conversions are possible for various types. In this section, we see some examples, starting with types derived from scalar types up to array conversions.

Root and derived types

Let's start with the conversion between a scalar type and its derived types. For example, we can convert back-and-forth between the Integer type and the derived Int type:

    
    
    
        
package Custom_Integers is

   type Int is new Integer
     with Dynamic_Predicate => Int /= 0;

   function Double (I : Integer)
                    return Integer is
     (I * 2);

end Custom_Integers;

    
        
with Ada.Text_IO;     use Ada.Text_IO;
with Custom_Integers; use Custom_Integers;

procedure Show_Conversion is
   Int_Var     : Int     := 1;
   Integer_Var : Integer := 2;
begin
   --  Int to Integer conversion
   Integer_Var := Integer (Int_Var);

   Put_Line ("Integer_Var : "
             & Integer_Var'Image);

   --  Int to Integer conversion
   --  as an actual parameter
   Integer_Var := Double (Integer (Int_Var));

   Put_Line ("Integer_Var : "
             & Integer_Var'Image);

   --  Integer to Int conversion
   --  using an expression
   Int_Var     := Int (Integer_Var * 2);

   Put_Line ("Int_Var :     "
             & Int_Var'Image);
end Show_Conversion;

In the Show_Conversion procedure from this example, we first convert from Int to Integer. Then, we do the same conversion while providing the resulting value as an actual parameter for the Double function. Finally, we convert the Integer_Var * 2 expression from Integer to Int.

Note that the converted value must conform to any constraints that the target type might have. In the example above, Int has a predicate that dictates that its value cannot be zero. This (dynamic) predicate is checked at runtime, so an exception is raised if it fails:

    
    
    
        
with Ada.Text_IO;     use Ada.Text_IO;
with Custom_Integers; use Custom_Integers;

procedure Show_Conversion is
   Int_Var     : Int;
   Integer_Var : Integer;
begin
   Integer_Var := 0;
   Int_Var     := Int (Integer_Var);

   Put_Line ("Int_Var : "
             & Int_Var'Image);
end Show_Conversion;

In this case, the conversion from Integer to Int fails because, while zero is a valid integer value, it doesn't obey Int's predicate.

Numeric type conversion

A typical conversion is the one between integer and floating-point values. For example:

    
    
    
        
with Ada.Text_IO; use Ada.Text_IO;

procedure Show_Conversion is
   F : Float   := 1.0;
   I : Integer := 2;
begin
   I := Integer (F);

   Put_Line ("I : "
             & I'Image);

   I := 4;
   F := Float (I);

   Put_Line ("F :   "
             & F'Image);
end Show_Conversion;