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.
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.
Extensive discussion (202 comments) about 15 months ago: https://news.ycombinator.com/item?id=42373437
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/
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.
That makes me think of the Inca's quipus.
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.