From: Andrew Polonsky <andrew....@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: What is UF, what is HoTT and what is a univalent type theory?
Date: Fri, 3 Jun 2016 04:53:47 -0700 (PDT) [thread overview]
Message-ID: <deb61dfc-f1f3-48fc-b208-b94caca612d4@googlegroups.com> (raw)
In-Reply-To: <5750A527.4060705@cs.bham.ac.uk>
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>
> Let me then come to the last of the three questions. What is UTT
> (univalent type theory)? As I conceive it:
>
> It is any Martin-Lof type theory that is compatible with the idea
> that equality/equivalence, as rendered by the identity type, is,
> in general, structure rather than merely a property.
>
I find this definition somewhat puzzling. Cubicaltt is certainly
compatible with the idea that equality is equivalence. But its path type
seems to be a very different concept compared to Martin-Lof identity type.
What is a Martin-Lof type theory anyway? Are type systems based on untyped
conversion (eg. Coq) Martin-Lof type theories? Are type theories with a
different notion of equality (eg. observational or cubical type theories)
also Martin-Lof type theories?
Andrew
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next prev parent reply other threads:[~2016-06-03 11:53 UTC|newest]
Thread overview: 23+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-06-02 21:29 Martin Escardo
2016-06-03 11:53 ` Andrew Polonsky [this message]
2016-06-03 12:49 ` [HoTT] " Vladimir Voevodsky
2016-06-03 14:12 ` Andrew Polonsky
2016-06-03 19:29 ` Vladimir Voevodsky
2016-06-03 22:05 ` andré hirschowitz
2016-06-04 8:38 ` Vladimir Voevodsky
2016-06-04 9:56 ` andré hirschowitz
2016-06-06 8:10 ` [HoTT] " Vladimir Voevodsky
2016-06-04 6:11 ` [HoTT] " Urs Schreiber
2016-06-06 7:14 ` Vladimir Voevodsky
2016-06-06 7:32 ` David Roberts
2016-06-06 10:56 ` [HoTT] " Vladimir Voevodsky
2016-06-06 11:40 ` David Roberts
2016-06-03 20:17 ` [HoTT] " Martin Escardo
[not found] ` <CAOvivQxw34SKUatt4aW-u4bLjgSq=K58i8E6+sBBAh6OzvzANg@mail.gmail.com>
2016-06-05 20:40 ` [HoTT] " Martin Escardo
[not found] ` <CAOvivQx0BHg2KCbWzav+0aW9knbEq521gxXBA3pDrFDxt8J0qA@mail.gmail.com>
2016-06-08 10:14 ` Martín Hötzel Escardó
2016-06-14 21:46 ` Michael Shulman
2016-06-14 22:15 ` Martin Escardo
2016-06-14 22:30 ` Michael Shulman
2016-06-14 23:33 ` Martin Escardo
2016-06-15 3:04 ` Michael Shulman
2016-06-08 14:37 ` Fwd: " Michael Shulman
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