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In
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...
, an abstract data type (ADT) is a mathematical model for data types. An abstract data type is defined by its behavior (
semantics Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comp ...
) from the point of view of a '' user'', of the data, specifically in terms of possible values, possible operations on data of this type, and the behavior of these operations. This mathematical model contrasts with data structures, which are concrete representations of data, and are the point of view of an implementer, not a user. Formally, an ADT may be defined as a "class of objects whose logical behavior is defined by a set of values and a set of operations"; this is analogous to an algebraic structure in mathematics. What is meant by "behaviour" varies by author, with the two main types of formal specifications for behavior being ''axiomatic (algebraic) specification'' and an ''abstract model;'' these correspond to axiomatic semantics and
operational semantics Operational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety or security, are verified by constructing proofs from logical statements about its execut ...
of an
abstract machine An abstract machine is a computer science theoretical model that allows for a detailed and precise analysis of how a computer system functions. It is analogous to a mathematical function in that it receives inputs and produces outputs based on pr ...
, respectively. Some authors also include the computational complexity ("cost"), both in terms of time (for computing operations) and space (for representing values). In practice, many common data types are not ADTs, as the abstraction is not perfect, and users must be aware of issues like
arithmetic overflow Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ce ...
that are due to the representation. For example, integers are often stored as fixed-width values (32-bit or 64-bit binary numbers), and thus experience integer overflow if the maximum value is exceeded. ADTs are a theoretical concept, in computer science, used in the design and analysis of
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, data structures, and software systems, and do not correspond to specific features of
computer language A computer language is a formal language used to communicate with a computer. Types of computer languages include: * Construction language – all forms of communication by which a human can specify an executable problem solution to a comput ...
s—mainstream computer languages do not directly support formally specified ADTs. However, various language features correspond to certain aspects of ADTs, and are easily confused with ADTs proper; these include
abstract type In programming languages, an abstract type is a type in a nominative type system that cannot be instantiated directly; a type that is not abstract – which ''can'' be instantiated – is called a ''concrete type''. Every instance of an abstrac ...
s,
opaque data type In computer science, an opaque data type is a data type whose concrete data structure is not defined in an interface. This enforces information hiding, since its values can only be manipulated by calling subroutines that have access to the missing ...
s,
protocols Protocol may refer to: Sociology and politics * Protocol (politics), a formal agreement between nation states * Protocol (diplomacy), the etiquette of diplomacy and affairs of state * Etiquette, a code of personal behavior Science and technology ...
, and design by contract. ADTs were first proposed by
Barbara Liskov Barbara Liskov (born November 7, 1939 as Barbara Jane Huberman) is an American computer scientist who has made pioneering contributions to programming languages and distributed computing. Her notable work includes the development of the Liskov su ...
and Stephen N. Zilles in 1974, as part of the development of the CLU language.


Abstract data types

For example,
integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
s are an ADT, defined as the values ..., −2, −1, 0, 1, 2, ..., and by the operations of addition, subtraction, multiplication, and division, together with greater than, less than, etc., which behave according to familiar mathematics (with care for
integer division Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication. At an elementary level the division of two natural numbers ...
), independently of how the integers are represented by the computer. Explicitly, "behavior" includes obeying various axioms (associativity and commutativity of addition, etc.), and preconditions on operations (cannot divide by zero). Typically integers are represented in a data structure as binary numbers, most often as
two's complement Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest place value (the leftmost bit in big- endian ...
, but might be binary-coded decimal or in
ones' complement The ones' complement of a binary number is the value obtained by inverting all the bits in the binary representation of the number (swapping 0s and 1s). The name "ones' complement" (''note this is possessive of the plural "ones", not of a sin ...
, but for most purposes the user can work with the abstraction rather than the concrete choice of representation, and can simply use the data as if the type were truly abstract. An ADT consists not only of operations but also of a domain of values, and of constraints on the defined operations. An "interface" typically refers only to the operations, and perhaps some of the constraints on the operations, such as pre-conditions and post-conditions; but not to other constraints such as relations between the operations. For example, an abstract stack, which is a last-in-first-out structure, could be defined by three operations: push, that inserts a data item onto the stack; pop, that removes a data item from it; and peek or top, that accesses a data item on top of the stack without removal. An abstract queue, which is a first-in-first-out structure, would also have three operations: enqueue, that inserts a data item into the queue; dequeue, that removes the first data item from it; and front, that accesses and serves the first data item in the queue. If these were the entire definitions, there would be no way of differentiating these two data types and their very different expected ordering behavior. Thus, a constraint is introduced that for a stack specifies that each pop always returns (and removes) the most recently pushed item that has not been popped yet, and for a queue (in contrast) specifies that pop operates on the least recently pushed item. When analyzing the efficiency of algorithms, one may also specify that all operations take the same time no matter how many data items have been pushed into the stack, and that the stack uses a constant amount of storage for each element. However, time bounds are not always considered part of the definition of an ADT.


Introduction

Abstract data types are purely theoretical entities, used (among other things) to simplify the description of abstract algorithms, to classify and evaluate data structures, and to formally describe the type systems of programming languages. However, an ADT may be implemented by specific data types or data structures, in many ways and in many programming languages; or described in a formal specification language. ADTs are often implemented as modules: the module's
interface Interface or interfacing may refer to: Academic journals * ''Interface'' (journal), by the Electrochemical Society * '' Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Linguistics'' * '' Int ...
declares procedures that correspond to the ADT operations, sometimes with comments that describe the constraints. This
information hiding In computer science, information hiding is the principle of segregation of the ''design decisions'' in a computer program that are most likely to change, thus protecting other parts of the program from extensive modification if the design decisio ...
strategy allows the implementation of the module to be changed without disturbing the
client Client(s) or The Client may refer to: * Client (business) * Client (computing), hardware or software that accesses a remote service on another computer * Customer or client, a recipient of goods or services in return for monetary or other valuabl ...
programs. The term abstract data type can also be regarded as a generalized approach of a number of algebraic structures, such as lattices, groups, and rings. The notion of abstract data types is related to the concept of data abstraction, important in
object-oriented programming Object-oriented programming (OOP) is a programming paradigm based on the concept of "objects", which can contain data and code. The data is in the form of fields (often known as attributes or ''properties''), and the code is in the form of ...
and design by contract methodologies for software development.


Defining an abstract data type

An abstract data type is defined as a mathematical model of the data objects that make up a data type as well as the functions that operate on these objects. There are no standard conventions for defining them. A broad division may be drawn between "imperative" (or "operational") and "functional" (or "axiomatic") definition styles.


Imperative-style definition

In the theory of
imperative programming In computer science, imperative programming is a programming paradigm of software that uses statements that change a program's state. In much the same way that the imperative mood in natural languages expresses commands, an imperative program ...
languages, an abstract data structure is conceived as an entity that is ''mutable''—meaning that it may be in different ''states'' at different times. Some operations may change the state of the ADT; therefore, the order in which operations are evaluated is important, and the same operation on the same entities may have different effects if executed at different times. This is analogous to the instructions of a computer, or the commands and procedures of an imperative language. To underscore this view it is customary to say that the operations are ''executed'' or ''applied'', rather than ''evaluated'', similar to the imperative style often used when describing abstract algorithms. (See
The Art of Computer Programming ''The Art of Computer Programming'' (''TAOCP'') is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. Volumes 1–5 are intended to represent the central core of com ...
by
Donald Knuth Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer sc ...
for more details).


Abstract variable

Imperative-style definitions of ADT often depend on the concept of an ''abstract variable'', which may be regarded as the simplest non-trivial ADT. An abstract variable ''V'' is a mutable entity that admits two operations: * store(''V'', ''x'') where ''x'' is a ''value'' of unspecified nature; * fetch(''V''), that yields a value, with the constraint that * fetch(''V'') always returns the value ''x'' used in the most recent store(''V'', ''x'') operation on the same variable ''V''. Fetching before storing can be disallowed, defined to have a certain result, or (less desirably), leave the behavior unspecified. As in many programming languages, the operation store(''V'', ''x'') is often written ''V'' ← ''x'' (or some similar notation), and fetch(''V'') is implied whenever a variable ''V'' is used in a context where a value is required. Thus, for example, ''V'' ← ''V'' + 1 is commonly understood to be a shorthand for store(''V'',fetch(''V'') + 1). In this definition, it is implicitly assumed that names are always distinct: storing a value into a variable ''U'' has no effect on the state of a distinct variable ''V''. To make this assumption explicit, one could add the constraint that * if ''U'' and ''V'' are distinct variables, the sequence is equivalent to . More generally, ADT definitions often assume that any operation that changes the state of one ADT instance has no effect on the state of any other instance of the same ADT, unless the ADT axioms define certain instances as connected (see aliased) in a specific way. The most common such connections include: * Aliasing, in which two or more names refer to the exact same data object. * Composition, in which an ADT is defined to contain instances of (the same or other) ADTs. * Reference, in which an ADT is defined to refer to instance of (the same or other) ADTs. For example, when extending the definition of an abstract variable to include abstract
records 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, r ...
, operations upon a field ''F'' of a record variable ''R'', clearly involve ''F'', which is distinct from, but also a part of, ''R''. The definition of an ADT may restrict the stored value(s) for its instances, to members of a specific set ''X'' called the ''range'' of those variables. For example, an ADT for an aggregate such as a Stack or Queue, may constrain all items in the queue to be integers, or at least to all be of a single type (see
homogeneity Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the Uniformity (chemistry), uniformity of a Chemical substance, substance or organism. A material or image that is homogeneous is uniform in compos ...
). As in programming languages, such restrictions may simplify the description and analysis of algorithms, and improve its readability. Note that this definition does not imply anything about the result of evaluating fetch(''V'') when ''V'' is ''un-initialized'', that is, before performing any store operation on ''V''. An algorithm that does so may be considered invalid, either (a) because the ADT prohibits such an operation, or (b) simply because its effect is not defined by the ADT. However, there are some important algorithms whose efficiency strongly depends on the assumption that such a fetch is legal, and returns some arbitrary value in the variable's range.)


Instance creation

Some algorithms need to create new instances of some ADT (such as new variables, or new stacks). To describe such algorithms, one usually includes in the ADT definition a create() operation that yields an instance of the ADT, usually with axioms equivalent to * the result of create() is distinct from any instance already in use by the algorithm. This axiom may be strengthened to exclude also partial aliasing with other instances. For practical use, such as axiom may still allow implementations of create() to yield a previously created instance that has become inaccessible to the program; however, defining that such an instance even is "the same" is difficult, especially in the abstract (though even a re-used block of memory is only "the same object" in certain senses).


Example: abstract stack (imperative)

As another example, an imperative-style definition of an abstract stack could specify that the state of a stack ''S'' can be modified only by the operations * push(''S'', ''x''), where ''x'' is some ''value'' of unspecified nature; * pop(''S''), that yields a value as a result, with the constraint that * For any value ''x'' and any abstract variable ''V'', the sequence of operations is equivalent to ''V'' ← ''x''. Since the assignment ''V'' ← ''x'', by definition, cannot change the state of ''S'', this condition implies that ''V'' ← pop(''S'') restores ''S'' to the state it had before the push(''S'', ''x''). From this condition and from the properties of abstract variables, it follows, for example, that the sequence : where ''x'', ''y'', and ''z'' are any values, and ''U'', ''V'', ''W'' are pairwise distinct variables, is equivalent to : Here it is implicitly assumed that operations on a stack instance do not modify the state of any other ADT instance, including other stacks; that is, * For any values ''x'', ''y'', and any distinct stacks ''S'' and ''T'', the sequence is equivalent to . An abstract stack definition usually includes also a Boolean-valued function empty(''S'') and a create() operation that returns a stack instance, with axioms equivalent to * create() ≠ ''S'' for any prior stack ''S'' (a newly created stack is distinct from all previous stacks); * empty(create()) (a newly created stack is empty); * not empty(push(''S'', ''x'')) (pushing something into a stack makes it non-empty).


Single-instance style

Sometimes an ADT is defined as if only one instance of it existed during the execution of the algorithm, and all operations were applied to that instance, which is not explicitly notated. For example, the abstract stack above could have been defined with operations push(''x'') and pop(), that operate on ''the'' only existing stack. ADT definitions in this style can be easily rewritten to admit multiple coexisting instances of the ADT, by adding an explicit instance parameter (like ''S'' in the previous example) to every operation that uses or modifies the implicit instance. On the other hand, some ADTs cannot be meaningfully defined without assuming multiple instances. This is the case when a single operation takes two distinct instances of the ADT as parameters. For an example, consider augmenting the definition of the abstract stack with an operation compare(''S'', ''T'') that checks whether the stacks ''S'' and ''T'' contain the same items in the same order.


Functional-style definition

Another way to define an ADT, closer to the spirit of
functional programming In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that ...
, is to consider each state of the structure as a separate entity. In this view, any operation that modifies the ADT is modelled as a
mathematical function In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the functi ...
that takes the old state as an argument and returns the new state as part of the result. Unlike the imperative operations, these functions have no
side effect In medicine, a side effect is an effect, whether therapeutic or adverse, that is secondary to the one intended; although the term is predominantly employed to describe adverse effects, it can also apply to beneficial, but unintended, consequence ...
s. Therefore, the order in which they are evaluated is immaterial, and the same operation applied to the same arguments (including the same input states) will always return the same results (and output states). In the functional view, in particular, there is no way (or need) to define an "abstract variable" with the semantics of imperative variables (namely, with fetch and store operations). Instead of storing values into variables, one passes them as arguments to functions.


Example: abstract stack (functional)

For example, a complete functional-style definition of an abstract stack could use the three operations: * push: takes a stack state and an arbitrary value, returns a stack state; * top: takes a stack state, returns a value; * pop: takes a stack state, returns a stack state. In a functional-style definition there is no need for a create operation. Indeed, there is no notion of "stack instance". The stack states can be thought of as being potential states of a single stack structure, and two-stack states that contain the same values in the same order are considered to be identical states. This view actually mirrors the behavior of some concrete implementations, such as linked lists with hash cons. Instead of create(), a functional-style definition of an abstract stack may assume the existence of a special stack state, the ''empty stack'', designated by a special symbol like Λ or "()"; or define a bottom() operation that takes no arguments and returns this special stack state. Note that the axioms imply that * push(Λ, ''x'') ≠ Λ. In a functional-style definition of a stack one does not need an empty predicate: instead, one can test whether a stack is empty by testing whether it is equal to Λ. Note that these axioms do not define the effect of top(''s'') or pop(''s''), unless ''s'' is a stack state returned by a push. Since push leaves the stack non-empty, those two operations are undefined (hence invalid) when ''s'' = Λ. On the other hand, the axioms (and the lack of side effects) imply that push(''s'', ''x'') = push(''t'', ''y'')
if and only if In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is b ...
''x'' = ''y'' and ''s'' = ''t''. As in some other branches of mathematics, it is customary to assume also that the stack states are only those whose existence can be proved from the axioms in a finite number of steps. In the abstract stack example above, this rule means that every stack is a ''finite'' sequence of values, that becomes the empty stack (Λ) after a finite number of pops. By themselves, the axioms above do not exclude the existence of infinite stacks (that can be popped forever, each time yielding a different state) or circular stacks (that return to the same state after a finite number of pops). In particular, they do not exclude states ''s'' such that pop(''s'') = ''s'' or push(''s'', ''x'') = ''s'' for some ''x''. However, since one cannot obtain such stack states with the given operations, they are assumed "not to exist".


Whether to include complexity

Aside from the behavior in terms of axioms, it is also possible to include, in the definition of an ADT operation, their algorithmic complexity.
Alexander Stepanov Alexander Alexandrovich Stepanov (russian: Алекса́ндр Алекса́ндрович Степа́нов; born November 16, 1950, Moscow) is a Russian-American computer programmer, best known as an advocate of generic programming and as th ...
, designer of the C++
Standard Template Library The Standard Template Library (STL) is a software library originally designed by Alexander Stepanov for the C++ programming language that influenced many parts of the C++ Standard Library. It provides four components called ''algorithms'', '' ...
, included complexity guarantees in the STL specification, arguing:


Advantages of abstract data typing


Encapsulation

Abstraction provides a promise that any implementation of the ADT has certain properties and abilities; knowing these is all that is required to make use of an ADT object.it make to used with Data type in programming language Perimitive and non perimitive data type.


Localization of change

Code that uses an ADT object will not need to be edited if the implementation of the ADT is changed. Since any changes to the implementation must still comply with the interface, and since code using an ADT object may only refer to properties and abilities specified in the interface, changes may be made to the implementation without requiring any changes in code where the ADT is used.


Flexibility

Different implementations of the ADT, having all the same properties and abilities, are equivalent and may be used somewhat interchangeably in code that uses the ADT. This gives a great deal of flexibility when using ADT objects in different situations. For example, different implementations of the ADT may be more efficient in different situations; it is possible to use each in the situation where they are preferable, thus increasing overall efficiency.


Typical operations

Some operations that are often specified for ADTs (possibly under other names) are * compare(''s'', ''t''), that tests whether two instances' states are equivalent in some sense; * hash(''s''), that computes some standard
hash function A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or simply ''hashes''. The values are usually ...
from the instance's state; * print(''s'') or show(''s''), that produces a human-readable representation of the instance's state. In imperative-style ADT definitions, one often finds also * create(), that yields a new instance of the ADT; * initialize(''s''), that prepares a newly created instance ''s'' for further operations, or resets it to some "initial state"; * copy(''s'', ''t''), that puts instance ''s'' in a state equivalent to that of ''t''; * clone(''t''), that performs ''s'' ← create(), copy(''s'', ''t''), and returns ''s''; * free(''s'') or destroy(''s''), that reclaims the memory and other resources used by ''s''. The free operation is not normally relevant or meaningful, since ADTs are theoretical entities that do not "use memory". However, it may be necessary when one needs to analyze the storage used by an algorithm that uses the ADT. In that case, one needs additional axioms that specify how much memory each ADT instance uses, as a function of its state, and how much of it is returned to the pool by free.


Examples

Some common ADTs, which have proved useful in a great variety of applications, are * Collection *
Container A container is any receptacle or enclosure for holding a product used in storage, packaging, and transportation, including shipping. Things kept inside of a container are protected on several sides by being inside of its structure. The term ...
*
List 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 unio ...
* String * Set *
Multiset In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the multiplicity of that e ...
*
Map A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes. Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although ...
*
Multimap In computer science, a multimap (sometimes also multihash, multidict or multidictionary) is a generalization of a map or associative array abstract data type in which more than one value may be associated with and returned for a given key. Both m ...
*
Graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...
*
Tree In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...
* Stack * Queue * Priority queue *
Double-ended queue In computer science, a double-ended queue (abbreviated to deque, pronounced ''deck'', like "cheque") is an abstract data type that generalizes a queue, for which elements can be added to or removed from either the front (head) or back (tail). ...
* Double-ended priority queue Each of these ADTs may be defined in many ways and variants, not necessarily equivalent. For example, an abstract stack may or may not have a count operation that tells how many items have been pushed and not yet popped. This choice makes a difference not only for its clients but also for the implementation. ; Abstract graphical data type An extension of ADT for computer graphics was proposed in 1979: an abstract graphical data type (AGDT). It was introduced by
Nadia Magnenat Thalmann Nadia Magnenat Thalmann is a computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer dis ...
, and Daniel Thalmann. AGDTs provide the advantages of ADTs with facilities to build graphical objects in a structured way.


Implementation

Implementing an ADT means providing one procedure or function for each abstract operation. The ADT instances are represented by some concrete data structure that is manipulated by those procedures, according to the ADT's specifications. Usually, there are many ways to implement the same ADT, using several different concrete data structures. Thus, for example, an abstract stack can be implemented by a linked list or by an
array An array is a systematic arrangement of similar objects, usually in rows and columns. Things called an array include: {{TOC right Music * In twelve-tone and serial composition, the presentation of simultaneous twelve-tone sets such that the ...
. In order to prevent clients from depending on the implementation, an ADT is often packaged as an ''
opaque data type In computer science, an opaque data type is a data type whose concrete data structure is not defined in an interface. This enforces information hiding, since its values can only be manipulated by calling subroutines that have access to the missing ...
'' in one or more modules, whose interface contains only the signature (number and types of the parameters and results) of the operations. The implementation of the module—namely, the bodies of the procedures and the concrete data structure used—can then be hidden from most clients of the module. This makes it possible to change the implementation without affecting the clients. If the implementation is exposed, it is known instead as a ''transparent data type.'' When implementing an ADT, each instance (in imperative-style definitions) or each state (in functional-style definitions) is usually represented by a
handle A handle is a part of, or attachment to, an object that allows it to be grasped and manipulated by hand. The design of each type of handle involves substantial ergonomic issues, even where these are dealt with intuitively or by following tr ...
of some sort., definition 4.4. Modern object-oriented languages, such as
C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...
and
Java Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's mos ...
, support a form of abstract data types. When a class is used as a type, it is an abstract type that refers to a hidden representation. In this model, an ADT is typically implemented as a class, and each instance of the ADT is usually an object of that class. The module's interface typically declares the constructors as ordinary procedures, and most of the other ADT operations as methods of that class. However, such an approach does not easily encapsulate multiple representational variants found in an ADT. It also can undermine the extensibility of object-oriented programs. In a pure object-oriented program that uses interfaces as types, types refer to behaviours, not representations.


Example: implementation of the abstract stack

As an example, here is an implementation of the abstract stack above in the C programming language.


Imperative-style interface

An imperative-style interface might be: typedef struct stack_Rep stack_Rep; // type: stack instance representation (opaque record) typedef stack_Rep* stack_T; // type: handle to a stack instance (opaque pointer) typedef void* stack_Item; // type: value stored in stack instance (arbitrary address) stack_T stack_create(void); // creates a new empty stack instance void stack_push(stack_T s, stack_Item x); // adds an item at the top of the stack stack_Item stack_pop(stack_T s); // removes the top item from the stack and returns it bool stack_empty(stack_T s); // checks whether stack is empty This interface could be used in the following manner: #include // includes the stack interface stack_T s = stack_create(); // creates a new empty stack instance int x = 17; stack_push(s, &x); // adds the address of x at the top of the stack void* y = stack_pop(s); // removes the address of x from the stack and returns it if (stack_empty(s)) // does something if stack is empty This interface can be implemented in many ways. The implementation may be arbitrarily inefficient, since the formal definition of the ADT, above, does not specify how much space the stack may use, nor how long each operation should take. It also does not specify whether the stack state ''s'' continues to exist after a call ''x'' ← pop(''s''). In practice the formal definition should specify that the space is proportional to the number of items pushed and not yet popped; and that every one of the operations above must finish in a constant amount of time, independently of that number. To comply with these additional specifications, the implementation could use a linked list, or an array (with dynamic resizing) together with two integers (an item count and the array size).


Functional-style interface

Functional-style ADT definitions are more appropriate for functional programming languages, and vice versa. However, one can provide a functional-style interface even in an imperative language like C. For example: typedef struct stack_Rep stack_Rep; // type: stack state representation (opaque record) typedef stack_Rep* stack_T; // type: handle to a stack state (opaque pointer) typedef void* stack_Item; // type: value of a stack state (arbitrary address) stack_T stack_empty(void); // returns the empty stack state stack_T stack_push(stack_T s, stack_Item x); // adds an item at the top of the stack state and returns the resulting stack state stack_T stack_pop(stack_T s); // removes the top item from the stack state and returns the resulting stack state stack_Item stack_top(stack_T s); // returns the top item of the stack state


ADT libraries

Many modern programming languages, such as C++ and Java, come with standard libraries that implement several common ADTs, such as those listed above.


Built-in abstract data types

The specification of some programming languages is intentionally vague about the representation of certain built-in data types, defining only the operations that can be done on them. Therefore, those types can be viewed as "built-in ADTs". Examples are the arrays in many scripting languages, such as
Awk AWK (''awk'') is a domain-specific language designed for text processing and typically used as a data extraction and reporting tool. Like sed and grep, it is a filter, and is a standard feature of most Unix-like operating systems. The AWK lang ...
,
Lua Lua or LUA may refer to: Science and technology * Lua (programming language) * Latvia University of Agriculture * Last universal ancestor, in evolution Ethnicity and language * Lua people, of Laos * Lawa people, of Thailand sometimes referred t ...
, and
Perl Perl is a family of two high-level, general-purpose, interpreted, dynamic programming languages. "Perl" refers to Perl 5, but from 2000 to 2019 it also referred to its redesigned "sister language", Perl 6, before the latter's name was offic ...
, which can be regarded as an implementation of the abstract list.


See also

*
Concept (generic programming) In generic programming, a concept is a description of supported operations on a type, including syntax and semantics. In this way, concepts are related to abstract types but concepts do not require a subtype relationship. Language use The term wa ...
*
Formal methods In computer science, formal methods are mathematically rigorous techniques for the specification, development, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the exp ...
*
Functional specification A functional specification (also, ''functional spec'', ''specs'', ''functional specifications document (FSD)'', ''functional requirements specification'') in systems engineering and software development is a document that specifies the functions ...
*
Generalized algebraic data type In functional programming, a generalized algebraic data type (GADT, also first-class phantom type, guarded recursive datatype, or equality-qualified type) is a generalization of parametric algebraic data types. Overview In a GADT, the product co ...
*
Initial algebra In mathematics, an initial algebra is an initial object in the category of -algebras for a given endofunctor . This initiality provides a general framework for induction and recursion. Examples Functor Consider the endofunctor sending ...
* Liskov substitution principle *
Type theory In mathematics, logic, and computer science, a type theory is the 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 theory as a fou ...
* '' Walls and Mirrors''


Notes


Citations


References

* *


Further reading

*


External links

*
Abstract data type
in NIST Dictionary of Algorithms and Data Structures {{DEFAULTSORT:Abstract Data Type Data types Type theory