alt Hacker News> it's very weird they're calling this "lambda-reduction"
That was my reaction as well, only ever having heard of β-reduction, α-conversion (to prevent variable collisions), and η-reduction (the logical equivalence of a β-redex of a term and a bound variable with the term itself, provided the variable does not occur free in said term). Sloppy use of nomenclature is absolutely a red flag.
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Yes.
To be transparent: I don't understand this stuff all that well and it's entirely possible I'm missing something, but everything here is weird AF.
- Who is the author? Why he has no affiliation?
- What is the main result of the paper? How does it improve on the state of the art? Even for stuff that's way beyond my pay grade, I can usually tell from the abstract. I'm completely baffled here.
- Why do they introduce graphical notation without corresponding formal definitions?
- Why is it written in this weird style where theorems are left implicit? Usually, there's at least a sketch of proof.
- Why does it not address that the thing they're claiming to do isn't elementary recursive as per https://doi.org/10.1006/inco.2001.2869?
Again, it's entirely possible that it's a skill issue on my part and I'd love to be corrected, but I'm completely baffled and I still have absolutely no idea of what I'm looking at. Am I the stupid one and it's obvious to everyone else?
The annihilating interaction between abstraction and application nodes is well-known in the area of interaction net research to ~correspond to β-reduction, as is also explained in the associated research paper [1].
α-conversion is not required in interaction nets. η-reduction is an additional rule not typically discussed, but see for example [2].
[1] https://arxiv.org/pdf/2505.20314
[2] https://www.sciencedirect.com/science/article/pii/S030439750...