Tree Calculus

#1

Post by tosh » Fri, Apr 03, 2026, 9:42 AM UTC

Re: Tree Calculus

#2

Post by timcobb » Thu, Apr 09, 2026, 12:34 PM UTC

I'm not used to math things being promoted like this (not to suggest that's a bad thing at all!). Can someone offer some context please.

Re: Tree Calculus

#3

Post by henearkr » Thu, Apr 09, 2026, 12:43 PM UTC

That makes me think of the Inca's quipus.

Re: Tree Calculus

#4

Post by macintux » Thu, Apr 09, 2026, 12:45 PM UTC

Extensive discussion (202 comments) about 15 months ago: https://news.ycombinator.com/item?id=42373437

Re: Tree Calculus

#5

Post by eitally » Thu, Apr 09, 2026, 12:48 PM UTC

Much better intro article about tree calculus here, vs the actual site: https://olydis.medium.com/a-visual-introduction-to-tree-calc...

Re: Tree Calculus

#6

Post by macintux » Thu, Apr 09, 2026, 12:49 PM UTC

eitally wrote: post #5

Much better intro article about tree calculus here, vs the actual site: https://olydis.medium.com/a-visual-introduction-to-tree-calc...

Another resource I found in HN discussions: https://latypoff.com/tree-calculus-visualized/

Re: Tree Calculus

#7

Post by [deleted] » Thu, Apr 09, 2026, 12:53 PM UTC

[deleted]

Re: Tree Calculus

#8

Post by tripplyons » Thu, Apr 09, 2026, 1:15 PM UTC

The reduction rules seem kind of arbitrary to me. At that point why don't you just use combinators instead of defining a set of 5 ways their operator can be used?

Re: Tree Calculus

#9

Post by seanhunter » Thu, Apr 09, 2026, 1:31 PM UTC

timcobb wrote: post #2

I'm not used to math things being promoted like this (not to suggest that's a bad thing at all!). Can someone offer some context please.

This isn't a math thing[1], it's a theoretical computing model (ie instead of a Turing machine or lambda calculus, you can use this instead) that you might study as part of studying computation theory or other bits of theoretical computer science.

[1] or not pure maths anyway. It's applied maths like all computer science.

Re: Tree Calculus

#10

Post by olydis » Thu, Apr 09, 2026, 1:51 PM UTC

tripplyons wrote: post #8

The reduction rules seem kind of arbitrary to me. At that point why don't you just use combinators instead of defining a set of 5 ways their operator can be used?

A good point! From the “visual introduction” post mentioned elsewhere: Rules 1 and 2 seem arbitrary […], but behave analogous to the K and S operators of combinatory logic, which is sufficient to bootstrap λ-calculus. Rules 3a-c “triage” what happens next based on whether the argument tree is a leaf, stem or fork. This allows writing reflective programs.

See Barry’s post https://github.com/barry-jay-personal/blog/blob/main/2024-12... for more discussion.