Combinators

Could somebody provide a bit of context on what exactly this is? It seems interesting, but I have no idea what I am looking at.

The notation used seems rather confusing, not even showing the list of arguments. For example, the argument swapping combinator C which is normally defined as

    C f x y = f y x

    C f x y = y `f` x

(Show HN?) There is a deep and lovely connection between the Y-combinator and the classic version of Godel's incompleteness theorem: https://gregfjohnson.com/incompleteness/

I wish universal and eternal patterns like this were studied more often in software engineering. Perhaps we would have a chance in hell of finding canonical representations of common structures and even programs instead of basket weaving majors fucking reinventing the wheel every 5 minutes with yet another half-baked poorly understood Python or JavaScript instantiation of a common pattern. Imagine still writing for loops and munging indices instead of expressing things in terms of higher order functions like folds or maps...

Eh, I don't need to imagine; we're still stuck at that same level of infantilism. Instead of actually graduating to higher order atoms and primitives of thought though, we can just have the AI slop out another 100k LOC. Then the system will have so much incidental complexity that it becomes impossible to distill out its essence, because there no longer is one.

The logical combinators that I know all have definitions in the untyped lambda calculus. Is there a typed variant of logical combinators?

Does anyone have a grasp of how this relates to interaction nets?

A bit of an aside: I wonder how much array-oriented languages like APL and J would benefit from being implemented on top of an interaction net machine?

omega and y are missing buddy! I was so looking forward to having them represented in APL

The y-combinator is widely regarded as the best combinator :)