[HN Gopher] Lambda Calculus - Animated Beta Reduction of Lambda ...
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       Lambda Calculus - Animated Beta Reduction of Lambda Diagrams
        
       Author : perryprog
       Score  : 135 points
       Date   : 2025-11-24 05:17 UTC (17 hours ago)
        
 (HTM) web link (cruzgodar.com)
 (TXT) w3m dump (cruzgodar.com)
        
       | __grob wrote:
       | This is sick, loved the 2swap video on this. Happy to see more
       | content visualizing lambda calculus and Tromp lambda diagrams.
        
       | ggm wrote:
       | The number of reduction steps in division.
        
       | Vosporos wrote:
       | Cheers, I love it!
        
       | tromp wrote:
       | You can enter (ln.n(lc.la.lb.cb(lf.lx.f(afx)))Fn0)7 to compute
       | the function Col' from [1] to 7, resulting in (3*7+1)/2 = 11.
       | Unfortunately, this visualization is much less insightful than
       | showing the 7 successive succ&swap operations:
       | 7  0          0  8          8  1          1  9          9  2
       | 2 10         10  3          3 11
       | 
       | [1] https://news.ycombinator.com/item?id=46022965
        
       | killerstorm wrote:
       | There's a model of computation called 'interaction nets' /
       | 'interaction calculus', which reduces in a more physically-
       | meaningful, local, topologically-smooth way.
       | 
       | I.e. you can see from these animations that LC reductions have
       | some "jumping" parts. And that does reflect LC nature, as a
       | reduction 'updates' many places at once.
       | 
       | IN basically fixes this problem. And this locality can enable
       | parallelism. And there's an easy way to translate LC to IN, as
       | far as I understand.
       | 
       | I'm a noob, but I feel like INs are severely under-rated. I dunno
       | if there's any good interaction net animations. I know only one
       | person who's doing some serious R&D with interaction nets -
       | that's Victor Taelin.
        
         | hmokiguess wrote:
         | Speaking of Victor Taelin, what's the latest on
         | https://higherorderco.com/ ? His work is really inspiring and
         | amazing
        
         | tromp wrote:
         | > there's an easy way to translate LC to IN
         | 
         | While easy, it sadly doesn't preserve semantics. Specifically,
         | when you duplicate a term that ends up duplicating itself,
         | results will diverge.
         | 
         | There exist more involved semantics preserving translations,
         | using so-called croissants and brackets, or with the recent
         | rephrased approach of [1].
         | 
         | [1] https://arxiv.org/abs/2505.20314
        
       | dloss wrote:
       | Some more example programs in Lambda Calculus here, including a
       | compliant brainf#*k interpreter: https://justine.lol/lambda/
        
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       (page generated 2025-11-24 23:01 UTC)