[HN Gopher] Interactive l-Reduction
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       Interactive l-Reduction
        
       Author : jy14898
       Score  : 110 points
       Date   : 2025-11-24 20:48 UTC (3 days ago)
        
 (HTM) web link (deltanets.org)
 (TXT) w3m dump (deltanets.org)
        
       | qsort wrote:
       | 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?
        
         | papes_ wrote:
         | The author, Daniel Augusto Rizzi Salvadori' and Github user,
         | 'https://github.com/danaugrs' align. Couldn't comment on the
         | actual content, though.
        
           | forgotpwd16 wrote:
           | Affiliation they mean with an institute/company funding their
           | research/work. It's quite rare, if it ever happens, for
           | someone to find an innovative algorithm, let alone write a
           | technical paper, as hobbyist.
        
             | psychoslave wrote:
             | What a strange expectation. Obviously humans didn't wait
             | these institutions to create ideas and notations. The fact
             | that these institutions now exist don't make individual
             | with own desire to express novel idea disappear. All the
             | more when these institutions with their elitist mindset
             | will actively reject whatever is going too much of the
             | rails of their own social bubbles.
        
         | arethuza wrote:
         | HN Guidelines: _" Don't be curmudgeonly. Thoughtful criticism
         | is fine, but please don't be rigidly or generically negative."_
        
           | qsort wrote:
           | 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 fact
           | that's well-known to every undergraduate student.
           | 
           | I'm sorry if this gives reviewer #2 vibes, but this doesn't
           | look right to me and I'm asking if someone with actual
           | expertise in the field can clarify what's happening.
        
             | koolala wrote:
             | The AI slop statement is harsh. The website looks nice.
        
         | mrkeen wrote:
         | The interactive lambda-calculus interpreter looks like it does
         | the right thing, not that I've tried to push it too hard.
         | 
         | Can't comment on the delta-nets. If you're looking for a real
         | person who's been plugging away at parallel & optimal reduction
         | of lambda terms, this is where to look:
         | https://github.com/VictorTaelin
         | 
         | I don't think "lambda-reduction" is a red flag. The "real" term
         | would be "beta-reduction" (but that's the incumbent algorithm
         | which TFA claims to replace or improve on - so why not give it
         | a new name?)
         | 
         | But if I were to go sniffing for red flags:
         | 
         | From the first commit:
         | 
         | lambdacalc.ts: // The original lambda calculus introduced by
         | Church was the 'relevant' lambda calculus which doesn't allow
         | for weakening/erasure. This is why I add the '+' below to
         | indicate that the lambda calculus started at 1936 but was
         | extended afterwards.
         | 
         | What?
         | 
         | util.ts: Why is this full of Gaussian Elimination of Matrices?
         | The paper doesn't mention it
        
           | koolala wrote:
           | Weak vs. "strong" lambda calculus maybe? Typed vs untyped?
        
         | anonnon wrote:
         | > it's very weird they're calling this "lambda-reduction"
         | 
         | That was my reaction as well, only ever having heard of
         | b-reduction, a-conversion (to prevent variable collisions), and
         | e-reduction (the logical equivalence of a b-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.
        
           | marvinborner wrote:
           | The annihilating interaction between abstraction and
           | application nodes is well-known in the area of interaction
           | net research to ~correspond to b-reduction, as is also
           | explained in the associated research paper [1].
           | 
           | a-conversion is not required in interaction nets. e-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/S030439
           | 750...
        
           | qsort wrote:
           | 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?
        
             | etiamz wrote:
             | Note that, in the interaction net literature, it is pretty
             | common to introduce graphical notation without
             | corresponding textual counterparts. See the works of
             | Lafont, Lamping, Asperti, Guerrini, and many others [1].
             | (However, the textual calculus can be absolutely crucial
             | for formal proof.)
             | 
             | The absence of proofs and benchmarks undermines the paper
             | for me as well. I find it absolutely critical to
             | demonstrate how the approach works in comparison with
             | already established software, such as BOHM [2].
             | 
             | Parallel beta reduction not being elementarily recursive is
             | not a thing to address, nor a thing one can address.
             | Lamping's abstract algorithm already performs the minimal
             | amount of work to reduce a term -- one cannot improve it
             | further.
             | 
             | From my understanding, the paper aims to optimize the
             | bookkeeping overhead present in earlier implementations of
             | optimal reduction. However, as I said, the absence of
             | formal/empirical evidence of correctness and extensive
             | benchmarks makes the contributions of the paper debatable.
             | 
             | [1] https://github.com/etiamz/interaction-net-resources
             | 
             | [2] https://github.com/asperti/BOHM1.1
        
         | danaugrs wrote:
         | Author here. Other experts in this field have also used the
         | term "lambda reduction", including Levy himself [1] and Lamping
         | [2], both which are referenced in the Delta-Nets paper.
         | "Lambda-reduction" is clearly an abbreviation of Lambda-calculi
         | reduction.
         | 
         | [1] https://dl.acm.org/doi/abs/10.1145/143165.143172
         | 
         | [2] https://dl.acm.org/doi/pdf/10.1145/96709.96711
        
       | asgr wrote:
       | reminds me of https://github.com/HigherOrderCO/HVM
       | 
       | I see Salvatore has a fork, so they are obviously aware of it.
       | unsure whether theyre proposing the exact same thing without
       | reference or citation...
        
         | marvinborner wrote:
         | This is quite different. Salvadori's work aims for optimal
         | reduction of the full lambda calculus (which requires something
         | called "bookkeeping"/"oracle"), while HOC works on
         | optimal/parallel reduction of a certain subset of the lambda
         | calculus.
         | 
         | Both approaches have been researched for a long time now, where
         | HOC's subset is typically referred to as "abstract algorithm".
         | For example, a version of the lambdas calculus where any
         | variable can be used at most once (the "affine lambda
         | calculus"), can be reduced optimally with interaction nets
         | without requiring any bookkeeping.
         | 
         | The novel thing about Salvadori's work is that it develops a
         | new (and better explained) bookkeeping mechanism.
        
       | tromp wrote:
       | I linked to the paper in a recent comment [1]. The author has
       | been active in the Higher Order Community Discord channel for
       | quite a while. The Higher Order Company [2] is developing HVM
       | (Higher Order Virtual Machine), a high performance implementation
       | of interaction nets for both CPUs and GPUs, and started the
       | channel to discuss development and related topics, such as the
       | Bend language for programming the HVM, discussed on HN at [3].
       | 
       | The paper manages to present previous work on Levy's optimal beta
       | reduction in a more streamlined fashion, generalizing duplicators
       | to so-called replicators that avoid the need for separate book-
       | keeping gadgets (like croissants and brackets) . Its author also
       | proves himself to be a skilled programmer in bringing his theory
       | to life with this web based evaluator.
       | 
       | The app contrasts traditional graph-based l-calculus reduction
       | (which replaces nodes with entire subgraphs) with interaction
       | (which makes only local modifications and hence needs more
       | steps), while showing that semantics is preserved.
       | 
       | [1] https://news.ycombinator.com/item?id=46034355
       | 
       | [2] https://higherorderco.com/
       | 
       | [3] https://news.ycombinator.com/item?id=40390287
        
       | danaugrs wrote:
       | Author here. Thanks for posting.
       | 
       | I spent several years' worth of weekends working on this, and I'm
       | glad to see it here on Hacker News.
       | 
       | I started working on this problem when I learned about Lamping's
       | algorithm for optimal lambda reduction [1]. He invented a
       | beautiful algorithm (often referred to as his "abstract
       | algorithm"), which uses fan-in and fan-out nodes to reduce lambda
       | terms optimally (with optimal sharing). Unfortunately, in order
       | to make it fully work, some fans needed to duplicate one another
       | while others needed to cancel one another. To determine this
       | correctly Lamping had to extend his abstract algorithm with
       | several delimiter node types and many additional graph reduction
       | rules. These delimiter nodes perform "bookkeeping", making sure
       | the right fan nodes match. I was dissatisfied with the need for
       | these additional nodes and rules. There had to be a better way.
       | 
       | My goal was to try to implement Lamping's abstract algorithm
       | without adding any delimiter nodes, and to do it under the
       | interaction net paradigm to ensure perfect confluence. I tried
       | countless solutions, and finally Delta-Nets was born. Feel free
       | to ask any questions.
       | 
       | I recently started building a programming language on top of
       | Delta-Nets, called Pur (https://pur.dev/).
       | 
       | Feel free to follow along this journey:
       | 
       | https://x.com/danaugrs
       | 
       | https://x.com/purlanguage
       | 
       | [1] https://dl.acm.org/doi/pdf/10.1145/96709.96711
        
       | xjm wrote:
       | I find it much easier to see what is going on when selecting
       | l-calculus instead of D-Nets. E.g. for the mandatory _Y
       | Combinator_ ,
       | 
       | lf.(lx.f (x x)) (lx.f (x x))
       | 
       | for which the difference with
       | 
       | lf.(lx.f (x x)) (lx.f (x x) f)
       | 
       | is very clear, whereas with D-nets the difference is more subtle.
       | I guess it is because the visualization has more information than
       | with the l-calculus.
        
       | fnord77 wrote:
       | 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
        
         | refulgentis wrote:
         | Cosign, 10 hours in and comments are exclusively people who
         | seemingly know each other already riffing _on top_ of something
         | that 's not clear to an audience outside the community, or
         | replying to a coarser version of request with ~0 information.
         | (some tells: referring to other people by first name; having a
         | 1:1 discussion about the meaning of a fork by some other
         | person)
        
         | layer8 wrote:
         | It's about term reduction in lambda calculus:
         | https://en.wikipedia.org/wiki/Lambda_calculus#Reduction_stra...
        
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