<div dir="ltr">It is known that UIP is inconsistent with univalence.<div><div><div>Does this typecheck even after disabling UIP(==K axiom?) ?</div><div>I might be wrong, but I think that UIP is baked into the typechecker of Agda.</div>
<div>But, UIP can be disabled somehow?</div><div><div><br></div></div></div></div></div><div class="gmail_extra"><br clear="all"><div><div>-- Abhishek</div><a href="http://www.cs.cornell.edu/~aa755/" target="_blank">http://www.cs.cornell.edu/~aa755/</a></div>
<br><br><div class="gmail_quote">On Mon, Jan 6, 2014 at 3:42 PM, Maxime Dénès <span dir="ltr"><<a href="mailto:mail@maximedenes.fr" target="_blank">mail@maximedenes.fr</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Bingo, Agda seems to have the same problem:<br>
<br>
module Termination where<br>
<br>
open import Relation.Binary.Core<br>
<br>
data Empty : Set where<br>
<br>
data Box : Set where<br>
wrap : (Empty → Box) → Box<br>
<br>
postulate<br>
iso : (Empty → Box) ≡ Box<br>
<br>
loop : Box -> Empty<br>
loop (wrap x) rewrite iso = loop x<br>
<br>
gift : Empty → Box<br>
gift ()<br>
<br>
bug : Empty<br>
bug = loop (wrap gift)<br>
<br>
However, I may be missing something due to my ignorance of Agda. It may be well known that the axiom I introduced is inconsistent. Forgive me if it is the case.<span class="HOEnZb"><font color="#888888"><br>
<br>
Maxime.</font></span><div class="HOEnZb"><div class="h5"><br>
<br>
On 01/06/2014 01:15 PM, Maxime Dénès wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
The anti-extensionality bug is indeed related to termination. More precisely, it is the subterm relation used by the guard checker which is not defined quite the right way on dependent pattern matching.<br>
<br>
It is not too hard to fix (we have a patch), but doing so without ruling out any interesting legitimate example (dealing with recursion on dependently typed data structures) is more challenging.<br>
<br>
I am also curious as to whether Agda is impacted. Let's try it :)<br>
<br>
Maxime.<br>
<br>
On 01/06/2014 12:59 PM, Altenkirch Thorsten wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Which bug was this?<br>
<br>
I only saw the one which allowed you to prove anti-extensionality? But<br>
this wasn't related to termination, or?<br>
<br>
Thorsten<br>
<br>
On 06/01/2014 16:54, "Cody Roux" <<a href="mailto:cody.roux@andrew.cmu.edu" target="_blank">cody.roux@andrew.cmu.edu</a>> wrote:<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Nice summary!<br>
<br>
<br>
On 01/06/2014 08:49 AM, Altenkirch Thorsten wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Agda enforces termination via a termination checker which is more<br>
flexible but I think less principled than Coq's approach.<br>
</blockquote>
That's a bit scary given that there was an inconsistency found in<br>
the Coq termination checker just a couple of weeks ago :)<br>
<br>
BTW, has anyone tried reproducing the bug in Agda?<br>
<br>
<br>
Cody<br>
</blockquote>
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