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      • Applied to a function with one variable, the Y combinator usually does not terminate. More interesting results are obtained by applying the Y combinator to functions of two or more variables. The additional variables may be used as a counter, or index. The resulting function behaves like a while or a for loop in an imperative language.
      en.wikipedia.org › wiki › Fixed-point_combinator
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  3. Oct 15, 2019 · def fact(x): if x == 0: return 1 else: return fact(x - 1) * x. To see how it works, consider that fact(3) computes fact(2) * 3 which is fact(1) * 2 * 3 == fact(0) * 1 * 2 * 3 == 1 * 1 * 2 * 3 == 6. For brevity, we’ll write it in a style that’s a bit more functional: def fact(x): return 1 if x == 0 else fact(x - 1) * x.

  4. Aug 22, 2022 · Y Combinator. The Y Combinator can take a non-recursive function like fact_nr and convert it to a true recursive version. Here is the Y Combinator definition in the form usually found in literature. def Y(fn_nr): return (lambda x: fn_nr(lambda y: x(x)(y)))(lambda x: fn_nr(lambda y: x(x)(y))) or in a simpler form

  5. Jul 16, 2011 · Y-combinator is a fixed-point combinator. Fixed point of a function is an element of the function's domain that is mapped to itself by the function. That is to say, c is a fixed point of the function f(x) if f(c) = c. This means f(f(...f(c)...)) = fn(c) = c.

    Code sample

    public static Func<T, TResult> Y<T, TResult>(Func<Func<T, TResult>, Func<T, TResult>> F) {
      return
      t =>
      F(
      Y(F)...
  6. Nov 22, 2018 · What is Y-combinator⌗ In terms of the functional programming field, Y-combinator is expressed on the lambda calculus format: λf. (λx. (f (x x))) (λx. (f (x x))). With Y-combinator, we can implement recursion without defining functions explicitly. As you may know, recursion is equivalent to iteration, thus we can assure that lambda calculus ...

  7. Mar 15, 2024 · Y Combinator (YC) is a name that resonates across the startup ecosystem, known for being a catalyst that propels small startups into global powerhouses. Serving as a launchpad for companies like Airbnb, Dropbox, Stripe, and Reddit, Y Combinator has become synonymous with innovation, networking, and success in the startup world.

  8. Some useful ones are twice(f) = \x -> f(f(x)), flip(op)-> \x y -> y op x, (.) as in (f.g) x = f(g(x)), ($) can help with map(called <$> in infix) as in ($5) <$> [(+1), (*2)] = [6, 10], curry can be used in Lisp/Python/JavaScript for partial application, and uncurry can be used for functions that require records(tuples) in Haskell.

  9. Jul 15, 2017 · Follow. 7 min read. ·. Jul 15, 2017. 36. The Y-combinator is a function that lets us do something neat: it allows us to encapsulate recursion in functions. This article shows how this...

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