Functional programming (Ofer Abarbanel online library)

In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that each return a value, rather than a sequence of imperative statements which change the state of the program.

In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can. This allows programs to be written in a declarative and composable style, where small functions are combined in a modular manner.

Functional programming is sometimes treated as synonymous with purely functional programming, a subset of functional programming which treats all functions as deterministic mathematical functions, or pure functions. When a pure function is called with some given arguments, it will always return the same result, and cannot be affected by any mutable state or other side effects. This is in contrast with impure procedures, common in imperative programming, which can have side effects (such as modifying the program’s state or taking input from a user). Proponents of purely functional programming claim that by restricting side effects, programs can have fewer bugs, be easier to debug and test, and be more suited to formal verification.[1][2]

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,[3][4][5][6] Clojure, Wolfram Language,[7][8] Racket,[9] Erlang,[10][11][12] OCaml,[13][14] Haskell,[15][16] and F#.[17][18] Functional programming is also key to some languages that have found success in specific domains, like R in statistics,[19][20] J, K and Q in financial analysis, and XQuery/XSLT for XML.[21][22] Domain-specific declarative languages like SQL and Lex/Yacc use some elements of functional programming, such as not allowing mutable values.[23] In addition, many other programming languages support programming in a functional style or have implemented features from functional programming, such as C++11, Kotlin,[24] Perl,[25] PHP,[26] Python,[27] Raku,[28] and Scala.[29]


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,[30] 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.[31]

Church later developed a weaker system, the simply-typed lambda calculus, which extended the lambda calculus by assigning a type to all terms.[32] This forms the basis for statically-typed functional programming.

The first functional programming language, LISP, was developed in the late 1950s for the IBM 700/7000 series of scientific computers by John McCarthy while at Massachusetts Institute of Technology (MIT).[33] LISP functions were defined using Church’s lambda notation, extended with a label construct to allow recursive functions.[34] Lisp first introduced many paradigmatic features of functional programming, though early Lisps were multi-paradigm languages, and incorporated support for numerous programming styles as new paradigms evolved. Later dialects, such as Scheme and Clojure, and offshoots such as Dylan and Julia, sought to simplify and rationalise Lisp around a cleanly functional core, while Common Lisp was designed to preserve and update the paradigmatic features of the numerous older dialects it replaced.[35]

Information Processing Language (IPL), 1956, is sometimes cited as the first computer-based functional programming language.[36] It is an 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 an assembly-level language, code can be data, so IPL can be regarded as having higher-order functions. However, it relies heavily on the mutating list structure and similar imperative features.

Kenneth E. Iverson developed 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. In the early 1990s, Iverson and Roger Hui created J. In the mid-1990s, Arthur Whitney, who had previously worked with Iverson, created K, which is used commercially in financial industries along with its descendant Q.

John Backus presented FP in his 1977 Turing Award lecture “Can Programming Be Liberated From the von Neumann Style? A Functional Style and its Algebra of Programs”.[37] He defines functional programs as being built up in a hierarchical way by means of “combining forms” that allow an “algebra of programs”; in modern language, this means that functional programs follow the principle of compositionality.[citation needed] Backus’s paper popularized research into functional programming, though it emphasized function-level programming rather than the lambda-calculus style now associated with functional programming.

The 1973 language ML was created by Robin Milner at the University of Edinburgh, and David Turner developed the language SASL at the University of St Andrews. Also in Edinburgh in the 1970s, Burstall and Darlington developed the functional language NPL.[38] NPL was based on Kleene Recursion Equations and was first introduced in their work on program transformation.[39] Burstall, MacQueen and Sannella then incorporated the polymorphic type checking from ML to produce the language Hope.[40] ML eventually developed into several dialects, the most common of which are now OCaml and Standard ML.

In the 1970s, Guy L. Steele and Gerald Jay Sussman developed Scheme, as described in the Lambda Papers and the 1985 textbook Structure and Interpretation of Computer Programs. Scheme was the first dialect of lisp to use lexical scoping and to require tail-call optimization, features that encourage functional programming.

In the 1980s, Per Martin-Löf developed intuitionistic type theory (also called constructive type theory), which associated functional programs with constructive proofs expressed as dependent types. This led to new approaches to interactive theorem proving and has influenced the development of subsequent functional programming languages.[citation needed]

The lazy functional language, Miranda, developed by David Turner, initially appeared in 1985 and had a strong influence on Haskell. With Miranda being proprietary, Haskell began with a consensus in 1987 to form an open standard for functional programming research; implementation releases have been ongoing since 1990.

More recently it has found use in niches such as parametric CAD courtesy of the OpenSCAD language built on the CSG geometry framework, although its restriction on reassigning values (all values are treated as constants) has led to confusion among users who are unfamiliar with functional programming as a concept.[41]

Functional programming continues to be used in commercial settings.[42][43][44]

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