Unanswered Questions
17 questions with no upvoted or accepted answers
23
votes
0
answers
571
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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 ...
- 3,200
12
votes
0
answers
169
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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 ...
- 3,200
5
votes
0
answers
168
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What are the conditions for Agda to detect that induction-recursion has a least fixed point?
This is a 3rd in a series of questions, spurred by my attempts to encode an argument by Danielsson [1] [2] regarding existence of syntactically non-strictly positive datatype.
The idea (rephrased):
...
- 107
4
votes
0
answers
53
views
Introductory resources on rewriting logic
Hi I would like to grasp the theory behind Maude [1], [2]
Are there any recommended video lecture notes, talks or introductory notes?
I have been exposed to Functional Analysis, Topology and some Term ...
- 2,300
3
votes
0
answers
129
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Uniform notions of pattern matching at dependent types with impredicative proof strength
I am looking for axioms/inference rules that satisfy the following 3 conditions:
can be added to predicative intensional Martin-Löf type theory, so $\Pi$, $\Sigma$, equality type, with W-types, ...
- 547
3
votes
0
answers
93
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Where is the discriminate tactic defined in Coq?
One can read the Coq documentation about discriminate tactic here.
Were is this tactic actually defined?
2
votes
0
answers
65
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Have Hyperdoctrines been formalized?
I was thinking of formalizing them myself for a project if they haven't been already, and I looked in libraries and couldn't find anything.
I was thinking of coq in particular because it's the only ...
- 143
2
votes
0
answers
62
views
Elimination rules of inductive types
Why does the elimination rule of inductive types sometimes allow the target type to depend on the inductive type and sometimes not? I am confused by that. Is it correct that it makes no difference in ...
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2
votes
0
answers
84
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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 ...
- 141
1
vote
0
answers
70
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Heterogeneous lists, large indices
Recently I had cause to define a type of heterogeneous lists in Lean, and wrote
...
- 111
1
vote
0
answers
46
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how to inductively define paths from paths using unimath
I'd like to define a type of graph where given a set of edges, we can define another graph that has everything from graph 1 but extends the set of edges by adding higher level edges to parallel edges(...
- 71
1
vote
0
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63
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Why does Coq not allow constructor argument types to be strictly positive mutual inductive types?
Note: Apologies for the wicked mouthful of a title. I'm still getting acquainted with Coq terminology, so I might not have chosen the best words. If you have a better title suggestion, edits are more ...
- 143
1
vote
0
answers
48
views
Can you always replace mutually recursive references with parameters?
This is a follow up to a question someone else previously posted: Expressivity of mutual/nested inductives vs. regular inductives.
pigworker answered that
Adopting Agda-ish notation, the basic ...
- 143
1
vote
0
answers
180
views
Descriptions of heterogenous datatypes
When attempting to describe the datatype as appearing in my previous question, using indexed descriptions in style of The Gentle Art of Levitation to describe this datatype (using Agda for examples):
<...
- 547
0
votes
0
answers
36
views
Simple and proper methods in Isar
https://isabelle.systems/cookbook/src/proofs/methods/Chained_Facts.thy
talks about
We note a slight difference. In the variant with intro, a trivial goal remains
that we need to solve by ‹assumption›....
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