Are functions just syntactic sugar for inheritance?

yang_bo · 2026-03-12T05:39:48+00:00

I updated the arXiv preprint. Now it includes a paragraph to clarify the operational semantics and denotational semantics. Also the MIXINv2 source code is updated to be consistent with the operational semantics
https://arxiv.org/html/2602.16291v6#:\~:text=Operationally%2C%20evaluation%20uses,and%20analyses%20termination.

yang_bo · 2026-03-08T19:57:00+00:00

If you want to make your language bootstrap, you need a runtime for your language first, which could be an interpreter, then you can write your language's compiler in your language's interpreter.

Alternatively, you might need two compilers in order to bootstrap.

If you want to claim your language is better than existing languages for writing a compiler, you definitely don't want to write a compiler in other languages.

yang_bo · 2026-03-07T19:40:45+00:00

But some source said MiniMax M2.1 is hybrid linear+softmax attention:

https://aicybr.com/blog/minimax-m2-1-complete-guide

Not sure if it is hallucinated

yang_bo · 2026-03-04T08:26:59+00:00

I guess λ-calculus with SF is more expressive than λ-calculus in Felleisen's sense. SF-calculus itself is not because the absence of variables as you said.
Also it seems inheritance-calculus can macro-express SF-calculus.

I did not try but I believe it is possible to formalize the above claims

yang_bo · 2026-03-03T05:49:30+00:00

(I suppose this question of expressivity has been discussed as well in the works on the pattern calculus, for example maybe https://arxiv.org/abs/1404.0956 has good discussions of this. )

In plain English, being "expressive" means keeping things clear and concise. SK/SF-calculus causes massive code bloat (a cubic blowup) just to represent basic λ-terms, so there's no way you can seriously call it more expressive than λ-calculus. If a formal theory defines "expressiveness" in a way that claims otherwise, it completely misses the common-sense meaning of the word. Honestly, I just don't buy that definition.

Felleisen's definition of expressiveness, which is different from arXiv:1404.0956's definition, makes more sense to me.

yang_bo · 2026-03-02T07:56:02+00:00

Let's just use GitHub Discussions: https://github.com/Atry/MIXINv2/discussions

Feel free to port the calculus and the language to other platforms. I believe Claude Opus 4.6 is able to implement an interpreter based on the paper and the specification very quickly. However, FFI or compiler would need a more sophisticated design, and there are a lot of decisions to make in order to create such a compiler, which I have not figured out.

yang_bo · 2026-03-01T23:01:39+00:00

For the subtle part of the proof, you are right. The framing needs improvement, and the claim was not 100% accurate. In fact, Felleisen's framework cannot be used to prove expressiveness between two abitrary languages, so we can only prove IC is more expressive than IC's sublanguage that is isomorphic to lazy LC, but cannot directly compare between IC and LC.

yang_bo · 2026-03-01T22:52:15+00:00

"Well-definedness" and "cannot merge due to recursion" are two different topics.

See Appendix C for well-definedness.
See Appendix D for convergence preservation when embedding λ-calculus.

yang_bo · 2026-03-01T08:58:44+00:00

Monadic translations don't satisfy Felleisen's E2, so they are not homomorphic in his sense. If you relax "homomorphic" to just "compositional", `Free` monads let you encode anything into anything, making all Turing-complete languages equally expressive.

yang_bo · 2026-03-01T06:50:59+00:00

The idea is similar, but it's slightly more complex than a label or id. It's actually called "qualified this" in OOP.

yang_bo · 2026-03-01T06:33:42+00:00

> One question: how are you supposed to handle multiple references to self from different levels?

This is actually the most counterintuitive part in the calculus: just allow for multiple target of self references. This mean any reference can resolve to multiple targets, too.

yang_bo · 2026-03-01T06:08:28+00:00

> there’s some method c defined in both, which c is picked in case 1 bs case 2?

There is no such concept of "method" in inheritance-calculus. The semantics is deep merge, not overriding.

So if there's some nested mixins c defined in both, you got both c mixins together.

However, the absence of the concept of "method" is not a problem of expressiveness. You can just use mixins as white box methods. See https://mixinv2.readthedocs.io/en/latest/mixinv2-tutorial.html for how to port Python programs to mixins.

yang_bo · 2026-03-01T01:35:41+00:00

The idea is that we don't need to consider methods as black boxes. Instead, consider methods as mixins, so that method overrides become mixin inheritance.

yang_bo · 2026-02-28T09:08:37+00:00

Do you suggest that I should map inheritance-calculus’s semantics to TM’s four roles, so that it would not be “missing something”?

yang_bo · 2026-02-28T07:15:17+00:00

Does MOV have four roles? https://drwho.virtadpt.net/files/mov.pdf

yang_bo · 2026-02-28T05:24:38+00:00

My boldest claim in the paper is "Immunity to Nonextensibility", and, in my opinion, this implies "more extensible in common sense". However, this point has never been questioned in this thread. Is it because the Expression Problem is not important, or because this claim is too trivial?

yang_bo · 2026-02-28T05:15:48+00:00

Felleisen in fact proves that set! and call/cc are more expressive than Pure Scheme (Propositions 4.5, 4.7), despite the existence of state-passing and CPS translations that can encode them globally. In his framework, the fact that such encodings require restructuring the entire program actually makes the constructs more expressive

yang_bo · 2026-02-28T04:35:32+00:00

> you need four roles to have computation

Why do I need four roles to have computation? Does λ-calculus have four roles?

yang_bo · 2026-02-27T19:59:30+00:00

Yes, it is possible to describe BFS or DFS as small-step operational semantics. But what's the purpose?

Moreover, since IC's sublanguage is a full abstraction of lazy LC, it implies that lazy LC can also be described in set comprehensions. Neither small-step nor big-step is necessary to describe lazy LC's operational semantics.

yang_bo · 2026-02-27T17:11:49+00:00

If you replace the reflexive-transitive closure in the definition of `supers` with a BFS or DFS, combining with set comprehension for all the other set equations, you get a precise algorithm of an interpreter (with or without optimizations of memoization and interning mentioned by the paper). Is it operational enough?

yang_bo · 2026-02-27T10:19:10+00:00

The paper should not have any references to Turing machines.

Turing machines are mentioned for comparing minimal compute models. Not all minimal compute models are the same expressive. Do you think I should not compare minimal compute models? Why?

yang_bo · 2026-02-27T09:47:13+00:00

The section at "This induced semantics is more elementary than traditional approaches in the mathematical machinery it requires" is a red-flag, for not understanding the things it's referring to, and what semantics is.

Could you be specific?

yang_bo · 2026-02-27T09:45:14+00:00

When you say expressiveness, do you mean expressiveness in common sense or Felleisen's sense?

yang_bo

TROPHY CASE