This link below gives a better description of it, along with the definitions of the reduction rules. (which I got from further down in this thread)

But what I believe was meant by the above was: "delta E1 E1" creates a new "reduction tree" (my own made up term) with E1 being the left child of this new root node, and E2 being the right child of this new root node - and which then begins applying the reduction on this newly constructed tree.

https://olydis.medium.com/a-visual-introduction-to-tree-calc...

Overall the concept seems pretty interesting - and it's nice to see someone come up with something both novel in the space and at the same time seemly "applicable".

@dang, pleaaase can we get proper markdown formatting on HN? I tried adding two spaces after each line, but I don't want paragraphs between code

    > f = λa λb concat ["Hello ", a, " ", b, "!"] 
    > f "Jane" "Doe" 
    Hello Jane Doe!

    > g = f "Admiral" 
    > invert g "Hello Admiral Alice!" 
    Alice

This is indeed much better. I couldn't really follow the original, but this one made it click. Pretty cool!

I feel like neither of these just give actual formal definitions, which would be much clearer.

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

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.

Tangential, but I read his New Kind of Science book. It's an interesting book, but I found the first chapter to be pretty amusing.

The first chapter is so completely self-aggrandizing about how this book will change your life and the world and the entirety of science and mathematics and you should feel lucky for reading it.

The cellular automata stuff is pretty cool, but I don't feel like it lived up to the hype of the first chapter.

A lambda calculus variant Quite niche, so people who read about it know what a calculus is

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.

I think it might be a bad thing. I'm no stranger to math or computer science, but even after staring at the front page for a minute I was ready to dismiss this as the ravings of a lunatic.

It's like they had the idea of marketing this like a software project, not realizing that most front pages of software projects are utter bunk as well. It introduces terminology and syntax with no motivation or explanation.

Even once trying to get into "Quick Start" and "Specification" I was still mystified as to what it is or why I should want to play with it, or care. I had to go to the link mentioned upthread to get any sense of what this was or how it worked.

I think it's just badly written.

That being said, what seems to be proposed is a structure and calculus that are an alternative to lambda-calculus. The structures, as you can probably guess from the picture, are binary trees, ostensibly unlabeled except that there is significance to the ordering of the children. The calculus appears to be rules about how trees can be "reduced", and there is where the analogy to lambda calculus comes in.

Hopefully someone who actually knows this stuff can see whether I managed to get all that right – because I promise you, none of that understanding came from the website.