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In functional programming, functions are treated as [[first-class citizen]]s, meaning that they can be bound to names (including local [[Identifier (computer languages)|identifiers]]), passed as [[Parameter (computer programming)|arguments]], and [[Return value|returned]] from other functions, just as any other [[data type]] can. This allows programs to be written in a [[Declarative programming|declarative]] and [[Composability|composable]] style, where small functions are combined in a [[Modular programming|modular]] manner.
Functional programming is sometimes treated as synonymous with [[purely functional programming]], a subset of functional programming
Functional programming has its roots in [[academia]], evolving from the [[lambda calculus]], a formal system of computation based only on functions. Functional programming has historically been less popular than imperative programming, but many functional languages are seeing use today in industry and education, including [[Common Lisp]], [[Scheme (programming language)|Scheme]],<ref name="clinger1987"/><ref name="hartheimer1987"/><ref name="kidd2007"/><ref name="cleis2006"/> [[Clojure]], [[Wolfram Language]],<ref name="reference.wolfram.com">{{cite web |title=Wolfram Language Guide: Functional Programming |url=http://reference.wolfram.com/language/guide/FunctionalProgramming.html |year=2015 |access-date=2015-08-24}}</ref><ref name="Amath-CO"/> [[Racket (programming language)|Racket]],<ref name="racket-video-games"/> [[Erlang (programming language)|Erlang]],<ref name="erlang-faq"/><ref name="armstrong2007"/><ref name="larson2009"/> [[Elixir (programming language)|Elixir]],<ref>{{Cite web|title=The Elixir Programming Language|url=https://elixir-lang.org/|access-date=2021-02-14}}</ref> [[OCaml]],<ref name="minksy2008"/><ref name="leroy2007"/> [[Haskell]],<ref name="haskell-industry"/><ref name="hudak2007"/> and [[F Sharp (programming language)|F#]].<ref name="quantFSharp">{{cite conference |last=Mansell |first=Howard |title=Quantitative Finance in F# |url=http://cufp.galois.com/2008/abstracts.html#MansellHoward |year=2008 |conference=CUFP 2008 |access-date=2009-08-29 |archivedate=2015-07-08 |archiveurl=https://web.archive.org/web/20150708125937/http://cufp.galois.com/2008/abstracts.html#MansellHoward |url-status=dead }}</ref><ref name="businessAppsFSharp">{{cite conference |last=Peake |first=Alex |title=The First Substantial Line of Business Application in F# |url=http://cufp.galois.com/2009/abstracts.html#AlexPeakeAdamGranicz |year=2009 |conference=CUFP 2009 |access-date=2009-08-29 |archive-url=https://web.archive.org/web/20091017070140/http://cufp.galois.com/2009/abstracts.html#AlexPeakeAdamGranicz |archive-date=2009-10-17 |url-status=dead }}</ref> [[Lean (proof assistant)|Lean]] is a functional programming language commonly used for verifying mathematical theorems.<ref>{{cite conference |conference=Conference on Automated Deduction |title=The Lean 4 Theorem Prover and Programming Language |last1=de Moura |first1=Leonardo |last2=Ullrich |first2=Sebastian |date=July 2021 |book-title=Lecture Notes in Artificial Intelligence |volume=12699 |pages=625–635 |issn=1611-3349 |doi=10.1007/978-3-030-79876-5_37 |doi-access=free}}</ref> Functional programming is also key to some languages that have found success in specific domains, like [[JavaScript]] in the Web,<ref>{{Cite web|last=Banz|first=Matt|date=2017-06-27|title=An introduction to functional programming in JavaScript|url=https://opensource.com/article/17/6/functional-javascript|access-date=2021-01-09|website=Opensource.com|language=en}}</ref> [[R (programming language)|R]] in statistics,<ref name="useR"/><ref name="Chambers"/> [[J (programming language)|J]], [[K (programming language)|K]] and [[Q (programming language from Kx Systems)|Q]] in financial analysis, and [[XQuery]]/[[XSLT]] for [[XML]].<ref name="Novatchev"/><ref name="Mertz"/> Domain-specific declarative languages like [[SQL]] and [[Lex (software)|Lex]]/[[Yacc]] use some elements of functional programming, such as not allowing [[mutable object|mutable values]].<ref name="Chamberlin_Boyce"/> In addition, many other programming languages support programming in a functional style or have implemented features from functional programming, such as [[C++11]], [[C Sharp (programming language)|C#]],<ref>{{Citation|title=Functional Programming with C# - Simon Painter - NDC Oslo 2020| date=8 August 2021 |url=https://www.youtube.com/watch?v=gvyTB4aMI4o| archive-url=https://ghostarchive.org/varchive/youtube/20211030/gvyTB4aMI4o| archive-date=2021-10-30|language=en|access-date=2021-10-23}}{{cbignore}}</ref> [[Kotlin (programming language)|Kotlin]],<ref name=":0">{{Cite web|url=https://kotlinlang.org/docs/tutorials/kotlin-for-py/functional-programming.html|title=Functional programming - Kotlin Programming Language|website=Kotlin|access-date=2019-05-01}}</ref> [[Perl]],<ref>{{cite book |last=Dominus |first=Mark J. |author-link=Mark Jason Dominus |title=Higher-Order Perl |publisher=[[Morgan Kaufmann]] |year=2005 |isbn=978-1-55860-701-9 |title-link=Higher-Order Perl}}</ref> [[PHP]],<ref>{{cite book |last=Holywell |first=Simon |title=Functional Programming in PHP |publisher=php[architect] |year=2014 |isbn=9781940111056}}</ref> [[Python (programming language)|Python]],<ref name="AutoNT-13">{{cite web |url=https://www.python.org/community/pycon/dc2004/papers/24/metaclasses-pycon.pdf |archive-url=https://web.archive.org/web/20090530030205/http://www.python.org/community/pycon/dc2004/papers/24/metaclasses-pycon.pdf |archive-date=30 May 2009 |title=Python Metaclasses: Who? Why? When? |last=The Cain Gang Ltd. |access-date=27 June 2009 |url-status=dead |df=dmy-all }}</ref> [[Go (programming language)|Go]],<ref>{{Cite web|last=|first=|date=22 December 2020|title=GopherCon 2020: Dylan Meeus - Functional Programming with Go|url=https://www.youtube.com/watch?v=wqs8n5Uk5OM|access-date=|website=YouTube}}</ref> [[Rust (programming language)|Rust]],<ref>{{Cite web|title=Functional Language Features: Iterators and Closures - The Rust Programming Language|url=https://doc.rust-lang.org/book/ch13-00-functional-features.html|access-date=2021-01-09|website=doc.rust-lang.org}}</ref> [[Raku (programming language)|Raku]],<ref>{{cite web|last=Vanderbauwhede |first=Wim |url=https://wimvanderbauwhede.github.io/articles/decluttering-with-functional-programming/|archive-url=https://web.archive.org/web/20200728013926/https://wimvanderbauwhede.github.io/articles/decluttering-with-functional-programming/|archive-date=28 July 2020|title=Cleaner code with functional programming |date=18 July 2020 |access-date=6 October 2020}}</ref> [[Scala (programming language)|Scala]],<ref name="effective-scala"/> and [[Java (programming language)|Java (since Java 8)]].<ref name="java-8-javadoc"/>
Due to their [[composability]], functional programming paradigms can be suitable for [[microservices]]-based architectures. <ref>{{Cite book |last=Rodger |first=Richard |title=The Tao of Microservices |publisher=Manning |isbn=9781638351733}}</ref>▼
== History ==
The [[lambda calculus]], developed in the 1930s by [[Alonzo Church]], is a [[formal system]] of [[computation]] built from [[function application]]. In 1937 [[Alan Turing]] proved that the lambda calculus and [[Turing machines]] are equivalent models of computation,<ref>{{cite journal|first=A. M.|last=Turing|doi=10.2307/2268280|title=Computability and λ-definability|year=1937|journal=The Journal of Symbolic Logic|pages=153–163|volume=2|issue=4|publisher=Cambridge University Press|jstor=2268280|s2cid=2317046}}</ref> showing that the lambda calculus is [[Turing complete]]. Lambda calculus forms the basis of all functional programming languages. An equivalent theoretical formulation, [[combinatory logic]], was developed by [[Moses Schönfinkel]] and [[Haskell Curry]] in the 1920s and 1930s.<ref>{{cite book|author1=Haskell Brooks Curry|author2=Robert Feys|title=Combinatory Logic|url=https://archive.org/details/combinatorylogic0002curr|url-access=registration|access-date=10 February 2013|year=1958|publisher=North-Holland Publishing Company}}</ref>
Church later developed a weaker system, the [[simply
The first [[High-level programming language|high-level]] functional programming language, [[Lisp (programming language)|Lisp]], was developed in the late 1950s for the [[IBM 700/7000 series#Scientific Architecture|IBM 700/7000 series]] of scientific computers by [[John McCarthy (computer scientist)|John McCarthy]] while at [[Massachusetts Institute of Technology]] (MIT).<ref>{{cite
[[Information Processing Language]] (IPL), 1956, is sometimes cited as the first computer-based functional programming language.<ref>The memoir of [[Herbert A. Simon]] (1991), ''Models of My Life'' pp.189-190 {{ISBN|0-465-04640-1}} claims that he, Al Newell, and Cliff Shaw are "...commonly adjudged to be the parents of [the] artificial intelligence [field]," for writing [[Logic Theorist]], a program that proved theorems from ''[[Principia Mathematica]]'' automatically. To accomplish this, they had to invent a language and a paradigm that, viewed retrospectively, embeds functional programming.</ref> It is an [[assembly language|assembly-style language]] for manipulating lists of symbols. It does have a notion of ''generator'', which amounts to a function that accepts a function as an argument, and, since it is
[[Kenneth E. Iverson]] developed [[APL (programming language)|APL]] in the early 1960s, described in his 1962 book ''A Programming Language'' ({{ISBN|9780471430148}}). APL was the primary influence on [[John Backus]]'s [[FP (programming language)|FP]]. In the early 1990s, Iverson and [[Roger Hui]] created [[J (programming language)|J]]. In the mid-1990s, [[Arthur Whitney (computer scientist)|Arthur Whitney]], who had previously worked with Iverson, created [[K (programming language)|K]], which is used commercially in financial industries along with its descendant [[Q (programming language from Kx Systems)|Q]].
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Functional programs do not have assignment statements, that is, the value of a variable in a functional program never changes once defined. This eliminates any chances of side effects because any variable can be replaced with its actual value at any point of execution. So, functional programs are referentially transparent.<ref>{{cite web|last1=Hughes |first1=John |title=Why Functional Programming Matters |url=http://www.cse.chalmers.se/~rjmh/Papers/whyfp.pdf |publisher=[[Chalmers University of Technology]]}}</ref>
Consider [[C (programming language)|C]] assignment statement <code>x=x
Now, consider another function such as <syntaxhighlight lang="c" inline>int plusone(int x) {return x+1;}</syntaxhighlight> ''is'' transparent, as it does not implicitly change the input x and thus has no such [[side effect (computer science)|side effects]].
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=== Imperative vs. functional programming ===
The following two examples (written in [[
Traditional imperative loop:
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.map(a => a * 10)
.reduce((a, b) => a + b, 0);
</syntaxhighlight>Sometimes the abstractions offered by functional programming might lead to development of more robust code that avoids certain issues that might arise when building upon large amount of complex, imperative code, such as [[
=== Simulating state ===
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Alternative methods such as [[Hoare logic]] and [[uniqueness type|uniqueness]] have been developed to track side effects in programs. Some modern research languages use [[effect system]]s to make the presence of side effects explicit.<ref>{{
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</syntaxhighlight>
has the mean execution time of 4.76 ms, while the second one, in which <syntaxhighlight lang="clojure" inline>.equals</syntaxhighlight> is a direct invocation of the underlying [[Java (programming language)|Java]] method, has a mean execution time of 2.8 μs – roughly 1700 times faster. Part of that can be attributed to the type checking and exception handling involved in the implementation of <syntaxhighlight lang="clojure" inline>even?</syntaxhighlight>
One distinguishing feature of [[Rust (programming language)|Rust]] are ''zero-cost abstractions''. This means that using them imposes no additional runtime overhead. This is achieved thanks to the compiler using [[loop unrolling]], where each iteration of a loop, be it imperative or using iterators, is converted into a standalone [[Assembly language|Assembly]] instruction, without the overhead of the loop controlling code. If an iterative operation writes to an array, the resulting array's elements [[Register allocation|will be stored in specific CPU registers]], allowing for [[Time complexity|constant-time access]] at runtime.<ref>{{Cite web |title=Comparing Performance: Loops vs. Iterators - The Rust Programming Language |url=https://doc.rust-lang.org/book/ch13-04-performance.html |access-date=2024-04-29 |website=doc.rust-lang.org}}</ref>
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It is possible to use a functional style of programming in languages that are not traditionally considered functional languages.<ref>{{cite journal |last=Hartel |first=Pieter |author2=Henk Muller |author3=Hugh Glaser |title=The Functional C experience |journal=Journal of Functional Programming |volume=14 |issue=2 |pages=129–135 |date=March 2004 |url=http://www.ub.utwente.nl/webdocs/ctit/1/00000084.pdf |doi=10.1017/S0956796803004817 |s2cid=32346900 |accessdate=2006-05-28 |archivedate=2011-07-19 |archiveurl=https://web.archive.org/web/20110719201553/http://www.ub.utwente.nl/webdocs/ctit/1/00000084.pdf |url-status=deviated }}; {{cite web |title=Functional programming in Python, Part 3 |url=http://www-128.ibm.com/developerworks/linux/library/l-prog3.html |archive-url=https://web.archive.org/web/20071016124848/http://www-128.ibm.com/developerworks/linux/library/l-prog3.html |archive-date=2007-10-16 |author=David Mertz |access-date=2006-09-17 |work=IBM developerWorks }}([https://web.archive.org/web/20071016124848/http://www-128.ibm.com/developerworks/linux/library/l-prog.html Part 1], [https://web.archive.org/web/20071016124848/http://www-128.ibm.com/developerworks/linux/library/l-prog2.html Part 2])</ref> For example, both [[D (programming language)|D]]<ref>{{cite web |url=http://www.digitalmars.com/d/2.0/function.html#pure-functions |title=Functions — D Programming Language 2.0 |publisher=Digital Mars |date=30 December 2012}}</ref> and [[Fortran 95]]<ref name=fortran95/> explicitly support pure functions.
[[JavaScript]], [[Lua (programming language)|Lua]],<ref>{{cite web|url=http://www.luafaq.org/#T1.2|title=Lua Unofficial FAQ (uFAQ)}}</ref> [[Python (programming language)|Python]] and [[Go (programming language)|Go]]<ref>{{Cite web|title=First-Class Functions in Go - The Go Programming Language|url=https://golang.org/doc/codewalk/functions/|access-date=2021-01-04|website=golang.org}}</ref> had [[First-class function|first class functions]] from their inception.<ref>{{cite web|url=https://brendaneich.com/2008/04/popularity/|first=Brendan|last= Eich|title=Popularity|date=3 April 2008}}</ref> Python had support for "[[anonymous function|lambda]]", "[[Map (higher-order function)|map]]", "[[Fold (higher-order function)|reduce]]", and "[[Filter (higher-order function)|filter]]" in 1994, as well as closures in Python 2.2,<ref>{{cite web |url=http://python-history.blogspot.de/2009/04/origins-of-pythons-functional-features.html |title=Origins of Python's "Functional" Features |last=van Rossum |first=Guido |author-link=Guido van Rossum |date=2009-04-21 |access-date=2012-09-27}}</ref> though Python 3 relegated "reduce" to the <code>functools</code> standard library module.<ref>{{cite web |url=https://docs.python.org/dev/library/functools.html#functools.reduce |title=functools — Higher order functions and operations on callable objects |publisher=Python Software Foundation |date=2011-07-31 |access-date=2011-07-31}}</ref> First-class functions have been introduced into other mainstream languages such as [[Perl]] 5.0 in 1994, [[PHP]] 5.3, [[Visual Basic 9]], [[C Sharp (programming language)|C#]] 3.0, [[C++11]], and [[Kotlin (programming language)|Kotlin]].<ref name=":0"/>{{citation needed|date=April 2015}}
In Perl, [[anonymous function|lambda]], [[Map (higher-order function)|map]], [[Fold (higher-order function)|reduce]], [[Filter (higher-order function)|filter]], and [[Closure (computer science)|closures]] are fully supported and frequently used. The book [[Higher-Order Perl]], released in 2005, was written to provide an expansive guide on using Perl for functional programming.
In PHP, [[anonymous class]]es, [[Closure (computer science)|closures]] and lambdas are fully supported. Libraries and language extensions for immutable data structures are being developed to aid programming in the functional style.
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In [[C Sharp (programming language)|C#]], anonymous classes are not necessary, because closures and lambdas are fully supported. Libraries and language extensions for immutable data structures are being developed to aid programming in the functional style in C#.
Many [[Object-oriented programming|object-oriented]] [[Design pattern (computer science)|design patterns]] are expressible in functional programming terms: for example, the [[strategy pattern]] simply dictates use of a higher-order function, and the [[visitor (design pattern)|visitor]] pattern roughly corresponds to a [[catamorphism]], or [[fold (higher-order function)|fold]].
Similarly, the idea of immutable data from functional programming is often included in imperative programming languages,<ref>{{cite book |title=Effective Java |edition=Second |first=Joshua |last=Bloch |chapter=Item 15: Minimize Mutability |isbn=978-0321356680 |date=2008 |publisher=Addison-Wesley |url-access=registration |url=https://archive.org/details/effectivejava00bloc_0}}</ref> for example the tuple in Python, which is an immutable array, and Object.freeze() in JavaScript.<ref>{{Cite web|last=|first=|date=|title=Object.freeze() - JavaScript {{!}} MDN|url=https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Object/freeze|access-date=2021-01-04|website=developer.mozilla.org|quote=The Object.freeze() method freezes an object. A frozen object can no longer be changed; freezing an object prevents new properties from being added to it, existing properties from being removed, prevents changing the enumerability, configurability, or writability of existing properties, and prevents the values of existing properties from being changed. In addition, freezing an object also prevents its prototype from being changed. freeze() returns the same object that was passed in.}}</ref>
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=== Spreadsheets ===
[[Spreadsheet]]s can be considered a form of pure, [[Higher-order function|zeroth-order]], strict-evaluation functional programming system.<ref name="Wakeling2007">{{cite journal|last1=Wakeling|first1=David|title=Spreadsheet functional programming|journal=Journal of Functional Programming|volume=17|issue=1|year=2007|pages=131–143|issn=0956-7968|doi=10.1017/S0956796806006186|s2cid=29429059|url=http://www.activemode.org/webroot/Workers/ActiveTraining/Programming/Pro_SpreadsheetFunctionalProgramming.pdf}}</ref> However, spreadsheets generally lack higher-order functions as well as code reuse, and in some implementations, also lack recursion. Several extensions have been developed for spreadsheet programs to enable higher-order and reusable functions, but so far remain primarily academic in nature.<ref name="excel">{{cite web |title=Improving the world's most popular functional language: user-defined functions in Excel |first1=Simon |last1=Peyton Jones |author-link1=Simon Peyton Jones |first2=Margaret |last2=Burnett|author2-link=Margaret Burnett |first3=Alan |last3=Blackwell |author-link3=Alan Blackwell |url=http://research.microsoft.com/~simonpj/Papers/excel/index.htm |date=March 2003 |archive-url=https://web.archive.org/web/20051016011341/http://research.microsoft.com/~simonpj/Papers/excel/index.htm |archive-date=2005-10-16}}</ref>
=== Microservices ===
▲Due to their [[composability]], functional programming paradigms can be suitable for [[microservices]]-based architectures.
=== Academia ===
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=== Education ===
Many [[University|universities]] teach functional programming.<ref name="oxfordFP">{{cite web|url=https://www.cs.ox.ac.uk/teaching/courses/2019-2020/fp/|title=Functional Programming: 2019-2020|publisher=University of Oxford Department of Computer Science|access-date=28 April 2020}}</ref><ref name="imperialFP">{{cite web|url=https://www.imperial.ac.uk/computing/current-students/courses/120_1/|title=Programming I (Haskell)|publisher=Imperial College London Department of Computing|access-date=28 April 2020}}</ref><ref name="nottinghamFP">{{cite web|url=https://www.nottingham.ac.uk/ugstudy/course/Computer-Science-BSc#yearsmodules|title=Computer Science BSc - Modules|access-date=28 April 2020}}</ref><ref name="mitFP">{{cite book|last1=Abelson|first1=Hal|author-link1=Hal Abelson|last2=Sussman|first2=Gerald Jay|author-link2=Gerald Jay Sussman |title=Structure and Interpretation of Computer Programs |url=http://mitpress.mit.edu/sicp/ |year=1985|publisher=MIT Press|chapter=Preface to the Second Edition|edition=2|bibcode=1985sicp.book.....A |chapter-url=https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-6.html}}</ref> Some treat it as an introductory programming concept<ref name="mitFP"/> while others first teach imperative programming methods.<ref name="nottinghamFP"/><ref name="61A">{{cite web|url=https://cs61a.org/articles/about.html|title=Computer Science 61A, Berkeley|author=John DeNero|date=Fall 2019|publisher=Department of Electrical Engineering and Computer Sciences, Berkeley|access-date=2020-08-14}}</ref>
Outside of computer science, functional programming is used to teach problem-solving, algebraic and geometric concepts.<ref name="bootstrapworld">{{Triangulation|196|Emmanuel Schanzer of Bootstrap}}</ref> It has also been used to teach classical mechanics, as in the book ''[[Structure and Interpretation of Classical Mechanics]]''.
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<ref name="larson2009">{{cite journal |last=Larson |first=Jim |title=Erlang for concurrent programming |journal=Communications of the ACM |volume= 52 |issue= 3 |date=March 2009 |doi=10.1145/1467247.1467263 |page=48 |s2cid=524392 |doi-access=free}}</ref>
<ref name="minksy2008">{{cite journal |last1=Minsky |first1=Yaron |last2=Weeks |first2=Stephen |title=Caml Trading — experiences with functional programming on Wall Street |journal=Journal of Functional Programming |volume=18 |issue=4 |pages=553–564 |date=July 2008 |doi=10.1017/S095679680800676X
<ref name="leroy2007">{{cite conference |last=Leroy |first=Xavier |title=Some uses of Caml in Industry |url=http://cufp.galois.com/2007/slides/XavierLeroy.pdf |conference=CUFP 2007 |access-date=2009-08-26 |archivedate=2011-10-08 |archiveurl=https://web.archive.org/web/20111008170929/http://cufp.galois.com/2007/slides/XavierLeroy.pdf |url-status=dead }}</ref><ref name="haskell-industry">{{cite web |title=Haskell in industry |work=Haskell Wiki |url=http://www.haskell.org/haskellwiki/Haskell_in_industry |access-date=2009-08-26 |quote=Haskell has a diverse range of use commercially, from aerospace and defense, to finance, to web startups, hardware design firms and lawnmower manufacturers.}}</ref>
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<ref name="Amath-CO">{{cite web |website=Department of Applied Math |publisher=University of Colorado |title=Functional vs. Procedural Programming Language |url=http://amath.colorado.edu/computing/mmm/funcproc.html |archive-url=https://web.archive.org/web/20071113175801/http://amath.colorado.edu/computing/mmm/funcproc.html |archive-date=2007-11-13 |access-date=2006-08-28 |url-status=dead }}</ref>
<ref name="Novatchev">{{cite web |url=
<ref name="Chamberlin_Boyce">{{cite journal |title=SEQUEL: A structured English query language |first1=Donald D. |last1=Chamberlin |author-link1=Donald D. Chamberlin |first2=Raymond F. |last2=Boyce |author-link2=Raymond F. Boyce |journal=Proceedings of the 1974 ACM SIGFIDET |pages=249–264 |year=1974}}</ref><ref name="Sim-Diasca">{{cite web |title=Sim-Diasca: a large-scale discrete event concurrent simulation engine in Erlang |url=http://research.edf.com/research-and-the-scientific-community/software/sim-diasca-80704.html |date=November 2011 |access-date=2011-11-08 |archive-date=2013-09-17 |archive-url=https://web.archive.org/web/20130917092159/http://research.edf.com/research-and-the-scientific-community/software/sim-diasca-80704.html |url-status=dead }}</ref>
<ref name="Spiewak">{{cite web |url=http://www.codecommit.com/blog/scala/implementing-persistent-vectors-in-scala |first=Daniel |last=Spiewak |title=Implementing Persistent Vectors in Scala |date=26 August 2008 |website=Code Commit |access-date=17 April 2012 |archivedate=23 September 2015 |archiveurl=https://web.archive.org/web/20150923205254/http://www.codecommit.com/blog/scala/implementing-persistent-vectors-in-scala |url-status=deviated }}</ref>
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== Further reading ==
* {{cite book |last1=Abelson |first1=Hal |author-link1=Hal Abelson |last2=Sussman |first2=Gerald Jay |author-link2=Gerald Jay Sussman |title=Structure and Interpretation of Computer Programs |url=https://mitpress.mit.edu/9780262510363/structure-and-interpretation-of-computer-programs/ |year=1985 |publisher=MIT Press|bibcode=1985sicp.book.....A }}
* Cousineau, Guy and Michel Mauny. ''The Functional Approach to Programming''. Cambridge, UK: [[Cambridge University Press]], 1998.
* Curry, Haskell Brooks and Feys, Robert and Craig, William. ''Combinatory Logic''. Volume I. North-Holland Publishing Company, Amsterdam, 1958.
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{{Programming paradigms navbox}}
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