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Jul 16, 2011 · A Y-combinator is a "functional" (a function that operates on other functions) that enables recursion, when you can't refer to the function from within itself. In computer-science theory, it generalizes recursion, abstracting its implementation, and thereby separating it from the actual work of the function in question.
Aug 5, 2015 · To do this, I thought of using the Lambda Calculus' Y combinator. Here's the first definition: Y = λf.(λx.f(x x))(λx.f(x x)) Here's the reduced definition: Y g = g(Y g) I attempted to write them in C# like this: // Original. Lambda Y = f => (new Lambda(x => f(x(x)))(new Lambda(x => f(x(x))))); // Reduced.
May 18, 2011 · EDIT: While chessweb or anyone else corroborates his answer, temporarily consider his answer correct and this one wrong. It seems the answer is yes. Apparently the exact same combinator appears here, midway down the page: (define Y. (lambda (f) (f (lambda (x) ((Y f) x))))) edited May 18, 2011 at 8:38. answered Jan 14, 2011 at 1:41.
Jun 19, 2023 · Questions tagged [y-combinator] The Y combinator is a higher-order function that allows a function that does not know its own name to call itself. It is the fundamental basis of recursion. Learn more…. Top users. Synonyms. Stack Overflow. Questions. Help.
Nov 29, 2011 · Thankfully the fathers of computing solved this problem ages ago by discovering Fixed-Point Combinators, with the most popular being the Y Combinator. I've made various attempts to get a Y combinator set up, but they can't get past the compiler.
fix2 is a y-combinator (specifically, it is a combinator for functions with two arguments; the first argument is the function (for the purpose of recursion), the second argument is a "proper" function argument). It creates recursive functions. bll::ret(...) appears to create some form of a function object, the body of which is
Nov 25, 2010 · The Y combinator can't be typed using Hindley-Milner types, the polymorphic lambda calculus on which Haskell's type system is based. You can prove this by appeal to the rules of the type system. I don't know if it's possible to type the Y combinator by giving it a higher-rank type. It would surprise me, but I don't have a proof that it's not ...
I've recently come across this proposal that wants to add a Y Combinator to the Standard Library, and after reading it, it seems extremely similar to what I am doing here. Unfortunately, the concept of the Y Combinator still doesn't "click" for me - I am missing something and I cannot visualize how to generalize what I did with the self parameter for any function, avoiding the step boilerplate.
Jun 19, 2022 · 1. I found a implementation of Y-Combinator which supports Fn. However I want to have a version of FnMut. However, FnMut can not be wrapped into Rc, so I wrap them in Rc<RefCell>. The following code can make a[i] = i in a recursive way. It is the simplest code I have found to test if we can call itself inside a closure. move |i| {. if i < n ...
Jun 14, 2012 · The existence of a Y combinator in JavaScript should imply that every JavaScript function has a fixed point (since for every function g, Y(g) and g(Y(g)) should be equal). However, it isn't hard to come up with functions without fixed points that violate Y(g) = g(Y(g)) (see here). Even certain functionals do not have fixed points (see here).
