Questions tagged [soft-question]

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Formalization of Analytic Number Theory

Is there any formalization, in any proof checking environment (Lean, Isabelle, etc.) of basic analytic number theory, say everything in a book like the Titchmarsh book (The Theory of the Riemann Zeta ...
  • 121
4 votes
1 answer

Why is it hard to formalize informal proofs?

Say I have some informal but rigorous argument in line with eg real analysis. Currently, it is a massive PITA to do algebraic manipulations in proof assistants like Coq or Isabelle. However, in ...
14 votes
3 answers

Counterexamples in Type Theory

The title pretty much covers it. I'm wondering if someone is maintaining a list of counterexamples in type theory. I'm aware of Counterexamples in Type Systems, which I think is very nice, but I guess ...
  • 328
8 votes
2 answers

Figures on computer proof assistant usage

I'm interested in figures on computer proof assistant usage. To put this in perspective, I have a server which I am making at the moment, and I only feel like committing time to setting up four or ...
3 votes
1 answer

How can you represent a dependent type visually?

So, obviously for a term $t$ of type $T$, I would represent it as: T +-----------+ | | | t | | | +-----------+ That is a node ...
4 votes
2 answers

Pragmatic encodings of inductive inductive types

What's the most pragmatic encoding for inductive-inductive types such as for a universe of types? In pseudo Coq syntax. ...
1 vote
1 answer

How does Lean4 (or a typical PA) represent lambda functions or in other words arbitrary expressions?

Question: Say I wanted my language to support various operator symbols, the semantics of which are defined by the user or by axioms. I'm wondering whether Lean4 (or a typical well-known PA) just ...
-3 votes
1 answer

Could we speed up ATP or ATD using a directed graph that appears to work like a gigantic brain?

So I'm not sure how things are done in Lean4 or Coq, but I'm interested in their search features. For example, "Search for all theorems that get satisfied given a user-defined list of ...
17 votes
2 answers

What are the advantages to impredicativity?

Mostly when I read about impredicativity I see people bemoaning its downsides. But it's not clear to me why I would want impredicativity in the first place. Impredicativity is useful for analyzing ...
11 votes
1 answer

Naming conventions (letter case, underscores, &c) for Coq

Does Coq have an established convention/style for constructors, variables, terms, &c? An established convention that isn't exceptionless is totally fine. For example, terms should be lowercase ...
  • 2,651
15 votes
1 answer

Why should you "never resort to polymorphism when initiality would do"?

In the concluding statement of "universe hierarchies", Conor McBride calls it [...] that key lesson which I learned from James McKinna: never resort to polymorphism when initiality will do. ...
9 votes
2 answers

Which proof assistant would you advise me to learn (in 2022) considering my interests?

I am a math teacher in college. I’m very interested in type theory. So far, I got the general idea of it but I would like to go deeper. I am interested in philosophy of maths, in foundations of maths, ...
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