type MyTable = array ..4,1..2of integer, defines a new array data type called MyTable. The declaration var A: MyTable then defines a variable A of that type, which is an aggregate of eight elements, each being an integer variable identified by two indices. In the Pascal program, those elements are denoted A ,1/code>, A ,2/code>, A ,1/code>, …, A ,2/code>.K. Jensen and Niklaus Wirth, ''PASCAL User Manual and Report''. Springer. Paperback edition (2007) 184 pages, Special array types are often defined by the language's standard libraries
A library is a collection of materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or digital access (soft copies) materials, and may be a physical location or a vir ...
.
Dynamic list
In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a collection of nodes which ...
s are also more common and easier to implement than dynamic array
In computer science, a dynamic array, growable array, resizable array, dynamic table, mutable array, or array list is a random access, variable-size list data structure that allows elements to be added or removed. It is supplied with standard lib ...
s. Array types are distinguished from record
A record, recording or records may refer to:
An item or collection of data Computing
* Record (computer science), a data structure
** Record, or row (database), a set of fields in a database related to one entity
** Boot sector or boot record, ...
types mainly because they allow the element indices to be computed at run time, as in the Pascal assignment A ,J:= A -I,2*J/code>. Among other things, this feature allows a single iterative statement to process arbitrarily many elements of an array variable.
In more theoretical contexts, especially in type theory
In mathematics, logic, and computer science, a type theory is the formal system, formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theor ...
and in the description of abstract algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
s, the terms "array" and "array type" sometimes refer to an abstract data type
In computer science, an abstract data type (ADT) is a mathematical model for data types. An abstract data type is defined by its behavior (semantics) from the point of view of a '' user'', of the data, specifically in terms of possible values, po ...
(ADT) also called ''abstract array'' or may refer to an ''associative array
In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms an ...
'', a mathematical
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
model with the basic operations and behavior of a typical array type in most languages — basically, a collection of elements that are selected by indices computed at run-time.
Depending on the language, array types may overlap (or be identified with) other data types that describe aggregates of values, such as lists
A ''list'' is any set of items in a row. List or lists may also refer to:
People
* List (surname)
Organizations
* List College, an undergraduate division of the Jewish Theological Seminary of America
* SC Germania List, German rugby union ...
and strings. Array types are often implemented by array data structure
In computer science, an array is a data structure consisting of a collection of ''elements'' ( values or variables), each identified by at least one ''array index'' or ''key''. An array is stored such that the position of each element can be c ...
s, but sometimes by other means, such as hash table
In computing, a hash table, also known as hash map, is a data structure that implements an associative array or dictionary. It is an abstract data type that maps keys to values. A hash table uses a hash function to compute an ''index'', ...
s, linked list
In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a collection of nodes whi ...
s, or search tree
In computer science, a search tree is a tree data structure used for locating specific keys from within a set. In order for a tree to function as a search tree, the key for each node must be greater than any keys in subtrees on the left, and les ...
s.
History
Heinz Rutishauser
Heinz Rutishauser (30 January 1918 – 10 November 1970) was a Swiss mathematician and a pioneer of modern numerical mathematics and computer science.
Life
Rutishauser's father died when he was 13 years old and his mother died three years la ...
's programming language Superplan (1949–1951) included multi-dimensional arrays. Rutishauser however although describing how a compiler for his language should be built, did not implement one.
Assembly languages and low-level languages like BCPL generally have no syntactic support for arrays.
Because of the importance of array structures for efficient computation, the earliest high-level programming languages, including FORTRAN (1957), COBOL
COBOL (; an acronym for "common business-oriented language") is a compiled English-like computer programming language designed for business use. It is an imperative, procedural and, since 2002, object-oriented language. COBOL is primarily ...
(1960), and Algol 60
ALGOL 60 (short for ''Algorithmic Language 1960'') is a member of the ALGOL family of computer programming languages. It followed on from ALGOL 58 which had introduced code blocks and the begin and end pairs for delimiting them, representing a k ...
(1960), provided support for multi-dimensional arrays.
Abstract arrays
An array data structure can be mathematically modeled as an abstract data structure
In computer science, an abstract data type (ADT) is a mathematical model for data types. An abstract data type is defined by its behavior (semantics) from the point of view of a '' user'', of the data, specifically in terms of possible values, po ...
(an ''abstract array'') with two operations
:''get''(''A'', ''I''): the data stored in the element of the array ''A'' whose indices are the integer tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements. An -tuple is a sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, referred to as ''the empty tuple''. An -tuple is defi ...
''I''.
:''set''(''A'',''I'',''V''): the array that results by setting the value of that element to ''V''.
These operations are required to satisfy the axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy o ...
s
:''get''(''set''(''A'',''I'', ''V''), ''I'') = ''V''
:''get''(''set''(''A'',''I'', ''V''), ''J'') = ''get''(''A'', ''J'') if ''I'' ≠ ''J''
for any array state ''A'', any value ''V'', and any tuples ''I'', ''J'' for which the operations are defined.
The first axiom means that each element behaves like a variable. The second axiom means that elements with distinct indices behave as disjoint
Disjoint may refer to:
*Disjoint sets, sets with no common elements
*Mutual exclusivity, the impossibility of a pair of propositions both being true
See also
*Disjoint union
*Disjoint-set data structure
{{disambig
Resizing
Some languages allow dynamic array
In computer science, a dynamic array, growable array, resizable array, dynamic table, mutable array, or array list is a random access, variable-size list data structure that allows elements to be added or removed. It is supplied with standard lib ...
s (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= 0,20,30
The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline of ...
, that inserts three new elements (10,20, and 30) before element "''A'' . Resizable arrays are conceptually similar to lists
A ''list'' is any set of items in a row. List or lists may also refer to:
People
* List (surname)
Organizations
* List College, an undergraduate division of the Jewish Theological Seminary of America
* SC Germania List, German rugby union ...
, 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
In computer science, a dynamic array, growable array, resizable array, dynamic table, mutable array, or array list is a random access, variable-size list data structure that allows elements to be added or removed. It is supplied with standard lib ...
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.
See also
* Array access analysis In computer science, array-access analysis is a compiler analysis approach used to decide the read and write access patterns to elements or portions of arrays.
The major data type manipulated in scientific programs is the array. The define/use ana ...
* Array database management system
Array database management systems (array DBMSs) provide database services specifically for arrays (also called raster data), that is: homogeneous collections of data items (often called pixels, voxels, etc.), sitting on a regular grid of one, two, ...
* Bounds-checking elimination
In computer science, bounds-checking elimination is a compiler optimization useful in programming languages or runtime systems that enforce bounds checking, the practice of checking every index into an array to verify that the index is within the d ...
* Delimiter-separated values
Formats that use delimiter-separated values (also DSV)DSV stands for ''Delimiter Separated Values'' store two-dimensional arrays of data by separating the values in each row with specific delimiter characters. Most database and spreadsheet program ...
* Index checking
In computer programming, bounds checking is any method of detecting whether a variable is within some bounds before it is used. It is usually used to ensure that a number fits into a given type (range checking), or that a variable being used as ...
* Parallel array In computing, a group of parallel arrays (also known as structure of arrays or SoA) is a form of implicit data structure that uses multiple arrays to represent a singular array of records. It keeps a separate, homogeneous data array for each field ...
* Sparse array
Sparse is a computer software tool designed to find possible coding faults in the Linux kernel. Unlike other such tools, this static analysis tool was initially designed to only flag constructs that were likely to be of interest to kernel dev ...
* Variable-length array In computer programming, a variable-length array (VLA), also called variable-sized or runtime-sized, is an array data structure whose length is determined at run time (instead of at compile time).
In C, the VLA is said to have a variably modified ...
References
External links
NIST's Dictionary of Algorithms and Data Structures: Array
{{Data types
*
Data types
Composite data types