[Agda] Weird termination problem

[Thorsten Altenkirch]

I have posted a (new?) issue:
https://github.com/agda/agda/issues/4846

Here is my small example:

f : (ℕ → ℕ) × ℕ
proj₁ f zero = zero
proj₁ f (suc x) = suc (proj₁ f x)
proj₂ f = zero

It works with no flag but fails with no-K. No I don’t think we should add this to the docs, it would be better to fix it.

Thorsten

From: Jason -Zhong Sheng- Hu <fdhzs2010 at hotmail.com>
Date: Saturday, 15 August 2020 at 16:51
To: William Harrison <william.lawrence.harrison at gmail.com>, Thorsten Altenkirch <psztxa at exmail.nottingham.ac.uk>
Cc: "agda at lists.chalmers.se" <agda at lists.chalmers.se>
Subject: Re: [Agda] Weird termination problem

Hi Thorsten,

the example I saw uses copattern as you did. not sure how K would interfere with the termination process but it does look like a bug to me.

Thanks,
Jason Hu
https://hustmphrrr.github.io/
________________________________
From: Agda <agda-bounces at lists.chalmers.se> on behalf of William Harrison <william.lawrence.harrison at gmail.com>
Sent: August 15, 2020 10:30 AM
To: Thorsten Altenkirch <Thorsten.Altenkirch at nottingham.ac.uk>
Cc: agda at lists.chalmers.se <agda at lists.chalmers.se>
Subject: Re: [Agda] Weird termination problem

Hi Thorsten,

If you came up with a pithy example and then integrated in with the Agda docs (specifically https://agda.readthedocs.io/en/v2.6.1/language/without-k.html), that’s be welcome. By me, at least.

Bill
Sent from my iPad


On Aug 15, 2020, at 10:21 AM, Thorsten Altenkirch <Thorsten.Altenkirch at nottingham.ac.uk> wrote:

I found

https://github.com/agda/agda/issues/2890

but this mentions “with” which I wasn’t using. Also increasing termination depth didn’t help in my case.



I can try to cook up a short example but maybe this is a known issue?



Thorsten



From: Agda <agda-bounces at lists.chalmers.se> on behalf of Thorsten Altenkirch <Thorsten.Altenkirch at nottingham.ac.uk>
Date: Saturday, 15 August 2020 at 15:16
To: Jason -Zhong Sheng- Hu <fdhzs2010 at hotmail.com>, "agda at lists.chalmers.se" <agda at lists.chalmers.se>
Subject: Re: [Agda] Weird termination problem



Yes, indeed this worked. And the difference was that in the previous version I hadn’t used no-K.



Thanks a lot – I was truly stumped. And I do remember that there were some issues with termination checking when switching on no-K.



Cheers,

Thorsten



From: Jason -Zhong Sheng- Hu <fdhzs2010 at hotmail.com>
Date: Saturday, 15 August 2020 at 15:10
To: Thorsten Altenkirch <psztxa at exmail.nottingham.ac.uk>, "agda at lists.chalmers.se" <agda at lists.chalmers.se>
Subject: Re: Weird termination problem



I once saw someone else's code where termination checker also failed with no good reason. the author worked around it by turning on K. could you see if K works around it for you?



Thanks,

Jason Hu

https://hustmphrrr.github.io/

________________________________

From: Agda <agda-bounces at lists.chalmers.se> on behalf of Thorsten Altenkirch <Thorsten.Altenkirch at nottingham.ac.uk>
Sent: August 15, 2020 9:25 AM
To: agda at lists.chalmers.se <agda at lists.chalmers.se>
Subject: [Agda] Weird termination problem



Hi,



I just transferred some code form my lecture notes to my book draft and now the termination checker complains where there was no problem before:



thm : {P : Form} → ([] ⊢ P) ⇔ ⊢sk P

proj₁ thm d = skC→sk (⊢→⊢skC d)

proj₂ thm SS = S-d

proj₂ thm KK = K-d

proj₂ thm (app d e) = app (proj₂ thm d) (proj₂ thm e)



so here ⊢sk P is inductively defined and there should be no problem – and indeed there wasn’t before. But now



Termination checking failed for the following functions:

  thm

Problematic calls:

  proj₂ thm e



I can’t make any sense out of it. Has anybody an inkling what could have happened or any advice what I could do to fix it.



I can prove the <= direction on its own with no problems. The definition of ⇔ is exactly the same as before and it doesn’t help if I expand it. Also the definition of products is the same as before.



If you want to have a look at the code please let me know – I will give you access to the repo.



Cheers,

Thorsten



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