For those of us who don't know what a Y-Combinator is or why it's useful, I found a SO answer [1] that makes sense to me:
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. The benefit of not needing a
compile-time name for the recursive function is
sort of a bonus. =)
I've use something very similar in practice. Haskell's fixed point operator is:
fix f = let x = f x in x
This allows you to turn a non-recursive function into a recursive one, it factors the recursion out. It turns out that you can write a similar combinator (usually called mfix or memofix as I recall) that will result in a memoized version of the same recursive function.
So it allows you to abstract away the memoization, write it once and then use it on any recursive function. That way you can write quite natural recursive functions and just memoize them in one wrapper call.
I used this in competitive programming for a while, it was nice for certain types of dynamic programming problems where the interesting part is the recursive definition, so once I found that there wasn't any more to write. Quite satisfying when it applied.
Functional programming: Making you feel clever by allowing you to solve problems that nobody else even knew existed, in order to let you do what everyone else could do from the start.
I’m not sure about it actually being used in compilers. However as I understand it the simply typed lambda calculus does not support recursive functions. If you want a typed functional language you have to introduce as a primitive a recursive combinatory like fix or the Y combinator.
Useful when you have a lambda that needs to call itself, but the language doesn't bind the name until after the lambda is parsed (so you can't call by name). This happens in a few languages I think, C++ and C# for sure.
I’ve used it for recursion in anonymous functions in C#. It is straightforward enough to implement. Was it the best choice? Probably not, but I took the opportunity when presented.
I’ve used it in a semi professional way (internal tooling in clojure). I’ve also written about it here (Practical applications of the ycombinator in clojure) [1].
There was a good practical ruby example for auto-vivification of hashes using the applicative ycombinator many years back, but I'm having trouble finding it.
Nope, but I felt good when I finally managed to write one from scratch, because I knew for sure there was a time when I couldn't. So maybe the same would happen for you too.
This SO answer is posted every time this topic comes up, so I've seen it many times (and, in fact, I provided one of the answers there, too) and it's still the one and only place I've ever seen "functional" used as a noun like that. I'm always tempted to edit it, but maybe I'm missing something?
