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{{short description |TechniqueSoftware forthat arrangingprovides complexityaccess ofthat computerhides systemsdetails}}

{{More citations needed|date=June 2011}}

{{Use dmy dates|date=December 2019}}

{{Quote box|quote=The essence of abstraction is preserving information that is relevant in a given context, and forgetting information that is irrelevant in that context.|source=– [[John Guttag|John V. Guttag]]<ref>{{Cite book | edition = Spring 2013 | publisher = The MIT Press | isbn = 9780262519632 | last = Guttag | first = John V. | title = Introduction to Computation and Programming Using Python | ___location = Cambridge, Massachusetts | date = 18 January 2013}}</ref>|width=25%}}

In [[software]], an '''abstraction''' provides access while hiding details that otherwise might make access more challenging.<ref name=":1">{{Cite journal |last1=Colburn |first1=Timothy |last2=Shute |first2=Gary |date=5 June 2007 |title=Abstraction in Computer Science |journal=Minds and Machines |language=en |volume=17 |issue=2 |pages=169–184 |doi=10.1007/s11023-007-9061-7 |issn=0924-6495 |s2cid=5927969}}</ref> It focuses attention on details of greater importance.<ref name=":0">{{Cite journal |last1=Kramer |first1=Jeff |date=1 April 2007 |title=Is abstraction the key to computing? |journal=Communications of the ACM |volume=50 |issue=4 |pages=36–42 |doi=10.1145/1232743.1232745 |issn=0001-0782 |s2cid=12481509}}</ref><ref>{{Cite journal |last1=Ben-Ari |first1=Mordechai |date=1 March 1998 |title=Constructivism in computer science education |journal=ACM SIGCSE Bulletin |volume=30 |issue=1 |pages=257, 257–261 |doi=10.1145/274790.274308 |issn=0097-8418 |doi-access=free}}</ref> Examples include the [[abstract data type]] which separates use from the representation of [[data (computer science)|data]]<ref>{{Cite book |last1=Liskov |first1=Barbara |chapter=Keynote address - data abstraction and hierarchy |s2cid=14219043 |date=1 May 1988 |title=Addendum to the proceedings on Object-oriented programming systems, languages and applications (Addendum) - OOPSLA '87 |journal=ACM SIGPLAN Notices |publisher=ACM |volume=23 |pages=17–34 |doi=10.1145/62138.62141 |isbn=0897912667}}</ref> and [[Function (computer programming)|functions]] that form a call tree that is more general at the base and more specific towards the leaves.

In [[software engineering]] and [[computer science]], '''abstraction''' is:

==Rationale==

* the process of removing physical, spatial, or temporal details<ref name=":1">{{Cite journal|last1=Colburn|first1=Timothy|last2=Shute|first2=Gary|s2cid=5927969|date=5 June 2007|title=Abstraction in Computer Science|journal=Minds and Machines|language=en|volume=17|issue=2|pages=169–184|doi=10.1007/s11023-007-9061-7|issn=0924-6495}}</ref> or [[Attribute (computing)|attributes]] in the study of objects or [[system]]s to focus attention on details of greater importance;<ref name=":0">{{Cite journal|last=Kramer|first=Jeff|s2cid=12481509|date=1 April 2007|title=Is abstraction the key to computing?|journal=Communications of the ACM|volume=50|issue=4|pages=36–42|doi=10.1145/1232743.1232745|issn=0001-0782}}</ref> it is similar in nature to the process of [[generalization]];

{{Quote box|quote=The essence of abstraction is preserving information that is relevant in a given context, and forgetting information that is irrelevant in that context.|source=– [[John Guttag|John V. Guttag]]<ref>{{Cite book | edition last1= Spring 2013Guttag | publisher first1=John The MIT PressV. | isbn date=18 9780262519632January | last = Guttag2013 | first = John V. | title = Introduction to Computation and Programming Using Python |edition=Spring ___location2013 |publisher=The MIT Press |___location=Cambridge, Massachusetts | date isbn= 18 January 2013978-0262519632}}</ref>|width=25%}}

* the creation of [[Abstract and concrete|abstract]] [[concept]]-[[Object (philosophy)|objects]] by mirroring common features or attributes of various non-abstract objects or systems of study<ref name=":0" /> – the result of the process of abstraction.

Computing mostly operates independently of the concrete world. The hardware implements a [[model of computation]] that is interchangeable with others.<ref>{{CitationCite journal |last1=Floridi |first1=Luciano needed|date=JuneSeptember 2008 |title=The Method of Levels of Abstraction |url=http://link.springer.com/10.1007/s11023-008-9113-7 |journal=Minds and Machines |language=en |volume=18 |issue=3 |pages=303–329 |doi=10.1007/s11023-008-9113-7|hdl=2299/2998 |s2cid=7522925 |issn=0924-6495|hdl-access=free|url-access=subscription 2018}}</ref> The software is structured in [[software architecture|architecture]]s to enable humans to create the enormous systems by concentrating on a few issues at a time. These architectures are made of specific choices of abstractions. [[Greenspun's Tenthtenth Rulerule]] is an [[aphorism]] on how such an architecture is both inevitable and complex.

[[Abstraction|Abstraction, in general]], is a fundamental concept in computer science and [[software development]].<ref>{{Cite journal|last=Ben-Ari|first=Mordechai|date=1 March 1998|title=Constructivism in computer science education|journal=ACM SIGCSE Bulletin|volume=30|issue=1|pages=257, 257–261|doi=10.1145/274790.274308|issn=0097-8418|doi-access=free}}</ref> The process of abstraction can also be referred to as '''modeling''' and is closely related to the concepts of ''[[theory]]'' and ''[[design]]''.<ref>{{Cite journal|last1=Comer|first1=D. E.|last2=Gries|first2=David|last3=Mulder|first3=Michael C.|last4=Tucker|first4=Allen|last5=Turner|first5=A. Joe|last6=Young|first6=Paul R. /Denning|s2cid=723103|date=1 January 1989|title=Computing as a discipline|journal=Communications of the ACM|volume=32|issue=1|pages=9–23|doi=10.1145/63238.63239|issn=0001-0782}}</ref> [[Conceptual model|Models]] can also be considered types of abstractions per their generalization of aspects of [[reality]].

ALanguage abstraction is 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 language]]s'' can be processed with a computer. An example of this abstraction process is the generational development of [[programming language]]s from the [[Firstfirst-generation programming language|]] ([[machine language]]) to the [[Secondsecond-generation programming language|]] ([[assembly language]]) and the [[Thirdthird-generation programming language|]] ([[high-level programming language]]). Each stage can be used as a stepping stone for the next stage. The language abstraction continues for example in [[scripting language]]s and [[___domain-specific programming language]]s.

Abstraction in computer science is closely related to [[Abstraction (mathematics)|abstraction in mathematics]] due to their common focus on building abstractions as objects,<ref name=":1" /> but is also related to other notions of abstraction used in other fields [[Abstraction (art)|such as art]].<ref name=":0" />

Within a programming language, some features let the programmer create new abstractions. These include [[subroutine]]s, [[moduleModular (programming)|modules]], [[polymorphismPolymorphism (computer science)|polymorphism]], and [[software component]]s. Some other abstractions such as [[software design pattern]]s and [[software architecture#ArchitectureArchitectural styles and examplespatterns|architectural styles]] remain invisible to a [[translatorTranslator (computing)|translator]] and operate only in the design of a system.

Abstractions may also refer to real-world objects and systems, rules of [[Computation|computational systems]] or rules of [[programming language]]s that carry or utilize features of abstraction itself, such as:

Some abstractions try to limit the range of concepts a programmer needs to be aware of, by completely hiding the abstractions that they in turn are built on. The software engineer and writer [[Joel Spolsky]] has criticisedcriticized these efforts by claiming that all abstractions are ''[[leaky abstraction|leaky]]'' – that they can never completely hide the details below;<ref>{{cite web |url=http://www.joelonsoftware.com/articles/LeakyAbstractions.html |title=The Law of Leaky Abstractions |last1=Spolsky |firstfirst1=Joel |date=11 November 2002 |author1-link=Joel Spolsky}}</ref> however, this does not negate the usefulness of abstraction.

* the usage of [[data type]]s to perform ''data abstraction'' to separate usage from working representations of [[data structure]]s within [[Computer program|programs]];<ref>{{Cite journal|last=Liskov|first=Barbara|s2cid=14219043|date=1 May 1988|title=Keynote address – data abstraction and hierarchy|journal=ACM SIGPLAN Notices|publisher=ACM|volume=23|pages=17–34|doi=10.1145/62138.62141|isbn=0897912667}}</ref>

* the concept of [[Procedure (computer science)|procedures, functions, or subroutines]] which represent a specific of implementing [[control flow]] in programs;

* the rules commonly named "abstraction" that generalize [[Expression (mathematics)|expressions]] using [[Free variables and bound variables|free and bound variables]] in the various versions of [[lambda calculus]];<ref>{{Cite book|title=The lambda calculus : its syntax and semantics|first=Hendrik Pieter|last=Barendregt|date=1984|publisher=North-Holland|isbn=0444867481|edition=Revised|___location=Amsterdam|oclc=10559084}}</ref><ref>{{Cite book|title=Lambda calculus with types|first=Hendrik Pieter|last=Barendregt|date=2013|publisher=Cambridge University Press|others=Dekkers, Wil., Statman, Richard., Alessi, Fabio., Association for Symbolic Logic.|isbn=9780521766142|___location=Cambridge, UK|oclc=852197712}}</ref>

* the usage of [[S-expression]]s as an abstraction of data structures and programs in the [[Lisp (programming language)|Lisp programming language]];<ref>{{Cite book|last1=Newell|first1=Allen|last2=Simon|first2=Herbert A.|date=1 January 2007|title=Computer science as empirical inquiry: symbols and search|publisher=ACM|pages=1975|doi=10.1145/1283920.1283930|isbn=9781450310499}}</ref>

* the process of reorganizing common behavior from non-abstract [[Class (computer programming)|classes]] into "abstract classes" using [[Inheritance (object-oriented programming)|inheritance]] to abstract over [[Inheritance (object-oriented programming)#Subclasses and superclasses|sub-classes]] as seen in the [[Object-oriented programming|object-oriented]] [[C++]] and [[Java (programming language)|Java]] programming languages.

==Rationale==

Computing mostly operates independently of the concrete world. The hardware implements a [[model of computation]] that is interchangeable with others.{{Citation needed|date=June 2018}} The software is structured in [[software architecture|architecture]]s to enable humans to create the enormous systems by concentrating 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 language]]s'' can be processed with a computer. An example of this abstraction process is the generational development of [[programming language]]s from the [[First-generation programming language|machine language]] to the [[Second-generation programming language|assembly language]] and the [[Third-generation programming language|high-level language]]. Each stage can be used as a stepping stone for the next stage. The language abstraction continues for example in [[scripting language]]s and [[___domain-specific programming language]]s.

Within a programming language, some features let the programmer create new abstractions. These include [[subroutine]]s, [[module (programming)|modules]], [[polymorphism (computer science)|polymorphism]], and [[software component]]s. Some other abstractions such as [[software design pattern]]s and [[software architecture#Architecture examples|architectural styles]] remain invisible to a [[translator (computing)|translator]] and operate only in the design of a system.

Some abstractions try to limit the range of concepts a programmer needs to be aware of, by completely hiding the abstractions that they in turn are built on. The software engineer and writer [[Joel Spolsky]] has criticised these efforts by claiming that all abstractions are ''[[leaky abstraction|leaky]]'' – that they can never completely hide the details below;<ref>{{cite web|url=http://www.joelonsoftware.com/articles/LeakyAbstractions.html|title=The Law of Leaky Abstractions|last1=Spolsky|first=Joel}}</ref> however, this does not negate the usefulness of abstraction.

Some abstractions are designed to inter-operate with other abstractions – for example, a programming language may contain a [[foreign function interface]] for making calls to the lower-level language.

==LanguageAbstraction features==

In simple terms, abstraction is removing irrelevant data so a program is easier to understand.{{Citation needed|date=June 2018}}

==Language features==

===Programming languages===

{{MainFurther|Programming language}}

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

* In [[object-oriented programming language]]s languages such as [[C++]], [[Object Pascal]], or [[Java (programming language)|Java]], the concept of '''abstraction''' has itself become a declarative statement – using the [[keywordSyntax (computer programming languages)|keywordsyntax]]s ''<code>virtual''function''(''parameters'') = 0;</code>'' (in [[C++]]) or the [[reserved word]]s (keywords) ''<code>abstract</code>''<ref name="Oracle Java abstract">{{cite web |url=http://docs.oracle.com/javase/tutorial/java/IandI/abstract.html |title=Abstract Methods and Classes|website=The Java™Java Tutorials |publisher=Oracle |accessdateaccess-date=4 September 2014}}</ref> and ''<code>interface</code>''<ref name="Oracle Java interface">{{cite web |url=http://docs.oracle.com/javase/tutorial/java/IandI/interfaceAsType.html |title=Using an Interface as a Type|website=The Java™Java Tutorials |publisher=Oracle |accessdateaccess-date=4 September 2014}}</ref> (in [[Java (programming language)|Java]]). After such a declaration, it is the responsibility of the programmer to implement a [[Class (computer science)|class]] to instantiate the [[Object (computer science)|object]] of the declaration.

* [[Functional programming language]]s languages commonly exhibit abstractions related to functions, such as [[lambda abstraction]]s (making a term into a function of some variable) and [[higher-order function]]s (parameters are functions). <ref>{{FOLDOC|Abstraction}}</ref><!-- This has to be merged in the following sections. -->

* Modern members of the [[List of Lisp-family programming languages|Lisp programming language family]] such as [[Clojure]], [[Scheme (programming language)|Scheme]] and [[Common Lisp]] support [[Macro (computer science)#Syntactic macros|macro systems]] to allow syntactic abstraction. Other programming languages such as [[Scala (programming language)|Scala]] also have macros, or very similar [[metaprogramming]] features (for example, [[Haskell (programming language)|Haskell]] has [[Template Haskell]], and [[OCaml]] has [[MetaOCaml]]). These can allow a programmerprograms to eliminateomit [[boilerplate code]], abstract away tedious function call sequences, implement new [[Control flow|control flow]] structures]], and implement [[Domain___domain-specific language|Domain Specific Languages]]s (DSLs)]], which allow ___domain-specific concepts to be expressed in concise and elegant ways. All of these, when used correctly, improve both the programmer's efficiency and the clarity of the[[source code]] by making the intended purpose more explicit. A consequence of syntactic abstraction is also that any Lisp dialect, and in fact almost any programming language, can, in principle, be implemented in any modern Lisp with significantly reduced (but still non-trivial in somemost cases) effort when compared to "more traditional" programming languages such as [[Python (programming language)|Python]], [[C (programming language)|C]] or [[Java (programming language)|Java]].

===Specification methods===

{{MainFurther|Formal specification}}

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

* Abstract-model based method (VDM, Z);

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===Specification languages===

{{MainFurther|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 [[Unified Modeling Language|UML]] (UML) specification language, for example, allows the definition of ''abstract'' classes, which in a waterfall project, remain abstract during the architecture and specification phase of the project.

==Control abstraction==

{{MainFurther|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 (programming language)|Pascal]]-like fashion:

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===Structured programming===

{{MainFurther|Structured programming}}

Structured programming involves the splitting of complex program tasks into smaller pieces with clear flow-control and interfaces between components, with a 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.

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==Data abstraction==

{{MainFurther|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.

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== Manual data abstraction ==

While much of data abstraction occurs through computer science and automation, there are times when this process is done manually and without programming intervention. One way this can be understood is through data abstraction within the process of conducting a [[systematic review]] of the literature. In this methodology, data is abstracted by one or several abstractors when conducting a [[meta-analysis]], with errors reduced through dual data abstraction followed by independent checking, known as [[adjudication]].<ref>{{Cite journal |last1=E |first1=Jian‐YuJian-Yu |last2=Saldanha |first2=Ian J. |last3=Canner |first3=Joseph |last4=Schmid |first4=Christopher H. |last5=Le |first5=Jimmy T. |last6=Li |first6=Tianjing |date=2020 |title=Adjudication rather than experience of data abstraction matters more in reducing errors in abstracting data in systematic reviews |journal=Research Synthesis Methods |language=en |volume=11 |issue=3 |pages=354–362 |doi=10.1002/jrsm.1396 |pmid=31955502 |s2cid=210829764 |issn=1759-2879}}</ref>

==Abstraction in object oriented programming==

{{MainFurther|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 (object-oriented programming)|encapsulation]] refers to the hiding of [[state (computer science)|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 [[polymorphismPolymorphism (computer science)|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 (object-oriented programming)|delegation]] or [[Inheritance (computerobject-oriented scienceprogramming)|inheritance]].

Various object-oriented programming languages offer similar facilities for abstraction, all to support a general strategy of [[polymorphismPolymorphism (computer science)|polymorphism]] in object-oriented programming, which includes the substitution of one [[typedata in object-oriented programming|type]] for another in the same or similar role. Although not as generally supported, a [[Computer configuration in object-oriented programming|configuration]] or image or package may predetermine a great many of these [[name binding|bindings]] at [[compile- time]], [[Linker (computing)|link- time]], or [[loadtimeLoader (computing)|load time]]. This would leave only a minimum of such bindings to change at [[Run time (program lifecycle phase)|run-time]].

[[Common Lisp Object System]] or [[Self (programming language)|Self]], for example, feature less of a class-instance distinction and more use of delegation for [[polymorphismPolymorphism in(computer object-oriented programmingscience)|polymorphism]]. Individual objects and functions are abstracted more flexibly to better fit with a shared functional heritage from [[Lisp (programming language)|Lisp]].

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

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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/hethey could concentrate instead on the feeding schedule. The two classes could be related using [[Inheritance (computerobject-oriented scienceprogramming)|inheritance]] or stand alone, and the programmer could define varying degrees of [[polymorphismPolymorphism (computer science)|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===

{{MainFurther|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 and design|object-oriented analysis]] or [[legacy analysis]].

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==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 one wishes to know what the result of the evaluation of a mathematical expression involving only integers +, -, ×, is worth [[modular arithmetic|modulo]] ''n'', then one needs 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 [[undecidable problem|undecidability]]. For instance, students in a class may be abstracted 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.

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==Levels of abstraction==

{{MainFurther|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 with varying amounts of detail. Each level uses a system of expression involving a unique set of objects and compositions that apply only to a particular ___domain.

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===Database systems===

{{MainFurther|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:

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[[Image:Data abstraction levels.png|thumb|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 is referred to as [[physical data independence]]. [[Database administrator]]s, 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 [[view (database)|view]]s for the same database.

===Layered architecture===

{{MainFurther|Abstraction layer}}

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

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* [[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 (object-oriented programming)|Encapsulation]] for abstractions that hide implementation details

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==References==

{{Reflist}}

{{refbegin}}

* {{FOLDOC}}

{{refend}}

==Further reading==

{{refbeginRefbegin}}

* {{cite book |author1last1=Abelson |first1=Harold |author1-link=Hal Abelson |last2=Sussman |first2=Gerald Jay |author2-link=Gerald Jay Sussman |last3=Sussman |first3=Julie |author3-link=Julie Sussman |date=25 July 1996 |title=Structure and Interpretation of Computer Programs |url=http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-10.html |accessdateaccess-date=22 June 2012 |edition=2|date=25 July 1996|publisher=MIT Press |isbn=978-0-262-01153-2 |url-status=dead |archive-url=https://web.archive.org/web/20090226050622/http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-10.html |archive-date=26 February 2009|url-status=dead}}

* {{cite web |lastlast1=Spolsky |firstfirst1=Joel |author1-link=Joel Spolsky |date=11 November 2002 |title=The Law of Leaky Abstractions |url=http://www.joelonsoftware.com/articles/LeakyAbstractions.html |work=Joel on Software|date=11 November 2002}}

* [httphttps://www.cs.cornell.edu/courses/cs211/2006sp/Lectures/L08-abstraction/08_abstraction.html Abstraction/information hiding] – CS211 course, Cornell University.

* {{cite book |last1=Roberts |authorfirst1=Eric S. Roberts|date=1997 |title=Programming Abstractions in C A Second Course in Computer Science|date=1997}}

* {{cite web |lastlast1=Palermo |firstfirst1=Jeffrey |date=29 July 2008 |title=The Onion Architecture |url=http://jeffreypalermo.com/blog/the-onion-architecture-part-1/ |work=Jeffrey Palermo|date=29 July 2008}}

*{{Cite journal|

| last1=Vishkin | first1=Uzi

| date=January 2011

| journal=Communications of the ACM

| volume=54

| issue=1

| date=January 2011

| title=Using simple abstraction to reinvent computing for parallelism

| pages=75–85

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| doi-access=free

}}

{{refendRefend}}

==External links==

* [https://sites.google.com/site/simulationarchitecture/ SimArch] example of layered architecture for distributed simulation systems.

{{Software engineering}}

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