Ada Programming/Types/array

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An array is a collection of elements which can be accessed by one or more index values. In Ada any definite type is allowed as element and any discrete type, i.e. Range, Modular or Enumeration, can be used as an index.

Declaring arrays

Ada's arrays are quite powerful and so there are quite a few syntax variations, which are presented below.

Basic syntax

The basic form of an Ada array is:

array (Index_Range) of Element_Type

where Index_Range is a range of values within a discrete index type, and Element_Type is a definite subtype. The array consists of one element of "Element_Type" for each possible value in the given range. If you for example want to count how often a specific letter appears inside a text, you could use:

type Character_Counter is array (Character) of Natural;

Very often, the index does not have semantic contents by itself, it is just used a means to identify elements for instance in a list. Thus, as a general advice, do not use negative indices in these cases. It is also a good style when using numeric indices, to define them starting in 1 instead of 0, since it is more intuitive for humans and avoids off-by-one errors.

There are, however, cases, where negative indices make sense. So use indices adapted to the problem at hand. Imagine you are a chemist doing some experiments depending on the temperature:

type Temperature is range -10 .. +40;  -- Celsius

type Experiment is array (Temperature ) of Something;

With known subrange

Often you don't need an array of all possible values of the index type. In this case you can subtype your index type to the actually needed range.

subtype Index_Sub_Type is Index_Type range First .. Last

array (Index_Sub_Type) of Element_Type

Since this may involve a lot of typing and you may also run out of useful names for new subtypes, the array declaration allows for a shortcut:

array (Index_Type range First .. Last) of Element_Type

Since First and Last are expressions of Index_Type, a simpler form of the above is:

array (First .. Last) of Element_Type

Note that if First and Last are numeric literals, this implies the index type Integer.

If in the example above the character counter should only count upper case characters and discard all other characters, you can use the following array type:

type Character_Counter is array (Character range 'A' .. 'Z') of Natural;

With unknown subrange

Sometimes the range actually needed is not known until runtime or you need objects of different lengths. In some languages you would resort to pointers to element types. Not with Ada. Here we have the box '<>', which allows us to declare indefinite arrays:

array (Index_Type range <>) of Element_Type;

When you declare objects of such a type, the bounds must of course be given and the object is constrained to them.

The predefined type String is such a type. It is defined as

 type String is array (Positive range <>) of Character;

You define objects of such an unconstrained type in several ways (the extrapolation to other arrays than String should be obvious):

 Text : String (10 .. 20);
 Input: String := Read_from_some_file;

(These declarations additionally define anonymous subtypes of String.) In the first example, the range of indices is explicitly given. In the second example, the range is implicitly defined from the initial expression, which here could be via a function reading data from some file. Both objects are constrained to their ranges, i.e. they cannot grow nor shrink.

With aliased elements

If you come from C/C++, you are probably used to the fact that every element of an array has an address. The C/C++ standards actually demand that.

In Ada, this is not true. Consider the following array:

 type Day_Of_Month is range 1 .. 31;
 type Day_Has_Appointment is array (Day_Of_Month) of Boolean;
 pragma Pack (Day_Has_Appointment);

Since we have packed the array, the compiler will use as little storage as possible. And in most cases this will mean that 8 boolean values will fit into one byte.

So Ada knows about arrays where more than one element shares one address. So what if you need to address each single element. Just not using pragma Pack is not enough. If the CPU has very fast bit access, the compiler might pack the array without being told. You need to tell the compiler that you need to address each element via an access.

 type Day_Of_Month is range 1 .. 31;
 type Day_Has_Appointment is array (Day_Of_Month) of aliased Boolean;

Arrays with more than one dimension

Arrays can have more than one index. Consider the following 2-dimensional array:

  type Character_Display is
     array (Positive range <>, Positive range <>) of Character;

This type permits declaring rectangular arrays of characters. Example:

  Magic_Square: constant Character_Display :=
     (('S', 'A', 'T', 'O', 'R'),
      ('A', 'R', 'E', 'P', 'O'),
      ('T', 'E', 'N', 'E', 'T'),
      ('O', 'P', 'E', 'R', 'A'),
      ('R', 'O', 'T', 'A', 'S'));

Or, stating some index values explicitly,

  Magic_Square: constant Character_Display(1 .. 5, 1 .. 5) :=
     (1 => ('S', 'A', 'T', 'O', 'R'),
      2 => ('A', 'R', 'E', 'P', 'O'),
      3 => ('T', 'E', 'N', 'E', 'T'),
      4 => ('O', 'P', 'E', 'R', 'A'),
      5 => ('R', 'O', 'T', 'A', 'S'));

The index values of the second dimension, those indexing the characters in each row, are in 1 .. 5 here. By choosing a different second range, we could change these to be in 11 .. 15:

  Magic_Square: constant Character_Display(1 .. 5, 11 .. 15) :=
     (1 => ('S', 'A', 'T', 'O', 'R'),
       ...

By adding more dimensions to an array type, we could have squares, cubes (or « bricks »), etc., of homogenous data items.

Finally, an array of characters is a string (see Ada Programming/Strings). Therefore, Magic_Square may simply be declared like this:

  Magic_Square: constant Character_Display :=
     ("SATOR",
      "AREPO",
      "TENET",
      "OPERA",
      "ROTAS");

Using arrays

Assignment

When accessing elements, the index is specified in parentheses. It is also possible to access slices in this way:

Vector_A (1 .. 3) := Vector_B (3 .. 5);

Note that the index range slides in this example: After the assignment, Vector_A (1) = Vector_B (3) and similarly for the other indices.

Also note that slice assignments are done in one go, not in a loop character by character, so that assignments with overlapping ranges work as expected:

Name: String (1 .. 13) := "Lady Ada     ";

Name (6 .. 13) := Name (1 .. 8);

The result is "Lady Lady Ada" (and not "Lady Lady Lad").

Slicing

As has been shown above, in slice assignments index ranges slide. Also subtype conversions make index ranges slide:

subtype Str_1_8 is String (1 .. 8);

The result of Str_1_8 (Name (6 .. 13)) has the new bounds 1 and 8 and contents "Lady Ada" and is not a copy. This is the best way to change the bounds of an array or of parts thereof.

Concatenate

The operator "&" can be used to concatenate arrays:

Name := First_Name & ' ' & Last_Name;

In both cases, if the resulting array does not fit in the destination array, Constraint_Error is raised.

If you try to access an existing element by indexing outside the array bounds, Constraint_Error is raised (unless checks are suppressed).

Array Attributes

There are four Attributes which are important for arrays: 'First, 'Last, 'Length and 'Range. Lets look at them with an example. Say we have the following three strings:

Hello_World  : constant String := "Hello World!";
World        : constant String := Hello_World (7 .. 11);
Empty_String : constant String := "";

Then the four attributes will have the following values:

Array	'First	'Last	'Length	'Range
Hello_World	1	12	12	1 .. 12
World	7	11	5	7 .. 11
Empty_String	1	0	0	1 .. 0

The example was chosen to show a few common beginner's mistakes:

The assumption that strings begin with the index value 1 is wrong (cf. World'First = 7 on the second line).
The assumption (which follows from the first one) that X'Length = X'Last is wrong.
The assumption that X'Last >= X'First; this is not true for empty strings.

The index subtype of predefined type String is Positive, therefore excluding 0 or -17 etc. from the set of possible index values, by subtype constraint (of Positive). Also, 'A' or 2.17e+4 are excluded, since they are not of type Positive.

The attribute 'Range is a little special as it does not return a discrete value but an abstract description of the array. One might wonder what it is good for. The most common use is in the for loop on arrays. When looping over all elements of an array, you need not know the actual index range; by using the attribute, one of the most frequent errors, accessing elements out of the index range, can never occur:

 for I in World'Range loop
   ... World (I)...
 end loop;

'Range can also be used in declaring a name for the index subtype:

subtype Hello_World_Index is Integer range Hello_World'Range;

The Range attribute can be convenient when programming index checks:

if K in World'Range then
   return World(K);
else
   return Substitute;
end if;

Empty or Null Arrays

As you have seen in the section above, Ada allows for empty arrays. Any array whose last index value is lower than the first index value is empty. And — of course — you can have empty arrays of all sorts, not just String:

type Some_Array is array (Positive range <>) of Boolean;

Empty_Some_Array : constant Some_Array (1 .. 0) := (others => False);

Also_Empty: Some_Array (42 .. 10);

Note: If you give an initial expression to an empty array (which is a must for a constant), the expression in the aggregate will of course not be evaluated since there are no elements actually stored.

Ada Programming/Types/array

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