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Higher-order function Y for which Y f = f (Y f)
In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator) is a higher-order function (i.e., a function that takes a
Fixed-point_combinator
Element mapped to itself by a mathematical function
computer science, a fixed-point combinator is a higher-order function f i x {\displaystyle {\mathsf {fix}}} that returns a fixed point of its argument function
Fixed_point_(mathematics)
Condition for a mathematical function to map some value to itself
first-order logic Lawvere's fixed-point theorem Discrete fixed-point theorems Earle-Hamilton fixed-point theorem Fixed-point combinator, which shows that every
Fixed-point_theorem
Smallest fixed point of a function from a poset
fixed point (lfp or LFP, sometimes also smallest fixed point) of a function from a partially ordered set ("poset" for short) to itself is the fixed point
Least_fixed_point
Topics referred to by the same term
Y combinator may refer to: Y Combinator, an American tech startup accelerator Y combinator (mathematics), a fixed-point combinator This disambiguation
Y_combinator
Root-finding algorithm
attractor and, with probability 1, form a dense set in the latter. Fixed-point combinator Cobweb plot Markov chain Infinite compositions of analytic functions
Fixed-point_iteration
Logical formalism using combinators instead of variables
extensional equality. A more interesting combinator is the fixed point combinator or Y {\displaystyle Y} combinator, which can be used to implement recursion
Combinatory_logic
Simple Turing complete logic
2007" https://ncatlab.org/nlab/show/fixed-point+combinator Bene, Adam (17 August 2017). "Fixed-Point Combinators in JavaScript". Bene Studio. Medium.
SKI_combinator_calculus
Mathematical paradox
{Y}}N)} , where Y {\displaystyle {\textsf {Y}}} denotes Curry's fixed-point combinator. Then X = ( N X ) = ( ( m X ) Z ) {\displaystyle X=(NX)=((mX)Z)}
Curry's_paradox
Functional programming language
convenience. (This expression above is simply `Yk, where Y denotes a fixed point combinator.) More built-ins were introduced in Unlambda version 2. Input is
Unlambda
Mathematical-logic system
"Fixed-Point Combinators in JavaScript". Bene Studio. Medium. Retrieved 2 August 2020. "CS 6110 S17 Lecture 5. Recursion and Fixed-Point Combinators"
Lambda_calculus
Theorem in computability theory
semantics, where another least fixed point theorem is used for the same purpose as the first recursion theorem. Fixed-point combinators, which are used in lambda
Kleene's_recursion_theorem
Concept in computer science
rec is an extension of the simple let expression which uses the fixed-point combinator to implement recursion. Dana Scott's LCF language was a stage in
Let_expression
Topics referred to by the same term
or "getting your fix", taking addictive drugs (from the 1960s) Fixed point combinator, in mathematics All pages with titles beginning with Fix All pages
Fix
Self-replicating program
sense. Computer programming portal Diagonal lemma Droste effect Fixed point combinator Self-modifying code Self-interpreter Self-replicating machine Self-replication
Quine_(computing)
Sentence, idea or formula that refers to itself
Recursive visual effect Fixed point (mathematics) – Element mapped to itself by a mathematical function Fixed-point combinator – Higher-order function
Self-reference
Academic subfield of computer science
\lambda } -calculus, but also important differences exist (e.g. fixed point combinator Y has normal form in combinatory logic but not in λ {\displaystyle
Theory_of_computation
Topics referred to by the same term
Phonetic Alphabet letter for a close front rounded vowel Y combinator, a fixed-point combinator in combinatory logic Y, the Bessel function Y, dependent
Y_(disambiguation)
Type system used in computer programming and mathematics
available, but can instead be expressed with a fixed point combinator. However, the fixpoint combinator cannot be formulated in a typed version of the
Hindley–Milner_type_system
Book by Raymond Smullyan
where he also answers The Grand Question. SKI combinator calculus B, C, K, W system Fixed-point combinator Lambda calculus Logic puzzle Brain teaser Paradox
To_Mock_a_Mockingbird
Mathematical function of a linear operator
λ is a complex scalar eigenvalue. Eigenvalues and eigenvectors Fixed point combinator Fourier transform eigenfunctions Hilbert–Schmidt theorem Spectral
Eigenfunction
Functional programming language
factorial n = foldl (*) 1 [1..n] -- Point-free style factorial = foldr (*) 1 . enumFromTo 1 Using Haskell's Fixed-point combinator allows this function to be written
Haskell
Process of repeating items in a self-similar way
awakening – Vivid and convincing dream about awakening from sleep Fixed point combinator – Higher-order function Y for which Y f = f (Y f)Pages displaying
Recursion
Concept in functional programming
arbitrary collection of base types, product types (tuples) and a fixed point combinator: data Lam :: * -> * where Lift :: a -> Lam a -- ^ lifted value Pair
Generalized algebraic data type
Generalized_algebraic_data_type
Family of higher-order functions
as g = foldr f v Also, in a lazy language with infinite lists, a fixed point combinator can be implemented via fold, proving that iterations can be reduced
Fold_(higher-order_function)
Ability to solve a problem by an effective procedure
\lambda } -calculus, but also important differences exist (e.g. fixed point combinator Y has normal form in combinatory logic but not in λ {\displaystyle
Computability
Typed lambda calculus
apparatus capable of defining functions anonymously and for the fixed-point combinator, which works around that restriction.) Then, with these two λ {\displaystyle
System_F
abstraction Church–Rosser theorem Extensionality Church numeral Fixed point combinator SKI combinator calculus B, C, K, W system SECD machine Graph reduction
List of functional programming topics
List_of_functional_programming_topics
Combinatory logic system
7. Larry Wos, William McCune (September 1988). "Searching for Fixed Point Combinators by Using Automated Theorem Proving: A Preliminary Report" (PDF)
B,_C,_K,_W_system
Semi-fictional hacking organization
American computer scientists are prominent in Episode 9 of the series. At one point in the anime, Lain is seen with code displayed on her handheld device that
Knights of the Lambda Calculus
Knights_of_the_Lambda_Calculus
Impact of English computer scientist
Good–Turing frequency estimation Turing completeness Turing degree Turing fixed-point combinator Turing Institute Turing Lecture Turing machine Turing patterns Turing
Legacy_of_Alan_Turing
Recursion without calling a function by name
function. This anonymous recursion can be produced generically via fixed-point combinators. Anonymous recursion is primarily of use in allowing recursion
Anonymous_recursion
Formal system in mathematical logic
allowed by the typing rules: it is impossible to find types for fixed-point combinators and the looping term Ω = ( λ x . x x ) ( λ x . x x )
Simply_typed_lambda_calculus
Dutch computer scientist (1945–2025)
infinitary lambda calculus, as co-author of TeReSe and for his fixed point combinator Yk = (L L L L L L L L L L L L L L L L L L L L L L L L L L) where
Jan_Willem_Klop
Templates in computer programming
the argument pack, with the expressions separated by commas. The fixed-point combinator is often implemented using variadic template arguments (note that
Variadic_template
Typed functional language
(of a term of type σ → τ to a term of type σ) λ-abstraction The Y fixed point combinator (making terms of type σ out of terms of type σ → σ) The successor
Programming Computable Functions
Programming_Computable_Functions
Branch of mathematics relating to posets
this formalism, one can obtain so-called fixed-point combinators (the best-known of which is the Y combinator); these, by definition, have the property
Domain_theory
Globalization meta-process
(p\ K))} The Y-Combinator calls its parameter (function) repeatedly on itself. The value is defined if the function has a fixed point. But the function
Lambda_lifting
Provability logic
1955. Neel, Krishnaswami (9 May 2016). "Löb's theorem is (almost) the Y combinator". Semantic Domain. Retrieved 9 April 2024. Smullyan 1986. Lindström 2006
Löb's_theorem
Organization that invests in startups
get a company to demo day, from which point the startup is on its own. The first seed accelerator was Y Combinator, started in Cambridge, Massachusetts
Startup_accelerator
Simple blogging platform
package, and custom themes. It was based in San Francisco and funded by Y Combinator. Updating to Posterous was similar to other blogging platforms. Posting
Posterous
American video surveillance company
CNN. Retrieved February 22, 2025. Bort, Julie (March 13, 2025). "Y Combinator's police surveillance darling Flock Safety raises $275M at $7.5B valuation"
Flock_Safety
Web search engine and browser
October 2020). "Here's an exclusive look at the pitch deck a 23-year-old Y Combinator alum used to raise $1 million for ethical bank cards". Business Insider
Ecosia
Versions of a JavaScript standard
introduces the replaceAll method for strings; Promise.any, a promise combinator that short-circuits when an input value is fulfilled; AggregateError,
ECMAScript_version_history
Representation of data of various types in lambda calculus
where λx.λy.λz.N is abbreviated as λxyz.N, as well as the two standard combinators, I ≡ λ x . x {\displaystyle I\equiv \lambda x.x} and K ≡ λ x y . x {\displaystyle
Church_encoding
for variables in mathematical expressions by using combinators. combinatory terms See combinator. commutativity A property of binary operations where
Glossary_of_logic
Software programming optimization technique
used memoization to reduce the exponential time complexity of parser combinators, describing the result as a memoizing purely functional top-down backtracking
Memoization
Style sheet language
used for pseudo-classes. Multiple simple selectors may be joined using combinators to specify elements by location, element type, id, class, or any combination
CSS
American footwear brand
Okara, Pakistan. In 2015, the couple moved to Mountain View as part of Y Combinator's accelerator program. They were inspired by the challenges that most people
Atoms_(shoes)
High-level programming language
handlers with an asynchronous action's eventual result. JavaScript supplies combinator methods, which allow developers to combine multiple JavaScript promises
JavaScript
General-purpose programming language
Geoffroy (2015). "Nom, A Byte oriented, streaming, Zero copy, Parser Combinators Library in Rust". 2015 IEEE Security and Privacy Workshops. pp. 142–148
Rust_(programming_language)
Digital storefront company selling video games and e-books
fraction of what HIB3 made, a very small (compared to the profits of HIB3) fixed amount of money" even though, according to Zubov, "when Steel Storm was
Humble_Bundle
Cryptographic protocols for securing data in transit
of sites". The Register. Archived from the original on 2012-02-10. "Y Combinator comments on the issue". 2011-09-20. Archived from the original on 2012-03-31
Transport_Layer_Security
American launch vehicle manufacturer
Playground Global, Social Capital, Tiger Global, Tribe Capital, and Y Combinator among others. In March 2025, former Google CEO Eric Schmidt replaced Ellis
Relativity_Space
Features in Haskell programming language
scanl (+) 1 fibs Using data recursion with Haskell's predefined fixpoint combinator: fibs = fix (\xs -> 0 : 1 : zipWith (+) xs (tail xs)) -- zipWith version
Haskell_features
New company developing a novel, scalable business
Accelerator investment model was introduced by Y Combinator that combined fixed terms investment model with fixed period intense bootcamp style training program
Startup_company
WordPress. Retrieved 24 April 2014. Ludwig, Sean (8 February 2013). "Y Combinator-backed Coinbase now selling over $1M Bitcoin per month". VentureBeat.
History_of_bitcoin
Function uniquely mapping two numbers into a single number
depth. A concrete example of such a binary tree-like structure is an SK combinator calculus expression. The function P 2 ( x , y ) := 2 x ( 2 y + 1 ) − 1
Pairing_function
Homomorphism from an initial algebra into another algebra
Yung Ahn; Sheard, Tim (2011). "A hierarchy of mendler style recursion combinators: taming inductive datatypes with negative occurrences". Proceedings of
Catamorphism
Punctuation and accent mark (~, ◌̃)
Draft). CSS Working Group. 11 November 2022. 15.4. Subsequent-sibling combinator (~). Archived from the original on 22 November 2024. Retrieved 28 November
Tilde
Type of grammar for describing formal languages
expression Top-down parsing language Comparison of parser generators Parser combinator Ford, Bryan (January 2004). "Parsing Expression Grammars: A Recognition
Parsing_expression_grammar
space built upon a programming semantic allowing fixed point combinatorics, such as the Y combinator, and data types. By 1971, λ-calculus was equipped
Computable_topology
1996 video game
'Super Mario 64 was built with a system written in Lisp'". Hacker News. Y Combinator. Archived from the original on April 27, 2011. Retrieved March 8, 2022
Super_Mario_64
Data-flow programming paradigm
Retrieved 2006-07-15. Blažević, Mario (2006). "Streaming Component Combinators". Proceedings of Extreme Markup Languages. Archived from the original
Flow-based_programming
Power supply with switching regulator
Archived from the original on 16 August 2021. Retrieved 21 March 2018. "Y Combinator's Xerox Alto: restoring the legendary 1970s GUI computer". arstechnica
Switched-mode_power_supply
Failed United States bill in 2011
and innovation. Paul Graham, the founder of venture capital company Y Combinator opposed the bill, and banned all SOPA-supporting companies from their
Stop_Online_Piracy_Act
for F# with C# and VB.Net support. FsCheck No Random testing (Fuzzing) combinator library based on QuickCheck for Haskell. FsMocks No F# mock library based
List of unit testing frameworks
List_of_unit_testing_frameworks
Aircraft powered directly by electricity, with no other engine needed
agency Vinnova and is an alumnus of Silicon Valley start-up accelerator Y Combinator. In March 2021, Toulouse-based Aura Aero announced the development of
Electric_aircraft
Houston and Arash Ferdowsi in 2007, and received seed funding from Y Combinator. Izrailevsky, Yuri (February 11, 2016). "Completing the Netflix Cloud
Timeline of Amazon Web Services
Timeline_of_Amazon_Web_Services
Bentley, Kevin (16 April 2024). "Descent 3 Source Code". Hacker News. Y Combinator. Archived from the original on 16 April 2024. Retrieved 16 April 2024
List of commercial video games with later released source code
List_of_commercial_video_games_with_later_released_source_code
Houston and Arash Ferdowsi in 2007, and received seed funding from Y Combinator. David Shaw. "Paperkey - an OpenPGP key archiver". Retrieved December
Timeline of digital preservation
Timeline_of_digital_preservation
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