Array
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An array is a structure concept for data types.
It groups elements of the same type.
An array provides random access to every of its elements, also known as components, by a linear index.
The word array
is a reserved word.
It always occurs in conjunction with the word of
.
Contents
notion
An array
is a limited and arranged aggregation of elements, all of which having the same data type called “base type”.
It has at least one discrete, bounded dimension, continuously enumerating all its elements.
Each element can be uniquely identified by one or more scalar values, called indices, along those dimensions.
A onedimensional array
resembles an ntuple, as it is known from mathematics, but has the constraint of being homogenous (all elements have the same type).
The range of all possible values such an array
can acquire is the homogenous nary Cartesian product of the base type.
A twodimensional array
resembles the mathematical concept named matrix, except for the homogeneity restriction.
usage
length
Originally, Pascal only knew arrays of fixed length (Standard Pascal). How many elements an array consists of had to be known at compiletime. Since this turned out to be a major constraint, and not to mention changes in computers’ hardware since then justified a step forward, variablelength arrays were introduced.
Extended Pascal defined the notion of “schemata” for this. Delphi introduced “dynamic arrays”. As of 2020 FPC only supports the latter regarding variablelength arrays, while support for “schemata” is planned.
Depending on whether an array is intended of being capable of changing its size, its definition varies, but just marginally. For a onedimensional static array the type definition looks like this:
array[indexType] of baseType
A dynamic array type definition is simply relieved of its dimension specification:
array of baseType
static arrays
In static arrays all dimensions’ ranges are known in advance. All dimension specifications have to be ordinal types. The following code shows valid array definitions, all of them static.
1 program staticArrayDemo(input, output, stderr);
2
3 type
4 // specifying ordinal types as index directly
5
6 /// allows selection of a character
7 /// based on a Boolean value
8 characterChoice = array[boolean] of UCS4char;
9
10 // enumerations
11
12 /// enumerates Cartesian axes
13 spaceAxis = (xAxis, yAxis, zAxis);
14 /// a point in threedimensional Euclidean space
15 locus = array[spaceAxis] of valReal;
16 /// a point in a twodimensional Euclidean plane
17 point = array[xAxis..yAxis] of valReal;
18
19 // integer subranges
20
21 level = array[24..24] of longint;
22 box = array[1..1, 1..1, 1..1] of boolean;
23 transformationMatrix = array[0..1, 0..1] of valReal;
24 begin
25 end.
As all array’s elements have to be addressable, there exists a maximum limit of elements an array can hold.
The sizeOf
every array type has to be less than ptrInt
’s maximum value.
dynamic arrays
A dynamic array is an approach of overcoming the limitation of knowing all dimensions sizes in advance. See its dedicated page for details.
addressing elements
An array’s element is addressed by naming the array variable’s identifier followed a valid index enclosed by square brackets.
1 program arrayAddressDemo(input, output, stderr);
2 var
3 msg: array[0..2] of char;
4 begin
5 msg[0] := 'H';
6 msg[1] := 'i';
7 msg[2] := '!';
8 writeLn(msg);
9 end.
Multidimensional arrays’ elements can be addressed in two ways: Either by commaseparating indices:
arrayVariable[firstDimensionIndex, secondDimensionIndex, thirdDimensionIndex]
Or by putting indices in dedicated square brackets:
arrayVariable[firstDimensionIndex][secondDimensionIndex][thirdDimensionIndex]
A third syntactically valid option would be mixing both styles, however, that is considered as bad style, maybe unless there is indication to group indices (e.g. x
, y
and z
coordinates versus other indices) it is OK.
Nonetheless, only the first mentioned notation is valid while defining array types.
Note, it is very important to specify indices in the defined order, within each dimensions’ range.
Consider the following program.
It will compile, but fail during runtime due to {$rangeChecks on}
:
program arrayAddressOrderDemo(input, output, stderr);
{$rangeChecks on}
var
i: integer;
f: array[0..1, 0..3] of boolean;
begin
for i := 0 to 7 do
begin
f[0, i] := true;
end;
end.
While the program would indeed iterate over every array’s element, it doesn’t do so in the intended way, but exploits the fact the array’s internal memory struturce is just a continous block of memory. This is bad style. The programmer in a highlevel language is not supposed to care about specific memory layouts. Cave: It is possible to tamper with other variables in this way. At any rate, a runtime error, namely “RTE 216 general protection fault”, will occur if an attempt is made in accessing memory which is not within the purview of the programmer.
When values contained in arrays are only read, thus the indexes do not matter, a for … in
loop can be used.
application
See for instance:
 array sort
 15puzzle’s or Peg’s game board states are stored as an array
In the default RTL’s system unit the function system.slice
returns the initial part of an array, similiar to Ruby’s notation arrayVariable[0, n]
.
Furthermore there is system.arrayStringToPPchar
.
Most statistical routines of the RTL’s math unit accept arrays as parameters, as well as some other routines.
see also
 Type information
 tutorial: 1dimensional arrays
 tutorial: multidimensional arrays
 example: multidimensional dynamic array
 Why Pascal is not my favorite programming language § “the size of an array is part of its type”
 defensive programming techniques
 vectorization
matrix
unit Flexible Array Member
simple data types 


complex data types 