Discussion of Homotopy Type Theory and Univalent Foundations
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From: Matt Oliveri <atmacen@gmail.com>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] Semantics of QIITs ?
Date: Mon, 20 May 2019 17:28:34 -0700 (PDT)	[thread overview]
Message-ID: <64897263-717c-4596-9397-76f03b4e1c38@googlegroups.com> (raw)
In-Reply-To: <96fea5d2-535c-43fc-9832-48ce96e916ca@www.fastmail.com>


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I'm not completely satisfied with Hugunin's technique, because it justifies 
only the "simple" elimination principle, rather than the general, 
"recursive-recursive" elimination principle implemented in Agda. As far as 
I can tell, realistic use cases for inductive-inductive families also need 
the recursive-recursive elimination principle, where the types of the maps 
out of later families depend on the maps out of earlier families. (I'm not 
sure how much of the other research on IIFs stops short of handling 
recursion-recursion, but I think it should be taken seriously.)

On Monday, May 20, 2019 at 7:26:12 PM UTC-4, Jon Sterling wrote:
>
> Echoing Andras, I recall that a new encoding due to Jasper Hugunin enable 
> us to interpret IITs without using UIP, and it is an open question to 
> determine whether Jasper's ideas can be extended to QIITs. I hope they can, 
> and someone should find out :) 
>
> Best, 
> Jon
>

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  reply	other threads:[~2019-05-21  0:28 UTC|newest]

Thread overview: 19+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2019-05-16 14:57 Bas Spitters
2019-05-16 15:39 ` Thorsten Altenkirch
2019-05-16 15:50   ` Bas Spitters
2019-05-16 16:15     ` András Kovács
2019-05-16 18:50       ` Bas Spitters
2019-05-20 16:16         ` Thorsten Altenkirch
2019-05-20 17:54           ` Bas Spitters
2019-05-20 18:35             ` Thorsten Altenkirch
2019-05-20 19:59               ` Jon Sterling
2019-05-20 21:04                 ` Bas Spitters
2019-05-20 22:17                   ` Thorsten Altenkirch
2019-05-20 23:26                     ` Jon Sterling
2019-05-21  0:28                       ` Matt Oliveri [this message]
2019-05-21  2:45                         ` Jasper Hugunin
2019-05-21  8:33                         ` Thorsten Altenkirch
2019-05-21 19:56                           ` Matt Oliveri
2019-05-21  8:39                       ` Thorsten Altenkirch
2019-05-21 11:47 ` [HoTT] " Andrew Swan
2019-05-21 12:14   ` Bas Spitters

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