21–29 of 29 posts
λf.(λx.f (x x)) (λx.f (x x))
for which the difference with
λf.(λx.f (x x)) (λx.f (x x) f)
is very clear, whereas with Δ-nets the difference is more subtle. I guess it is because the visualization has more information than with the λ-calculus.
What is this about? A pointer to a tutorial or a wiki link would be nice for someone who has no idea what this is. Thank you
What is this about? A pointer to a tutorial or a wiki link would be nice for someone who has no idea what this is. Thank you
Earlier quoted context omitted.
> 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.
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/…
Which makes the sloppy use of "λ-Reduction" in place of "β-reduction"--the only form of reduction or conversion applied here--even less defensible. Maybe them being non-native English speakers is partly to blame?
Earlier quoted context omitted.
HN Guidelines: "Don't be curmudgeonly. Thoughtful criticism is fine, but please don't be rigidly or generically negative."
I'm not being "generically" negative, I'm being very specifically negative. We have a paper from someone not working in the field, with no affiliation, and with an abstract that claims to "solve the longstanding enigma with groundbreaking clarity", a sentence never before uttered by a human being in flesh and blood, and that feels like it takes 4 (four) citations to justify that lambda calculus is Turing-complete, a…
What is this about? A pointer to a tutorial or a wiki link would be nice for someone who has no idea what this is. Thank you
The lambda calculus is an alternate model of computation created by Alonzo Church in the 1930s. It's basically a restricted programming language where the only things you can do are define anonymous functions, and apply those anonymous functions to input variables or the output of other functions.
The Lambda calculus statement And = λp.λq.p q p is more conventionally notated as And(p, q) = p(q(p)).
You can reduce lambda expressions -- basically, this is "Simplifying this program as far as possible" what you expect a good optimizing compiler to do.
When there are multiple possible simplifications, which one should you pick? This is a complicated problem people basically solved years ago, but the solutions are also complicated and have a lot of moving parts. OP came up with a graph-based system called ∆-Nets that is less complicated and more clearly explained than the older solutions. ∆-Nets is a lot easier for people to understand and implement, so it might have practical applications making better performance and tooling for lambda-calculus-based programming languages. Which might in turn have practical benefits for areas where those languages are used (e.g. compilers).
The linked simulation lets you write a lambda calculus program, see what it looks like as a ∆-Net graph, and click to simplify the graph.
It's only tangentially related to OP, but YouTube channel 2swap recently had an interesting video about lambda calculus that you don't have to be an expert to enjoy: https://www.youtube.com/watch?v=RcVA8Nj6HEo
What the hell is this? The linked paper: https://arxiv.org/pdf/2505.20314 claims the squiggles they introduce are apparently a model to solve Levy-optimal parallel reduction of lambda terms. But the author has no affiliation, it's very weird they're calling this "lambda-reduction" and it heavily smells of AI slop? I hope I'm wrong but it doesn't look right. Can anyone with expertise in this field chime in?
The author, Daniel Augusto Rizzi Salvadori' and Github user, ' https://github.com/danaugrs ' align. Couldn't comment on the actual content, though.
Please see my comment here: https://news.ycombinator.com/item?id=46069564