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Also of note, Y combinator has a short expression in this system, as Y = BU(CBU) = BU(BWB) = B(W(WK))(BWB), where U = WI = SII is the self-application combinator. Using just two combinators, B and W, an infinite number of fixpoint combinators can be constructed, [2] one example being B(WW)(BW(BBB)), discovered by R. Statman in ...
The simplest example of a combinator is I, the identity combinator, defined by (I x) = x. for all terms x. Another simple combinator is K, which manufactures constant functions: (K x) is the function which, for any argument, returns x, so we say ((K x) y) = x. for all terms x and y. Or, following the convention for multiple application, (K x y) = x
Y Combinator, LLC (YC) is an American technology startup accelerator and venture capital firm launched in March 2005 [1] which has been used to launch more than 4,000 companies. [2] The accelerator program started in Boston and Mountain View , expanded to San Francisco in 2019, and was entirely online during the COVID-19 pandemic. [ 3 ]
The Y combinator may also be used in implementing Curry's paradox. The heart of Curry's paradox is that untyped lambda calculus is unsound as a deductive system, and the Y combinator demonstrates this by allowing an anonymous expression to represent zero, or even many values. This is inconsistent in mathematical logic.
The application process is open to anyone but highly competitive. For instance, Y Combinator and TechStars have application acceptance rates between 1% and 3%. Seed investment in startups may be made, in exchange for equity. Typically, the investment is between US$20,000 to US$50,000 in the US, or £10,000 to £50,000 in Europe. [3]
Y Combinator—the startup incubator that helped launch DoorDash, Airbnb, Reddit, and Instacart—is backing a weapons maker for the first time, betting that it could shake up the defense industry ...
In the lambda calculus, which only uses functions of a single variable, this can be done via the Y combinator. First make the higher-order function of two variables be a function of a single variable, which directly returns a function, by currying:
The positive impact alternative meat products -- like plant-based meat or cultivated meat -- can have on the environment is striking. The Good Food Institute (GFI) estimates that alternative meat ...