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In order to learn what a fixed-point combinator is and is used for, I wrote my own. But instead of writing it with strictly anonymous functions, like Wikipedia's example, I just used define:
(define combine (lambda (functional)
(functional (lambda args (apply (combine functional) args))))
I've tested this with functionals for factorial and fibonacci, and it seems to work. Does this meet the formal definition of a fixed-point combinator?
925
The Y combinator is a formula which lets you implement recursion in a situation where functions can't have names but can be passed around as arguments, used as return values, and defined within other functions. It works by passing the function to itself as an argument, so it can call itself.
Basically, it's this: The Y combinator allows us to define recursive functions in computer languages that do not have built-in support for recursive functions, but that do support first-class functions. That's it.
The Y combinator is a central concept in lambda calculus, which is the formal foundation of functional languages. Y allows one to define recursive functions without using self-referential definitions.
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)))))
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