Editing Monad (functional programming) (section)

==History==
The term "monad" in programming dates to the [[APL (programming language)|APL]] and [[J (programming language)|J]] programming languages, which do tend toward being purely functional. However, in those languages, "monad" is only shorthand for a function taking one parameter (a function with two parameters being a "dyad", and so on).<ref name="APL">{{cite journal | author-link = Kenneth E. Iverson | last = Iverson | first = Kenneth | date = September 1987 | title = A dictionary of APL | url = http://www.jsoftware.com/papers/APLDictionary.htm | journal = APL Quote Quad | volume = 18 | issue = 1 | pages = 5–40 | doi = 10.1145/36983.36984 | s2cid = 18301178 | issn = 1088-6826 | access-date = 19 November 2018| url-access = subscription }}</ref>

The mathematician [[Roger Godement]] was the first to formulate the concept of a monad (dubbing it a "standard construction") in the late 1950s, though the term "monad" that came to dominate was popularized by category-theorist [[Saunders Mac Lane]].{{Citation needed|reason=Don't have a copy of Mac Lane's book right now, but that could probably work as a source here|date=October 2018}} The form defined above using {{mvar|bind}}, however, was originally described in 1965 by mathematician [[Heinrich Kleisli]] in order to prove that any monad could be characterized as an [[adjunction (category theory)|adjunction]] between two (covariant) functors.<ref name="Kleisli1965">{{cite journal | author-link = Heinrich Kleisli | last = Kleisli | first = Heinrich | date = 1965 | title = Every standard construction is induced by a pair of adjoint functors | url = https://www.ams.org/journals/proc/1965-016-03/S0002-9939-1965-0177024-4/S0002-9939-1965-0177024-4.pdf | journal = Proceedings of the American Mathematical Society | volume = 16 | issue = 3 | pages = 544–546 | doi = 10.1090/S0002-9939-1965-0177024-4 | access-date = 19 November 2018| doi-access = free }}</ref>

Starting in the 1980s, a vague notion of the monad pattern began to surface in the computer science community.
According to programming language researcher [[Philip Wadler]], computer scientist [[John C. Reynolds]] anticipated several facets of it in the 1970s and early 1980s, when he discussed the value of [[continuation-passing style]], of category theory as a rich source for formal semantics, and of the type distinction between values and computations.<ref name="Wadler1992" />
The research language [[Opal programming language|Opal]], which was actively designed up until 1990, also effectively based I/O on a monadic type, but the connection was not realized at the time.<ref name="Opal">{{cite tech report | editor = Peter Pepper | collaboration = The Opal Group | institution = Fachbereich Informatik, Technische Universität Berlin | title = The Programming Language Opal | date = November 1997 | edition = 5th corrected | citeseerx = 10.1.1.40.2748}}</ref>

The computer scientist [[Eugenio Moggi]] was the first to explicitly link the monad of category theory to functional programming, in a conference paper in 1989,<ref name="Moggi89">{{cite conference | author-link = Eugenio Moggi | last = Moggi | first = Eugenio | title = Computational lambda-calculus and monads | conference = Fourth Annual Symposium on Logic in computer science | location = Pacific Grove, California | date = June 1989 | url = https://www.disi.unige.it/person/MoggiE/ftp/lics89.pdf | citeseerx = 10.1.1.26.2787}}</ref> followed by a more refined journal submission in 1991. In earlier work, several computer scientists had advanced using category theory to provide semantics for the [[lambda calculus]]. Moggi's key insight was that a real-world program is not just a function from values to other values, but rather a transformation that forms ''computations'' on those values. When formalized in category-theoretic terms, this leads to the conclusion that monads are the structure to represent these computations.<ref name="Moggi1991" />

Several others popularized and built on this idea, including Philip Wadler and [[Simon Peyton Jones]], both of whom were involved in the specification of Haskell. In particular, Haskell used a problematic "lazy stream" model up through v1.2 to reconcile I/O with [[lazy evaluation]], until switching over to a more flexible monadic interface.<ref name="PeytonWadler1993">{{cite conference | author-link1 = Simon Peyton Jones | author-link2 = Philip Wadler | last1 = Peyton Jones | first1 = Simon L. | last2 = Wadler | first2 = Philip | title = Imperative functional programming | date = January 1993 | conference = 20th Annual ACM Symposium on Principles of Programming Languages | location = Charleston, South Carolina | url = https://www.microsoft.com/en-us/research/wp-content/uploads/1993/01/imperative.pdf | citeseerx = 10.1.1.53.2504}}</ref> The Haskell community would go on to apply monads to many problems in functional programming, and in the 2010s, researchers working with Haskell eventually recognized that monads are [[applicative functor]]s;<ref name= yorgey>Brent Yorgey [https://wiki.haskell.org/Typeclassopedia#Applicative Typeclassopedia]</ref>{{efn|By GHC version 7.10.1, and going forward, Haskell began enforcing Haskell's 2014 Applicative Monad proposal (AMP) which requires the insertion of 7 lines of code into any existing modules which use monads.<ref name= applMonadProposal>Stack overflow  [https://stackoverflow.com/questions/31652475/defining-a-new-monad-in-haskell-raises-no-instance-for-applicative (8 Sep 2017) Defining a new monad in haskell raises no instance for Applicative]</ref>}} and that both monads and [[arrow (computer science)|arrow]]s are [[monoid]]s.<ref>Brent Yorgey [https://wiki.haskell.org/Typeclassopedia#Monoid Monoids]</ref>

At first, programming with monads was largely confined to Haskell and its derivatives, but as functional programming has influenced other paradigms, many languages have incorporated a monad pattern (in spirit if not in name). Formulations now exist in [[Scheme (programming language)|Scheme]], [[Perl]], [[Python (programming language)|Python]], [[Racket (programming language)|Racket]], [[Clojure]], [[Scala (programming language)|Scala]], [[F Sharp (programming language)|F#]], and have also been considered for a new [[ML (programming language)|ML]] standard.{{Citation needed|date=October 2018}}