Questions tagged [agda]
For questions regarding Agda: the programming language / proof assistant.
70
questions
5
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1
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232
views
How to convince Agda that definition is terminating in the presence of unapplied recursion?
In the following, termination check fails for Df:
...
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
7
votes
2
answers
293
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Proving strict positivity in Agda
In Agda we can prove termination of functions by using well-founded relations, is there a guideline for proving datatype declarations strictly positive, possibly via use of some container techniques ...
- 547
1
vote
1
answer
300
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Does Agda's --injective-type-constructors flag have canonicity?
Since 2010/01/07, when the Anti-classicality of Agda was proved by Chung-Kil Hur, Agda's --injective-type-constructors is separated from the main branch of Agda (...
- 279
3
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1
answer
140
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Can I specify `refl`'s parameter explicitly in Agda?
I'm working on some proofs in Agda that, for educational purposes, explicitly use the path induction principle (which I've defined myself) rather than pattern matching. In the theoretical mathematical ...
- 319
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votes
1
answer
185
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Application of `SSet` in Agda
Is there any presentable work that makes essential use of SSet in Agda? I kind of get the theory, but I'm not sure about the practical value of this. The ...
- 4,025
3
votes
1
answer
98
views
Using induction to define Indexed family of HITs in agda
I am looking to define a family of HITs parametrized by $\mathbb{N}$. I want $(-)$-glob : $\mathbb{N} \to Type$, so that $n$-glob is the n-dimensional glob. I know how to construct the n-$glob$ by ...
- 317
5
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1
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178
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Strictly-monotone "max" operation for constructive Brouwer-trees?
The Setting
I'm trying to use Agda's well-founded ordering to prove that something is terminating using Brouwer Trees i.e.
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- 971
4
votes
1
answer
111
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Agda Error after reload when successfully filling a goal
So I'm not sure what this error is and I'm not even sure how I would find out. I'm trying to code up a proof that refl is a right identity. I've gotten to this stage:
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- 317
5
votes
2
answers
247
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Agda: Cannot Instantiate Metavariable
I'm running into a certain error while trying to code something up in cubical Agda, but I can't understand the error. Here is my code:
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- 317
9
votes
2
answers
252
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How to access local definitions in Agda
I'm working in cubical agda. I am wondering how to access local definitions once outside of the local environment. For example, suppose I have the following code:
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- 317
4
votes
2
answers
190
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Turning off some sProp checks
In Definitional Proof Irrelevance Without K, inductives in sProp need to satisfy three conditions to allow large elimination:
(1) Every non-forced argument must be in sProp.
(2) The return types of ...
- 1,026
8
votes
2
answers
689
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Curly Braces and Lambdas in Agda
The docs on lambdas in Agda provide two forms of lambda: a curly brace based version, and the where syntax. But while writing some programs, I stumbled across a third version: one pattern, no braces, ...
9
votes
2
answers
468
views
Defining coercion for proof irrelevant equality
Say I would like to define coercion for proof irrelevant equality between types. In Coq I try
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- 2,300
6
votes
1
answer
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Proof of symmetry of universe-polymorphic Leibniz equality in Agda
Consider the following definition of universe-polymorphic Leibniz equality:
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- 6,316