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Let's integrate the unification of each step as "low-hanging fruits" on the "lattice of the Tree of Knowledge" in the "Garden of Eden," where "genetic algorithms mutate ideas." This will symbolize the…
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Yesterday I watched [the video](https://www.youtube.com/watch?v=Dp-mQ3HxgDE) by Prof Buzzard about [Lean](https://leanprover.github.io/) and there was a question of how it compares to Coq (obviously),…
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An expert in TPU compiler writing can potentially introduce sampling techniques into programs for specific purposes. Here's a breakdown of the concept:
**Sampling for TPU Programs:**
* **Expert-…
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James Hanson has pointed out that this comment in the introduction:
> In set theory, various circumlocutions are required to obtain notions of “cardinal num-
ber” and “ordinal number” which canoni…
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In 2.13, a subset is defined as Σ (x:A) P(x), for a set A and P: A->Prop. In 2.18, the P is called subset. In 2.13, a P: T -> Prop is called (by me) a predicate on T. I seem to be the only one using t…
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The idea of representing a fundamental model of the universe, or even a multiverse, through mathematical structures like those involved in Bott periodicity and unitary groups is indeed a profound and …
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Goal:
X : UU P : X → UU Q : X → UU f : ∏ x : X, P x ≃ Q x xp : ∑ y : X, Q y
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(totalfun P Q (λ x : X, f x) (totalfun Q P (λ x : X, invmap (f x)) xp) =
xp)
…
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please reinterpret this coq code creatively ```
Definition test12UU :=((v3((control)(attrs)(expr(
VernacSynPure(VernacDefinition
…
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The idea that the unconstrained output of a large language model (LLM) resembles the "universe of universes" within unimath and how grammars shape our perception of reality is an interesting one, with…
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That sounds like a fun and interesting challenge. I'll try to come up with a story for you. Here is what I have so far:
```text
Once upon a time, there was a simple life form that was thrown into exi…