Language support
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Multi-dimensional arrays
The number of indices needed to specify an element is called the dimension, dimensionality, or rank of the array type. (This nomenclature conflicts with the concept of dimension in linear algebra, which expresses the shape of a matrix. Thus, an array of numbers with 5 rows and 4 columns, hence 20 elements, is said to have dimension 2 in computing contexts, but represents a matrix that is said to be 4×5-dimensional. Also, the computer science meaning of "rank" conflicts with the notion of tensor rank, which is a generalization of the linear algebra concept of rank of a matrix.)
Many languages support only one-dimensional arrays. In those languages, a multi-dimensional array is typically represented by an Iliffe vector, a one-dimensional array of references to arrays of one dimension less. A two-dimensional array, in particular, would be implemented as a vector of pointers to its rows. Thus an element in row i and column j of an array A would be accessed by double indexing (A[i][j] in typical notation). This way of emulating multi-dimensional arrays allows the creation of jagged arrays, where each row may have a different size – or, in general, where the valid range of each index depends on the values of all preceding indices.
This representation for multi-dimensional arrays is quite prevalent in C and C++ software. However, C and C++ will use a linear indexing formula for multi-dimensional arrays that are declared with compile time constant size, e.g. by int A[10][20] or int A[m][n], instead of the traditional int **A. [8]
The C99 standard introduced Variable Length Array types that let define array types with dimensions computed in run time. The dynamic 4D array can be constructed using a pointer to 4d array, e.g. int (*arr)[t][u][v][w] = malloc(sizeof *arr); . The individual elements are accessed by first de-referencing an array pointer followed by indexing, e.g. (*arr)[i][j][k][l] . Alternatively, n-d arrays can be declared as pointers to its first element which is a (n-1) dimensional array, e.g. int (*arr)[u][v][w] = malloc(t * siezof *arr); and accessed using more idiomatic syntax, e.g. arr[i][j][k][l] .
Indexing notation
Most programming languages that support arrays support the store and select operations, and have special syntax for indexing. Early languages used parentheses, e.g. A(i,j), as in FORTRAN; others choose square brackets, e.g. A[i,j] or A[i][j], as in Algol 60 and Pascal (to distinguish from the use of parentheses for function calls).
Index types
Array data types are most often implemented as array structures: with the indices restricted to integer (or totally ordered) values, index ranges fixed at array creation time, and multilinear element addressing. This was the case in most "third generation" languages, and is still the case of most systems programming languages such as Ada, C, and C++. In some languages, however, array data types have the semantics of associative arrays, with indices of arbitrary type and dynamic element creation. This is the case in some scripting languages such as Awk and Lua, and of some array types provided by standard C++ libraries.
Bounds checking
Some languages (like Pascal and Modula) perform bounds checking on every access, raising an exception or aborting the program when any index is out of its valid range. Compilers may allow these checks to be turned off to trade safety for speed. Other languages (like FORTRAN and C) trust the programmer and perform no checks. Good compilers may also analyze the program to determine the range of possible values that the index may have, and this analysis may lead to bounds-checking elimination.
Index origin
Some languages, such as C, provide only zero-based array types, for which the minimum valid value for any index is 0. [9] This choice is convenient for array implementation and address computations. With a language such as C, a pointer to the interior of any array can be defined that will symbolically act as a pseudo-array that accommodates negative indices. This works only because C does not check an index against bounds when used.
Other languages provide only one-based array types, where each index starts at 1; this is the traditional convention in mathematics for matrices and mathematical sequences. A few languages, such as Pascal and Lua, support n-based array types, whose minimum legal indices are chosen by the programmer. The relative merits of each choice have been the subject of heated debate. Zero-based indexing can avoid off-by-one or fencepost errors. [10]
Highest index
The relation between numbers appearing in an array declaration and the index of that array's last element also varies by language. In many languages (such as C), one should specify the number of elements contained in the array; whereas in others (such as Pascal and Visual Basic .NET) one should specify the numeric value of the index of the last element. Needless to say, this distinction is immaterial in languages where the indices start at 1, such as Lua.
Array algebra
Some programming languages support array programming, where operations and functions defined for certain data types are implicitly extended to arrays of elements of those types. Thus one can write A+B to add corresponding elements of two arrays A and B. Usually these languages provide both the element-by-element multiplication and the standard matrix product of linear algebra, and which of these is represented by the * operator varies by language.
Languages providing array programming capabilities have proliferated since the innovations in this area of APL. These are core capabilities of domain-specific languages such as GAUSS, IDL, Matlab, and Mathematica. They are a core facility in newer languages, such as Julia and recent versions of Fortran. These capabilities are also provided via standard extension libraries for other general purpose programming languages (such as the widely used NumPy library for Python).
String types and arrays
Many languages provide a built-in string data type, with specialized notation ("string literals") to build values of that type. In some languages (such as C), a string is just an array of characters, or is handled in much the same way. Other languages, like Pascal, may provide vastly different operations for strings and arrays.
Array index range queries
Some programming languages provide operations that return the size (number of elements) of a vector, or, more generally, range of each index of an array. In C and C++ arrays do not support the size function, so programmers often have to declare separate variable to hold the size, and pass it to procedures as a separate parameter.
Elements of a newly created array may have undefined values (as in C), or may be defined to have a specific "default" value such as 0 or a null pointer (as in Java).
In C++ a std::vector object supports the store, select, and append operations with the performance characteristics discussed above. Vectors can be queried for their size and can be resized. Slower operations like inserting an element in the middle are also supported.
Slicing
An array slicing operation takes a subset of the elements of an array-typed entity (value or variable) and then assembles them as another array-typed entity, possibly with other indices. If array types are implemented as array structures, many useful slicing operations (such as selecting a sub-array, swapping indices, or reversing the direction of the indices) can be performed very efficiently by manipulating the dope vector of the structure. The possible slicings depend on the implementation details: for example, FORTRAN allows slicing off one column of a matrix variable, but not a row, and treat it as a vector; whereas C allow slicing off a row from a matrix, but not a column.
On the other hand, other slicing operations are possible when array types are implemented in other ways.
Resizing
Some languages allow dynamic arrays (also called resizable, growable, or extensible): array variables whose index ranges may be expanded at any time after creation, without changing the values of its current elements.
For one-dimensional arrays, this facility may be provided as an operation "append(A,x)" that increases the size of the array A by one and then sets the value of the last element to x. Other array types (such as Pascal strings) provide a concatenation operator, which can be used together with slicing to achieve that effect and more. In some languages, assigning a value to an element of an array automatically extends the array, if necessary, to include that element. In other array types, a slice can be replaced by an array of different size, with subsequent elements being renumbered accordingly – as in Python's list assignment "A[5:5] = [10,20,30]", that inserts three new elements (10,20, and 30) before element "A[5]". Resizable arrays are conceptually similar to lists, and the two concepts are synonymous in some languages.
An extensible array can be implemented as a fixed-size array, with a counter that records how many elements are actually in use. The append operation merely increments the counter; until the whole array is used, when the append operation may be defined to fail. This is an implementation of a dynamic array with a fixed capacity, as in the string type of Pascal. Alternatively, the append operation may re-allocate the underlying array with a larger size, and copy the old elements to the new area.
