Unanswered Questions
156 questions with no upvoted or accepted answers
22
votes
0
answers
568
views
Categorical semantics of Agda
I would like to know the state of the art regarding the categorical semantics of the type theory implemented by Agda — or at least some approximation of that type theory that is amenable to ...
- 3,190
20
votes
0
answers
233
views
What is known about performance bottlenecks in proof assistants?
Background
In my personal experience, the biggest bottleneck to broader adoption of proof assistants (in industry and mathematics) is the effort it takes to engineer proofs. (In lines of code, for ...
- 1,112
20
votes
0
answers
275
views
Can we automatically get around set-theoretic difficulties?
One of the main technical annoyances of working with (large) categories is the variety of set-theoretic difficulties that come about with it: if we use ZFC as background logic, then those large ...
- 1,013
15
votes
0
answers
211
views
Code generation from Locales and Sublocales in Isabelle
Problem Description
I stumbled on this limitation/misunderstanding several times when using locales and sublocales in Isabelle. As a minimal example, let us extend the locale from the example in ...
- 1,128
13
votes
0
answers
369
views
Unintentionally proven false theorem with type-in-type outside logic and foundations?
We are all familiar with Russell's paradox, and it is known that Per Martin-Löf proved that type-in-type is normalizing and consistent (which is false), by accidentally using an assumption in his meta-...
13
votes
0
answers
571
views
How to speed up Lean?
I've recently been writing my first somewhat serious proof in Lean. While doing that, I noticed that Lean gets slower very fast with increasing length of the proof (slower in the sense that whenever I ...
- 1,165
12
votes
0
answers
169
views
Rules for mutual inductive/coinductive types
Some proof assistants, like Agda and maybe Coq, allow families of mutually defined types, or nested definitions of types, in which some are inductive and others are coinductive. I have no idea what ...
- 3,190
12
votes
0
answers
197
views
Do any automated theorem provers have the ability to stop, save state, reboot computer, restore state, continue?
With automated theorem provers knowing ahead of time how long the search will take or even if it will find a solution is unknown. Often for long running searches one eventually just has to halt the ...
- 2,846
10
votes
0
answers
187
views
Is there a proof assistant (or an embedding) for the (co)end calculus?
A Higher-Order Calculus for Categories describes a system where you can conveniently perform manipulations with categories, functors, Yoneda embeddings etc. An example of the rules is: $$\frac{\Gamma ,...
- 2,846
10
votes
0
answers
318
views
What's "Swedish" style of doing type theory or proof assistants?
Jon Sterling said Conor McBride's universe polymorphism proposal to be:
seems to have worked well in Swedish experiments
I wonder, what does "Swedish" mean here? What kind of type theory ...
- 1,165
10
votes
0
answers
175
views
What are the practical differences between intensional and extensional type theories?
It is already proved that MLTT with equality reflection is equivalent to MLTT with an intensional equality, plus UIP and function extensionality. So theoretically the differences between intensional ...
- 4,025
9
votes
0
answers
307
views
Alternatives to universe levels
All of the type theory based proof assistants that I have seen have an infinite hierarchy of type universes to avoid the type of types being a term of itself. Are there alternative systems which could ...
- 91
9
votes
0
answers
133
views
Has there been any work on automated translation of tactic proofs to everyday language?
There are times when I've completed a proof with a lot of backwards reasoning, and I've kind of lost the thread of what I've actually done. It would be nice if there was something that could ...
- 373
8
votes
0
answers
171
views
Graph algorithms in Coq
We’re looking for a good library for reasoning about graphs in Coq. Some key features with would want to support include:
Topological sorting (ideally along with other graph algorithms)
Manipulation ...
- 81
8
votes
0
answers
296
views
What would a fully classical and fully univalent ITP and library look like?
Consider two developments in dependent type theory:
Lean’s mathlib library (as well many other ITP libraries) is unashamedly fully classical. There is no ...
- 9,095