Yon – a topos-oriented language with a content-addressed lattice heap (yon-lang.org)

Your audience, or whoever you aim your work at, should be treated with respect. Otherwise, why should they give you the time of day? Why would you expect them to respond positively to effort alone when effort (in code and in shit prose) is extremely cheap right now? Their time is not cheap ...

When I read the documentation, and it is extremely clear that you haven't taken the time to clarify your ideas, when much of it is LLM prose, when much of the content introduces highfalutin ideas without motivation, blending categorical concepts (which, by the way, should never be mixed with vague prose claims about the language), violating my reader context model, preventing me from understanding what problem exactly your language design is solving (where is that problem stated clearly?), it is a waste of my time.

> The work took 3 weeks in total ... it's worth a look, and I hope it will win some converts, and that someone will want to help me with its development.

You've gone too fast, too much is vague, nothing is clear.

I'd delete everything, start over, and try and explain just one of the ideas clearly. Seriously. This sounds harsh, but it's honestly the correct approach to something as subtle and nuanced as programming language design.

This language looks interesting, but I don’t understand the concepts. Does this stuff make sense to other people?

The heap is content-addressed over Λ₂₄: every value is mapped to a lattice point and canonicalized under the Conway group Co₀ (via libmmgroup), so the same content always lives at the same address.

What is ‘Λ₂₄’? What is a ‘lattice point’?

giving up the GC stopped being a renunciation, since cells are immutable and content-addressed, so there is nothing to trace and nothing to move

This kind of sounds like you’re saying that there’s nothing to free, which implies that nothing takes up memory, which I presume is not the case. Do you mean everything is immutable and content-addressed (like Git)? Doesn’t stuff still need to be freed somehow when the programs done with it, otherwise memory will grow for ever?

> Slots are stable for the life of the process; the heap grows with distinct content only.

So how is a program supposed to handle lots of unique content? Like a web server handling user requests?

> Yon allocates into xleech2, a content-addressed heap whose geometry is the Leech lattice Λ24: exactly 196,560 slots per heap.

What is the computational complexity of memory allocation into this Leech lattice? What applications did you have in mind where making allocation a maths problem in order to save time on comparisons makes sense? What is going to happen when a program exhausts your little heap?

Professional help might be necessary.

So if you want to define a world, I expect you to tell me how to supply objects + morphisms + the composition law + the site structure. I don't know what a "semantic site" is, just what a "site" is. You'd need to define it. Anyway, we then get to our first examples of declaring worlds:

  world Currency { Code is EUR, USD }
  world Status { State is on, off }

  world Sub subset of Currency  

So now I think, "OK, maybe you just declare part of the structure and fill it in later, before you actually use it..."

But then your example disproves that notion! You have

  world Shop { Code is X }

  place Account in Shop {
    balance number
    owner String
  }

  fun main(): number {
    be a holds new Account { balance 40 owner "ada" }
    be _p holds String.print(a.owner)
    return a.balance + 2
  }

I think a "topos inspired programming language" would be kind of cool if you could pull it off, but I think you really need to figure out how to sell it in the docs to at least one of the two communities above.

> Allocation hashes the bytes; identical content returns the existing slot

What happens when two distinct objects hash to the same slot? (This is inevitable by the pigeonhole principle, and highly likely even at modest object counts due to the Birthday problem)

Actually, that's in chapter 12; 11 is the standard library. Maybe the LLM got confused because the chapters are 0-indexed.

I was curious about that topic but it seems over my head. I don't think it works outside of mathematics? In programming, one can have two objects that are identical in both structure and value but have different identities. It's why lisp has eq, eql, equal, etc. How'd you get around that other than adding an identity property?

Also:

> A handle, what your variables actually hold for strings, sections, lists, trees, is that slot index, carried as an f64

Why does the handle need floating point?

1. Yon's documentation mentions "Homotopy type theory:"

  > the runnable HoTT fragment is refl/pair/fst/snd

  These are basic features of martin-lof type theory, not homotopy type theory. The documentation makes no reference of an interval type, which is generally the way to go for decidable type-checking in HoTT without univalence as an opaque axiom.
  
  Pi types are mentioned, but Yon does not have dependent types. From what I can tell, they are polymorphic, maybe even just simply-typed (except for identity types under Pi). See here in the repo: https://github.com/yon-language/yon/blob/523e363a4a00e8da1410a2521b1d7d1309d360ce/frontend/ast.ml#L37
  The datatype Ty only refers to other Ty's. Thus, it is not dependent. Terms cannot appear in types. Pi is explicitly indexed by a type defining its domain and codomain. A pi type is not a pi type if its codomain cannot depend on its domain.

  Yon dangerously allows propositions to be lifted to booleans. If I am interpreting correctly (docs are very vague), this means propositions can be lifted to terms. This causes an obvious failure of normalization due to assumed proof irrelevance (otherwise Prop would not be distinguished) (also see Coquand's paper on this https://arxiv.org/abs/1911.08174).

  Yon claims to be dependently-typed. See this in the repo: https://github.com/yon-language/yon/blob/523e363a4a00e8da1410a2521b1d7d1309d360ce/frontend/ast.ml#L21
  > Types in Yon Core kernel — the small dependent type theory used for the operational semantics.

  Suppose I'm reading the source code wrong. Conveniently, the comment one line below reveals, once again, that the "type theory" is simply-typed:

  >  *   T, U ::= Type_n                            universe of level n
  >  *         |  Pi(x:T). U                         dependent function

  Pi types eliminate into a FIXED type that does not depend on x. This means there is also no purpose for having a universe hierarchy.

  To confirm, I scoured the docs a bit for any examples using Pi types or Sigma types. I searched the docs, and could not find any, besides this example:

> place Account in W { balance number }

> fun takes_sub(s: { a : Account where Pi(x: Account). Pi(y: Account). Id(Account, x, y) }): number { return 0 }

> fun main(): number { return 0 }

Notably, the identity is the only constructor for Ty indexed by a term. That is, Pi types can ONLY eliminate into the identity. What if I want my Pi type to eliminate into anything else living in Prop? e.g., an existential like \forall (x : Nat), \exists (y : Nat), x < y. Unfortunately impossible in Yon.

This project is clea...

I was exploring this as a means to solving the open source, or rather the github conundrum, the problem of sharing code socially is that we need a canonical source, and this is sociologically driven than performance driven, and as it turns out, have devastating consequences for FOSS funding. I wanted to explore sharing code "interchangeably" in some sense to avoid this problem, but ultimately this seems unsolveable, even with exploration by Unison etc.

Imagine someone honestly interested in learning about category theory but not yet knowing where to start. Projects like this only serve to muddy the waters obscuring paths to actual learning and giving the impression that the subject is a joke.

I assure you brethren, that this project is unmitigated AI derived fresh organic faeculent material.

A pile of steaming sh*t like our esteemed elders used to say.

I will not bother reading anymore of this...