combinator

combinator

(theory)
A function with no free variables. A term is either a constant, a variable or of the form A B denoting the application of term A (a function of one argument) to term B. Juxtaposition associates to the left in the absence of parentheses. All combinators can be defined from two basic combinators - S and K. These two and a third, I, are defined thus:

S f g x = f x (g x) K x y = x I x = x = S K K x

There is a simple translation between combinatory logic and lambda-calculus. The size of equivalent expressions in the two languages are of the same order.

Other combinators were added by David Turner in 1979 when he used combinators to implement SASL:

B f g x = f (g x) C f g x = f x g S' c f g x = c (f x) (g x) B* c f g x = c (f (g x)) C' c f g x = c (f x) g

See fixed point combinator, curried function, supercombinators.
References in periodicals archive ?
Billionaire Sam Altman, 32, boss of start-up funding firm Y Combinator, wants to have his brain embalmed so it can later be simulated by a company called Nectome.
The biggest deals of last year involved Grammarly ($110 million from General Catalyst, IVP, and Spark Capital); BitFury ($30 million from Credit China Fintech Holdings); Petcube ($10 million from Almaz Capital, Y Combinator, AVentures Capital, U.
Launched in June 2016, the program aims to encourage Taipei's startups to get enrolled in incubators and seed accelerators located in foreign countries, such as 500 Startups, StartX, Techstars, and Y Combinator, and to participate in international entrepreneurial events, such as TECH IN ASIA, Disrupt, Web Summit, and Slush, so as to gain access to more resources that will help them grow and flourish, according to the DED.
Based in San Francisco, NuCypher, a Y Combinator alumnus, is a security and encryption platform for distributed systems including blockchain, Big Data, cloud and the Internet-of-Things.
The company was incubated by Y Combinator and has raised more than USD 17 million in funding from Union Square Ventures, Upfront Ventures, Hearst Ventures, Pritzker Group, Accel Partners, SV Angel and DJI.
They join existing investors Y Combinator, Uncork Capital, SV Angel, CrunchFund, Slow Ventures, Susa Ventures, FundersClub, Paul Buchheit (creator of Gmail), Justin Kan (co-founder of Twitch), Michael Siebel (co-founder of Twitch), Jared Friedman (co-founder of Scribd), Jacob Gibson (co-founder of Nerdwallet), Greg Brockman (former CTO of Stripe), and Joe Montana (Hall of Fame quarterback).
General Motors Ventures and ExxonMobil led Yoshi's Series A round of funding, with Y Combinator, Kevin Durant & Rich Kleiman (The Durant Company), Arab Angel and others also participating.
Tyson Ventures joins a strong group of investors including Origin Ventures, the Pritzker Group, startup incubator Y Combinator, Morningstar Inc.
BUSINESS accelerator Y Combinator is known for making intriguing and often wise investment decisions.
SendBird, a global provider of chat API and messaging SDK for in-app chat and messaging, raised USD 16 million during its Series A led by Shasta Ventures and August Capital with participation from existing investors at Y Combinator and FundersClub, the company said.
After getting a boost of USD 120k from American seed accelerator, Y Combinator, earlier in September, the start-up is expanding its offerings and looking to create a niche in the motorbike rental market.