Abstraction (computer science)

In computer science, abstraction is the process by which data and programs are defined with a representation similar to its pictorial meaning as rooted in the more complex realm of human life and language with their higher need of summarization and categorization (semantics), while hiding away the implementation details. Abstraction tries to reduce and factor out details so that the programmer can focus on a few concepts at a time. A system can have several abstraction layers whereby different meanings and amounts of detail are exposed to the programmer. For example, low-level abstraction layers expose details of the hardware where the program is run, while high-level layers deal with the business logic of the program.

The following English definition of abstraction helps to understand how this term applies to computer science, IT and objects:

abstraction - a concept or idea not associated with any specific instance^[1]

Abstraction captures only those details about an object that are relevant to the current perspective. The concept originated by analogy with abstraction in mathematics. The mathematical technique of abstraction begins with mathematical definitions, making it a more technical approach than the general concept of abstraction in philosophy. For example, in both computing and in mathematics, numbers are concepts in the programming languages, as founded in mathematics. Implementation details depend on the hardware and software, but this is not a restriction because the computing concept of number is still based on the mathematical concept.

In computer programming, abstraction can apply to control or to data: Control abstraction is the abstraction of actions while data abstraction is that of data structures.

• Control abstraction involves the use of subprograms and related concepts control flows
• Data abstraction allows handling data bits in meaningful ways. For example, it is the basic motivation behind datatype.

One can regard the notion of an object (from object-oriented programming) as an attempt to combine abstractions of data and code.

The same abstract definition can be used as a common interface for a family of objects with different implementations and behaviors but which share the same meaning. The inheritance mechanism in object-oriented programming can be used to define an abstract class as the common interface.

The recommendation that programmers use abstractions whenever suitable in order to avoid duplication (usually of code) is known as the abstraction principle. The requirement that a programming language provide suitable abstractions is also called the abstraction principle.

Rationale

Computing mostly operates independently of the concrete world: The hardware implements a model of computation that is interchangeable with others. The software is structured in architectures to enable humans to create the enormous systems by concentration on a few issues at a time. These architectures are made of specific choices of abstractions. Greenspun's Tenth Rule is an aphorism on how such an architecture is both inevitable and complex.

A central form of abstraction in computing is language abstraction: new artificial languages are developed to express specific aspects of a system. Modeling languages help in planning. Computer languages can be processed with a computer. An example of this abstraction process is the generational development of programming languages from the machine language to the assembly language and the high-level language. Each stage can be used as a stepping stone for the next stage. The language abstraction continues for example in scripting languages and domain-specific programming languages.

Within a programming language, some features let the programmer create new abstractions. These include the subroutine, the module, and the software component. Some other abstractions such as software design patterns and architectural styles remain invisible to a programming language and operate only in the design of a system.

Some abstractions try to limit the breadth of concepts a programmer needs by completely hiding the abstractions they in turn are built on. The software engineer and writer Joel Spolsky has criticised these efforts by claiming that all abstractions are leaky — that they can never completely hide the details below; however this does not negate the usefulness of abstraction. Some abstractions are designed to interoperate with others, for example a programming language may contain a foreign function interface for making calls to the lower-level language.

Language features

Programming languages

Main article: Programming language

Different programming languages provide different types of abstraction, depending on the intended applications for the language. For example:

• In object-oriented programming languages such as C++, Object Pascal, or Java, the concept of abstraction has itself become a declarative statement - using the keywords virtual (in C++) or abstract (in Java). After such a declaration, it is the responsibility of the programmer to implement a class to instantiate the object of the declaration.
• Functional programming languages commonly exhibit abstractions related to functions, such as lambda abstractions (making a term into a function of some variable), higher-order functions (parameters are functions), bracket abstraction (making a term into a function of a variable).

Specification methods

Main article: Formal specification

Analysts have developed various methods to formally specify software systems. Some known methods include:

• Abstract-model based method (VDM, Z);
• Algebraic techniques (Larch, CLEAR, OBJ, ACT ONE, CASL);
• Process-based techniques (LOTOS, SDL, Estelle);
• Trace-based techniques (SPECIAL, TAM);
• Knowledge-based techniques (Refine, Gist).

Specification languages

Main article: Specification language

Specification languages generally rely on abstractions of one kind or another, since specifications are typically defined earlier in a project (and at a more abstract level) than an eventual implementation. The UML specification language, for example, allows the definition of abstract classes, which remain abstract during the architecture and specification phase of the project.

Control abstraction

Main article: Control flow

Programming languages offer control abstraction as one of the main purposes of their use. Computer machines understand operations at the very low level such as moving some bits from one location of the memory to another location and producing the sum of two sequences of bits. Programming languages allow this to be done in the higher level. For example, consider this statement written in a Pascal-like fashion:

a := (1 + 2) * 5

To a human, this seems a fairly simple and obvious calculation ("one plus two is three, times five is fifteen"). However, the low-level steps necessary to carry out this evaluation, and return the value "15", and then assign that value to the variable "a", are actually quite subtle and complex. The values need to be converted to binary representation (often a much more complicated task than one would think) and the calculations decomposed (by the compiler or interpreter) into assembly instructions (again, which are much less intuitive to the programmer: operations such as shifting a binary register left, or adding the binary complement of the contents of one register to another, are simply not how humans think about the abstract arithmetical operations of addition or multiplication). Finally, assigning the resulting value of "15" to the variable labeled "a", so that "a" can be used later, involves additional 'behind-the-scenes' steps of looking up a variable's label and the resultant location in physical or virtual memory, storing the binary representation of "15" to that memory location, etc.

Without control abstraction, a programmer would need to specify all the register/binary-level steps each time he simply wanted to add or multiply a couple of numbers and assign the result to a variable. Such duplication of effort has two serious negative consequences:

1. it forces the programmer to constantly repeat fairly common tasks every time a similar operation is needed
2. it forces the programmer to program for the particular hardware and instruction set

Structured programming

Main article: Structured programming

Structured programming involves the splitting of complex program tasks into smaller pieces with clear flow-control and interfaces between components, with reduction of the complexity potential for side-effects.

In a simple program, this may aim to ensure that loops have single or obvious exit points and (where possible) to have single exit points from functions and procedures.

In a larger system, it may involve breaking down complex tasks into many different modules. Consider a system which handles payroll on ships and at shore offices:

• The uppermost level may feature a menu of typical end-user operations.
• Within that could be standalone executables or libraries for tasks such as signing on and off employees or printing checks.
• Within each of those standalone components there could be many different source files, each containing the program code to handle a part of the problem, with only selected interfaces available to other parts of the program. A sign on program could have source files for each data entry screen and the database interface (which may itself be a standalone third party library or a statically linked set of library routines).
• Either the database or the payroll application also has to initiate the process of exchanging data with between ship and shore, and that data transfer task will often contain many other components.

These layers produce the effect of isolating the implementation details of one component and its assorted internal methods from the others. Object-oriented programming embraced and extended this concept.

Data abstraction

Main article: Abstract data type

Data abstraction enforces a clear separation between the abstract properties of a data type and the concrete details of its implementation. The abstract properties are those that are visible to client code that makes use of the data type—the interface to the data type—while the concrete implementation is kept entirely private, and indeed can change, for example to incorporate efficiency improvements over time. The idea is that such changes are not supposed to have any impact on client code, since they involve no difference in the abstract behaviour.

For example, one could define an abstract data type called lookup table which uniquely associates keys with values, and in which values may be retrieved by specifying their corresponding keys. Such a lookup table may be implemented in various ways: as a hash table, a binary search tree, or even a simple linear list of (key:value) pairs. As far as client code is concerned, the abstract properties of the type are the same in each case.

Of course, this all relies on getting the details of the interface right in the first place, since any changes there can have major impacts on client code. As one way to look at this: the interface forms a contract on agreed behaviour between the data type and client code; anything not spelled out in the contract is subject to change without notice.

Languages that implement data abstraction include Ada and Modula-2. Object-oriented languages are commonly claimed^{[by whom?]} to offer data abstraction; however, their inheritance concept tends to put information in the interface that more properly belongs in the implementation; thus, changes to such information ends up impacting client code, leading directly to the Fragile binary interface problem.

Abstraction in object oriented programming

Main article: Object (computer science)

In object-oriented programming theory, abstraction involves the facility to define objects that represent abstract "actors" that can perform work, report on and change their state, and "communicate" with other objects in the system. The term encapsulation refers to the hiding of state details, but extending the concept of data type from earlier programming languages to associate behavior most strongly with the data, and standardizing the way that different data types interact, is the beginning of abstraction. When abstraction proceeds into the operations defined, enabling objects of different types to be substituted, it is called polymorphism. When it proceeds in the opposite direction, inside the types or classes, structuring them to simplify a complex set of relationships, it is called delegation or inheritance.

Various object-oriented programming languages offer similar facilities for abstraction, all to support a general strategy of polymorphism in object-oriented programming, which includes the substitution of one type for another in the same or similar role. Although not as generally supported, a configuration or image or package may predetermine a great many of these bindings at compile-time, link-time, or loadtime. This would leave only a minimum of such bindings to change at run-time.

Common Lisp Object System or self, for example, feature less of a class-instance distinction and more use of delegation for polymorphism. Individual objects and functions are abstracted more flexibly to better fit with a shared functional heritage from Lisp.

C++ exemplifies another extreme: it relies heavily on templates and overloading and other static bindings at compile-time, which in turn has certain flexibility problems.

Although these examples offer alternate strategies for achieving the same abstraction, they do not fundamentally alter the need to support abstract nouns in code - all programming relies on an ability to abstract verbs as functions, nouns as data structures, and either as processes.

Consider for example a sample Java fragment to represent some common farm "animals" to a level of abstraction suitable to model simple aspects of their hunger and feeding. It defines an Animal class to represent both the state of the animal and its functions:

public class Animal extends LivingThing
{
     private Location loc;
     private double energyReserves;
 
     public boolean isHungry() {
         return energyReserves < 2.5;
     }
     public void eat(Food f) {
         // Consume food
         energyReserves += f.getCalories();
     }
     public void moveTo(Location l) {
         // Move to new location
         loc = l;
     }
}

With the above definition, one could create objects of type Animal and call their methods like this:

thePig = new Animal();
theCow = new Animal();
if (thePig.isHungry()) {
    thePig.eat(tableScraps);
}
if (theCow.isHungry()) {
    theCow.eat(grass);
}
theCow.moveTo(theBarn);

In the above example, the class Animal is an abstraction used in place of an actual animal, LivingThing is a further abstraction (in this case a generalisation) of Animal.

If one requires a more differentiated hierarchy of animals — to differentiate, say, those who provide milk from those who provide nothing except meat at the end of their lives — that is an intermediary level of abstraction, probably DairyAnimal (cows, goats) who would eat foods suitable to giving good milk, and MeatAnimal (pigs, steers) who would eat foods to give the best meat-quality.

Such an abstraction could remove the need for the application coder to specify the type of food, so s/he could concentrate instead on the feeding schedule. The two classes could be related using inheritance or stand alone, and the programmer could define varying degrees of polymorphism between the two types. These facilities tend to vary drastically between languages, but in general each can achieve anything that is possible with any of the others. A great many operation overloads, data type by data type, can have the same effect at compile-time as any degree of inheritance or other means to achieve polymorphism. The class notation is simply a coder's convenience.

Object-oriented design

Main article: Object-oriented design

Decisions regarding what to abstract and what to keep under the control of the coder become the major concern of object-oriented design and domain analysis—actually determining the relevant relationships in the real world is the concern of object-oriented analysis or legacy analysis.

In general, to determine appropriate abstraction, one must make many small decisions about scope (domain analysis), determine what other systems one must cooperate with (legacy analysis), then perform a detailed object-oriented analysis which is expressed within project time and budget constraints as an object-oriented design. In our simple example, the domain is the barnyard, the live pigs and cows and their eating habits are the legacy constraints, the detailed analysis is that coders must have the flexibility to feed the animals what is available and thus there is no reason to code the type of food into the class itself, and the design is a single simple Animal class of which pigs and cows are instances with the same functions. A decision to differentiate DairyAnimal would change the detailed analysis but the domain and legacy analysis would be unchanged—thus it is entirely under the control of the programmer, and we refer to abstraction in object-oriented programming as distinct from abstraction in domain or legacy analysis.

Considerations

When discussing formal semantics of programming languages, formal methods or abstract interpretation, abstraction refers to the act of considering a less detailed, but safe, definition of the observed program behaviors. For instance, one may observe only the final result of program executions instead of considering all the intermediate steps of executions. Abstraction is defined to a concrete (more precise) model of execution.

Abstraction may be exact or faithful with respect to a property if one can answer a question about the property equally well on the concrete or abstract model. For instance, if we wish to know what the result of the evaluation of a mathematical expression involving only integers +, -, ×, is worth modulo n, we need only perform all operations modulo n (a familiar form of this abstraction is casting out nines).

Abstractions, however, though not necessarily exact, should be sound. That is, it should be possible to get sound answers from them—even though the abstraction may simply yield a result of undecidability. For instance, we may abstract the students in a class by their minimal and maximal ages; if one asks whether a certain person belongs to that class, one may simply compare that person's age with the minimal and maximal ages; if his age lies outside the range, one may safely answer that the person does not belong to the class; if it does not, one may only answer "I don't know".

The level of abstraction included in a programming language can influence its overall usability. The Cognitive dimensions framework includes the concept of abstraction gradient in a formalism. This framework allows the designer of a programming language to study the trade-offs between abstraction and other characteristics of the design, and how changes in abstraction influence the language usability.

Abstractions can prove useful when dealing with computer programs, because non-trivial properties of computer programs are essentially undecidable (see Rice's theorem). As a consequence, automatic methods for deriving information on the behavior of computer programs either have to drop termination (on some occasions, they may fail, crash or never yield out a result), soundness (they may provide false information), or precision (they may answer "I don't know" to some questions).

Abstraction is the core concept of abstract interpretation. Model checking generally takes place on abstract versions of the studied systems.

Levels of abstraction

Main article: Abstraction layer

Computer science commonly presents levels (or, less commonly, layers) of abstraction, wherein each level represents a different model of the same information and processes, but uses a system of expression involving a unique set of objects and compositions that apply only to a particular domain. ^[2] Each relatively abstract, "higher" level builds on a relatively concrete, "lower" level, which tends to provide an increasingly "granular" representation. For example, gates build on electronic circuits, binary on gates, machine language on binary, programming language on machine language, applications and operating systems on programming languages. Each level is embodied, but not determined, by the level beneath it, making it a language of description that is somewhat self-contained.

Database systems

Main article: Database management system

Since many users of database systems lack in-depth familiarity with computer data-structures, database developers often hide complexity through the following levels:

Data abstraction levels of a database system

Physical level: The lowest level of abstraction describes how a system actually stores data. The physical level describes complex low-level data structures in detail.

Logical level: The next higher level of abstraction describes what data the database stores, and what relationships exist among those data. The logical level thus describes an entire database in terms of a small number of relatively simple structures. Although implementation of the simple structures at the logical level may involve complex physical level structures, the user of the logical level does not need to be aware of this complexity. This referred to as Physical Data Independence. Database administrators, who must decide what information to keep in a database, use the logical level of abstraction.

View level: The highest level of abstraction describes only part of the entire database. Even though the logical level uses simpler structures, complexity remains because of the variety of information stored in a large database. Many users of a database system do not need all this information; instead, they need to access only a part of the database. The view level of abstraction exists to simplify their interaction with the system. The system may provide many views for the same database.

Layered architecture

The ability to provide a design of different levels of abstraction can

• simplify the design considerably
• enable different role players to effectively work at various levels of abstraction

Systems design and business process design can both use this. Some design processes specifically generate designs that contain various levels of abstraction.

Layered architecture partitions the concerns of the application into stacked groups (layers). It is a technique used in designing computer software, hardware, and communications in which system or network components are isolated in layers so that changes can be made in one layer without affecting the others.

See also

• Abstraction inversion for an anti-pattern of one danger in abstraction
• Abstract data type for an abstract description of a set of data
• Algorithm for an abstract description of a computational procedure
• Bracket abstraction for making a term into a function of a variable
• Data modeling for structuring data independent of the processes that use it
• Encapsulation for the categorical dual (other side) of abstraction
• Greenspun's Tenth Rule for an aphorism about an (the?) optimum point in the space of abstractions
• Higher-order function for abstraction where functions produce or consume other functions
• Lambda abstraction for making a term into a function of some variable
• Refinement for the opposite of abstraction in computing
• Substitution for the categorical left adjoint (inverse) of abstraction

Notes

This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL.

1. ^ Thefreedictionary.com
2. ^ Luciano Floridi, Levellism and the Method of Abstraction IEG – Research Report 22.11.04

Further reading

• Abelson, Harold, Gerald Jay Sussman with Julie Sussman. (1996) ISBN 0-262-01153-0 Structure and Interpretation of Computer Programs (Second edition). The MIT Press (See MIT.edu)
• Joel Spolsky. Joelonsoftware.com The Law of Leaky Abstractions. 2002-11-11.