First-class function: Difference between revisions

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{{Short description|Programming language feature}}

In [[computer science]], a [[programming language]] is said to have '''first-class functions''' if it treats [[function (programming)|function]]s as [[first-class citizen]]s. This means the language supports passing functions as arguments to other functions, returning them as the values from other functions, and assigning them to variables or storing them in data structures.<ref>{{cite book|first1=Harold|last1=Abelson|authorlink1=Harold Abelson|first2=Gerald Jay|last2=Sussman|authorlink2=Gerald Jay Sussman|title=Structure and Interpretation of Computer Programs|at=[https://archive.org/details/structureinterpr00abel/page/ Formulating Abstractions with Higher-Order Procedures]|publisher=MIT Press|year=1984|isbn=0-262-01077-1|url=https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-12.html#%_sec_1.3|access-date=2021-09-27|archive-date=2021-09-21|archive-url=https://web.archive.org/web/20210921155625/https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-12.html#%_sec_1.3|url-status=dead}}</ref> Some programming language theorists require support for [[anonymous function]]s (function literals) as well.<ref name="test">[http://www.worldcat.org/oclc/222529448 Programming language pragmatics], by Michael Lee Scott, section 11.2 "Functional Programming".</ref> In languages with first-class functions, the [[name (computer science)|names]] of functions do not have any special status; they are treated like ordinary [[variable (computer science)|variable]]s with a [[function type]].<ref>{{cite journal |title=The Implementation of Lua 5.0 |author1=Roberto Ierusalimschy |author1-link=Roberto Ierusalimschy |author2=Luiz Henrique de Figueiredo |author3=Waldemar Celes |journal=Journal of Universal Computer Science |doi=10.3217/jucs-011-07-1159 |doi-access=free |volume=11 |issue=7 |date=2005 |pages=1159–1176}}</ref> The term was coined by [[Christopher Strachey]] in the context of "functions as first-class citizens" in the mid-1960s.<ref name=strachey>{{cite journal|last1=Burstall |first1=Rod |last2=Strachey |first2=Christopher |title=Understanding Programming Languages |journal=[[Higher-Order and Symbolic Computation]] |date=2000 |volume=13 |issue=52 |pages=11–49 |doi=10.1023/A:1010052305354 |s2cid=1989590 |url=http://www.cs.cmu.edu/~crary/819-f09/Strachey67.pdf |url-status=bot: unknown |archiveurl=https://web.archive.org/web/20100216060948/http://www.cs.cmu.edu/~crary/819-f09/Strachey67.pdf |archivedate=February 16, 2010 }} (also on 2010-02-16</ref>

NewFirst-class functions are a necessity for the [[functional programming]] style, in which the use of [[higher-order function]]s is a standard practice. A simple example of a higher-ordered function is the ''[[map (higher-order function)|map]]'' function, which takes, as its arguments, a function and a list, and returns the list formed by applying the function to each member of the list. For a language to support ''map'', it must support passing a function as an argument.

There are certain implementation difficulties in passing functions as arguments or returning them as results, especially in the presence of [[non-local variable]]s introduced in [[nested function|nested]] and [[anonymous function]]s. Historically, these were termed the ''[[funarg problem]]s'', the name coming from "''function argument"''.<ref>[[Joel Moses]]. [https://dspace.mit.edu/handle/1721.1/5854 "The Function of FUNCTION in LISP, or Why the FUNARG Problem Should be Called the Environment Problem"]. MIT AI Memo 199, 1970.</ref> In early imperative languages these problems were avoided by either not supporting functions as result types (e.g. [[ALGOL 60]], [[Pascal (programming language)|Pascal]]) or omitting nested functions and thus non-local variables (e.g. [[C (programming language)|C]]). The early functional language [[Lisp (programming language)|Lisp]] took the approach of [[dynamic scoping]], where non-local variables refer to the closest definition of that variable at the point where the function is executed, instead of where it was defined. Proper support for [[lexically scoped]] first-class functions was introduced in [[Scheme (programming language)|Scheme]] and requires handling references to functions as [[closure (computer science)|closure]]s instead of bare [[function pointer]]s,<ref name="strachey"/> which in turn makes [[Garbage collection (computer science)|garbage collection]] a necessity.{{Citation needed|reason=Rust does it without GC|date=April 2025}}

== Concepts ==

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typedef struct {

int (*f)(int, int, int);

int *a;

int *b;

} closure_t;

void map(closure_t *closure, int x[], size_t n) {

for (int i = 0; i < n; ++i)

x[i] = (*closure->f)(*closure->a, *closure->b, x[i]);

}

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int a = 3;

int b = 1;

closure_t closure = {f, &a, &b};

map(&closure, l, 5);

}

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=== Assigning functions to variables ===

[[Assignment (computer science)|Assigning]] functions to [[variable (computer science)|variables]] and storing them inside (global) datastructuresdata structures potentially suffers from the same difficulties as returning functions.

<syntaxhighlight lang="haskell">

f :: [[Integer] -> [Integer]]

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=== Equality of functions ===

{{further information|Function equality}}

As one can test most literals and values for equality, it is natural to ask whether a programming language can support testing functions for equality. On further inspection, this question appears more difficult and one has to distinguish between several types of function equality:<ref>[[Andrew W. Appel]] (1995). [http://www.cs.princeton.edu/~appel/papers/conteq.pdf "Intensional Equality ;=) for Continuations"].</ref>

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; [[Intensional equality]]: Under intensional equality, two functions ''f'' and ''g'' are considered equal if they have the same "internal structure". This kind of equality could be implemented in [[interpreted language]]s by comparing the [[source code]] of the function bodies (such as in Interpreted Lisp 1.5) or the [[object code]] in [[compiled language]]s. Intensional equality implies extensional equality (assuming the functions are deterministic and have no hidden inputs, such as the [[program counter]] or a mutable [[global variable]].)

; [[Reference equality]]: Given the impracticality of implementing extensional and intensional equality, most languages supporting testing functions for equality use reference equality. All functions or closures are assigned a unique identifier (usually the address of the function body or the closure) and equality is decided based on equality of the identifier. Two separately defined, but otherwise identical function definitions will be considered unequal. Referential equality implies intensional and extensional equality. Referential equality breaks [[referential transparency]] and is therefore not supported in [[purityPure (computer science)function|pure]] languages, such as Haskell.

== Type theory ==

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| [[ALGOL 60]] || {{yes}} || {{no}} || {{yes}} || {{no}} || {{partial|Downwards}} || {{no}} || rowspan=6 | Have [[function type]]s.

|-

| [[ALGOL 68]] || {{yes}} || {{Partial|Yes}}<ref name=compa68pascal>{{cite journal|page=319|title=A comparison of PASCAL and Algol 68|journal=The Computer Journal|volume=21|number=4|year=1977|first=A.S.|last=Tanenbaum|doi=10.1093/comjnl/21.4.316|doi-access=free|url=https://research.vu.nl/files/110789276/11054}}</ref> || {{yes}} || {{yes}} || {{partial|Downwards}}<ref>{{Cite web|url=http://python-history.blogspot.nl/2009/04/origins-of-pythons-functional-features.html?showComment=1243166621952#c702829329923892023|title = The History of Python: Origins of Python's "Functional" Features|date = 21 April 2009}}</ref> || {{no}}

|-

| [[Pascal (programming language)|Pascal]] || {{yes}} || {{no}} || {{yes}} || {{no}} || {{partial|Downwards}} || {{no}}

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|-

| rowspan=9 | C family

| [[C (programming language)|C]] || {{yes}} || {{yes}} || {{Partial|Yes in GNU C}} || {{noPartial|Yes in Clang([[Blocks (C language extension)|Blocks]])}} || {{noPartial|Yes in Clang([[Blocks (C language extension)|Blocks]])}} || {{no}} || Has [[function pointer]]s.

|-

| [[C++]] || {{yes}} || {{yes}} || {{yes|C++11<ref>[https://stackoverflow.com/a/4324829 Nested functions using lambdas/closures]</ref>}} || {{yes|C++11}}<ref name=doc1968>Doc No. [http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n1968.pdf 1968]: V Samko; J Willcock, J Järvi, D Gregor, A Lumsdaine (February 26, 2006) ''Lambda expressions and closures for C++''</ref> || {{partial|C++11}}<ref name=doc1968/> || {{partial|C++11}} || Has function pointers, [[function object]]s. (Also, see below.)

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| [[Objective-C]] || {{yes}} || {{yes}} || {{partial|Using anonymous}} || {{yes|2.0 + Blocks<ref>{{cite web |url=https://developer.apple.com/mac/library/documentation/Cocoa/Conceptual/Blocks/Articles/00_Introduction.html |url-status=dead |archive-url=https://web.archive.org/web/20090831133626/http://developer.apple.com/mac/library/documentation/Cocoa/Conceptual/Blocks/Articles/00_Introduction.html |archive-date=2009-08-31 |title=Mac Dev Center: Blocks Programming Topics: Introduction}}</ref>}} || {{yes|2.0 + Blocks}} || {{no}} || Has function pointers.

|-

| [[Java (programming language)|Java]] || {{yes}} || {{yes}} || {{partial|Using anonymous}} || {{yes|Java 8}} || {{yes|Java 8}} || {{noyes}} || Has [[anonymous inner class]]es.

|-

| [[Go (programming language)|Go]] || {{yes}} || {{yes}} || {{partial|Using anonymous}} || {{yes}} || {{yes}} || {{yes}}<ref>{{cite web |url=https://play.golang.org/p/lZHXrX-yR6 |title=2 examples in Go that you can have partial application }}</ref> ||

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| [[Rust (programming language)|Rust]] || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}}<ref>{{cite web |url=https://docs.rs/partial_application |title=partial_application |website=Docs.rs |access-date=2020-11-03}}</ref> ||

|-

| rowspan=1012 | Functional languages || [[Lisp (programming language)|Lisp]] || {{partial|Syntax}} || {{partial|Syntax}} || {{yes}} || {{yes}} || {{partial|Common Lisp}} || {{no}} || (see below)

|-

| [[Scheme (programming language)|Scheme]] || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes|SRFI 26}}<ref>{{Cite web|url=http://srfi.schemers.org/srfi-26/srfi-26.html|title=SRFI 26: Notation for Specializing Parameters without Currying}}</ref> ||

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|-

| [[Haskell (programming language)|Haskell]] || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} ||

|-

| [[jq (programming language)|jq]] || {{yes}} || {{no}} || {{yes}} ||{{partial|Expressions only}} || {{partial|Downwards}} || {{no}}

|-

| [[Scala (programming language)|Scala]] || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} ||

|-

| [[Erlang (programming language)|Erlang]] || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} ||

|-

| [[Elixir (programming language)|Elixir]] || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} ||

|-

| [[F Sharp (programming language)|F#]] || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} ||

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: The identifier of a regular "function" in Ruby (which is really a method) cannot be used as a value or passed. It must first be retrieved into a <code>Method</code> or <code>Proc</code> object to be used as first-class data. The syntax for calling such a function object differs from calling regular methods.

: Nested method definitions do not actually nest the scope.

: Explicit currying with <code>[httphttps://wwwdocs.ruby-doclang.org/core-1.9.3en/master/Proc.html#method-i-curry]</code>.

==See also==

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==External links==

* [http://rosettacode.org/wiki/First-class_functions First-class functions] on [[Rosetta Code]].

* [http://www.ibm.com/developerworks/linux/library/l-highfunc/index.html Higher order functions] {{Webarchive|url=https://web.archive.org/web/20191112160401/http://www.ibm.com/developerworks/linux/library/l-highfunc/index.html|date=November 12, 2019}} at [[IBM developerWorks]]

{{data types}}