Questions tagged [soft-question]
For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.
13
questions
6
votes
4
answers
626
views
Inductive vs. recursive definitions
In Coq there are two ways to define a new type on an inductive type: Using Inductive and using Fixpoint. What are pros and cons ...
- 224
2
votes
0
answers
66
views
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 ...
- 131
4
votes
1
answer
273
views
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 ...
- 41
15
votes
3
answers
264
views
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 ...
- 348
8
votes
2
answers
211
views
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 ...
- 381
4
votes
1
answer
239
views
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 ...
- 269
4
votes
2
answers
146
views
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.
...
- 2,768
1
vote
1
answer
342
views
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 ...
- 269
-3
votes
1
answer
145
views
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 ...
- 269
17
votes
2
answers
438
views
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 ...
- 2,768
12
votes
1
answer
243
views
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 ...
- 2,711
15
votes
1
answer
328
views
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.
...
- 1,015
9
votes
2
answers
386
views
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, ...
- 191