Discussion of Homotopy Type Theory and Univalent Foundations
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From: Stefan Monnier <monnier@iro.umontreal.ca>
To: "Martín Hötzel Escardó" <escardo.martin@gmail.com>
Cc: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] Why did Voevodsky find existing proof assistants to be 'impractical'?
Date: Tue, 05 Nov 2019 19:06:04 -0500
Message-ID: <jwvbltpan88.fsf-monnier+INBOX@gnu.org> (raw)
In-Reply-To: <cb153658-548a-4fe9-91ed-fc2e3db33723@googlegroups.com> (=?windows-1252?Q?=22Mart=EDn=09H=F6tzel_Escard=F3=22's?= message of "Tue, 5 Nov 2019 15:14:07 -0800 (PST)")

> members of this list. The constructivity of univalence was an open problem 
> for a number of year, and I would say that, even if it is solved via the 
> cubical model, it is far from being fully understood.

In my case, I still find it odd in a situation such as:

    data Foo : Set -> Set where
      bar : Foo UnaryNat

since transport supposedly allows us to take a proof of equivalence
between UnaryNat and BinaryNat and turn a `bar` into something of type
`Foo BinaryNat` although I can't see any way to directly construct an
object of this type.


        Stefan


  reply index

Thread overview: 18+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2019-10-27 14:41 Nicolas Alexander Schmidt
2019-10-27 17:22 ` Bas Spitters
2019-11-03 11:38   ` Bas Spitters
2019-11-03 11:52     ` David Roberts
2019-11-03 19:13       ` Michael Shulman
2019-11-03 19:45         ` Valery Isaev
2019-11-03 22:23           ` Martín Hötzel Escardó
2019-11-04 23:20             ` Nicolas Alexander Schmidt
2019-11-04 18:42         ` Kevin Buzzard
2019-11-04 21:10           ` Michael Shulman
2019-11-04 23:26           ` David Roberts
2019-11-05 15:43           ` Daniel R. Grayson
2019-11-05 20:29             ` Yuhao Huang
2019-11-06 23:59               ` Daniel R. Grayson
2019-11-05 23:14           ` Martín Hötzel Escardó
2019-11-06  0:06             ` Stefan Monnier [this message]
2019-11-11 18:26               ` Licata, Dan
2019-11-03  7:29 ` Michael Shulman

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