Tootfinder

Extended Abstract: From Pattern Unification Towards Pattern Matching Unification
David Richter, Timon B\"ohler
https://arxiv.org/abs/2607.18455 https://arxiv.org/pdf/2607.18455 https://arxiv.org/html/2607.18455
arXiv:2607.18455v1 Announce Type: new
Abstract: We revisit the role of higher-order unification in dependently typed languages and identify a fundamental limitation of existing pattern-based fragments: their inability to synthesize functions defined by case analysis. Even simple and ubiquitous constraints arising from type inference, particularly from use of induction principles, fall outside the expressive power of Miller patterns and their modern extensions. We observe that such constraints naturally correspond to definitions by dependent pattern matching. Motivated by this correspondence, we propose integrating dependent pattern matching into the unification process. We present a prototype implementation of a small dependently typed language that collects delayed unification constraints and resolves them via a pattern matching compiler. Our approach successfully infers solutions that are rejected by current systems such as Rocq and Lean, suggesting a new direction for unification that unifies type inference and pattern matching compilation.
toXiv_bot_toot

This is the Wikipedia definition for human intelligence. Artificial intelligence (in the form of LLMs) does literally none of these things.
It doesn't act by itself, it isn't self-aware[1], it doesn't learn[2], it doesn't understand or form concepts[3], it doesn't logic or reason[4], it doesn't recognize patterns[5], plan, innovate, solve problems, make decisions[6], retain information or even use language to communicate[7].
LLMs are a simulated model (aka it's not real) of human intelligence. Models, in scientific parlance, are just that: they don't try to explain how a process works, they try to achieve the same outcome as a natural process (usually in an effort to perhaps learn something about that process).[8]
There simply is no "AI". Anyone telling you about how LLMs are sentient or sapient or will murder us is 100% bullshitting.
[1] There is nothing to be aware about, they don't have physicality. They're literally long lists of numbers.
[2] Models themselves are static, they're the result of machine learning, but can't grow beyond the initial state.
[3] LLMs don't "know" anything. It's matrix multiplications without permanence or embodiment. https://en.wikipedia.org/wiki/Understanding
[4] Because they can't understand or form concepts, they can't reason about them.
[5] This requires memory, which LLMs don't have. https://en.wikipedia.org/wiki/Pattern_recognition_(psychology)
[6] Memory and understanding are required. https://en.wikipedia.org/wiki/Decision-making
[7] All it does it getting an input in the form of a lot of numbers and returns statistically likely follow-up numbers.
[8] "A model is an informative representation of an object, person, or system." https://en.wikipedia.org/wiki/Model