# 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.

### 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:

```

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;

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```

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:

```

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;

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```

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`):

```

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;

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```

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:

```

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

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```

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:

```

procedure Show_Width_Attr is
package B_Str is new
(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;

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```

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;

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```

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.)

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;

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```

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 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;

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```

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;

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);

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 My_Integers; use My_Integers;

procedure Show_Base is

procedure Display_Saturate
(V1, V2 : One_To_Ten;
Op     : Display_Saturate_Op)
is
Res : One_To_Ten;
begin
case Op is
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,  8, Sub);
end Show_Base;

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```

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.

### 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;

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```

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;

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```

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

```

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;

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```

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 Enumeration_Renaming;
use  Enumeration_Renaming;

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

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```

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

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;

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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 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;

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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:

```

Colors range Blue .. Darkblue;

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```

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 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;

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```

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 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;

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```

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

```

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;

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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 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;

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```

### 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 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;

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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;

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```

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

Important

Note that we cannot use indefinite subtypes as discriminants. For example, the following code won't compile:

```

package Unconstrained_Types is

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

type Simple_Record (Arr : Integer_Array) is
record
L : Natural := Arr'Length;
end record;

end Unconstrained_Types;

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```

`Integer_Array` is a correct type declaration — although the type itself is indefinite after the declaration. However, we cannot use it as the discriminant in the declaration of `Simple_Record`. We could, however, have a correct declaration by using discriminants as access values:

```

package Unconstrained_Types is

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

type Integer_Array_Access is
access Integer_Array;

type Simple_Record
(Arr : Integer_Array_Access) is
record
L : Natural := Arr'Length;
end record;

end Unconstrained_Types;

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```

By adding the `Integer_Array_Access` type and using it in `Simple_Record`'s type declaration, we can indirectly use an indefinite type in the declaration of another indefinite type. We discuss this topic later in another chapter.

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;

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```

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;

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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);

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;

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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;

(AA : Integer_Array;
HH : String);

with Show_Integer_Array;

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

with Unconstrained_Types; use Unconstrained_Types;

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
"First example");
"Second example");
end Using_Unconstrained_Type;

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```

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 (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;

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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.

### 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;

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;

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```

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 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;

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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`.

## 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;

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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;

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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:

```

type Integer_List;

type Next is access Integer_List;

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

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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.

## 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;

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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;

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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;

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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;

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```

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;

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```

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.

### 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;

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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
--  recursive calls, as this is the
--  operator we're currently in.
begin
return Private_Integer (Res);
end "+";

end Private_Integers;

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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;

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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;

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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;

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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;

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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.

### 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 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;

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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 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;

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```