Unanswered Questions
17 questions with no upvoted or accepted answers
23
votes
0
answers
571
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 ...
- 3,200
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 ...
- 3,200
9
votes
0
answers
309
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
6
votes
0
answers
84
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What are Generic Arguments in Coq and how are they structured in their OCaml code?
I was trying to figure out why it seems that in a Coq generic argument there seems to be 3 arguments to the constructor GenArg when according to me there should ...
- 9,195
6
votes
0
answers
137
views
How to write heavily indexed proofs?
I've been playing with hereditary substitution. However, things get very awkward because substitution isn't total unless you index by the environment somehow.
In my old approach terms were not indexed ...
- 2,868
5
votes
0
answers
168
views
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
3
votes
0
answers
103
views
Using crude but effective stratification & cong to implement transitivity of `=`
Suppose I have
cong : {A B : Type} (f : A -> B) (p : a = b) : f a = f b
coe : (A : I -> Type) -> A 0 -> A 1
It is ...
- 2,300
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 ...
- 722
1
vote
0
answers
70
views
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
views
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
answers
32
views
How to Show a Term in TinyIdris?
I am trying to follow the code of TinyIdris and print out the basic definitions such as Terms. But I couldn't apply the Show ...
- 2,220
1
vote
0
answers
62
views
Embedding proof assistance in an application
Context
Perhaps this is too open-ended a question for StackExchange, in which case I apologize, but otherwise here goes:
I have a project I'm toying around with, the core of which is what I'd call &...
- 111
1
vote
0
answers
63
views
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