From: Michael Shulman <shulman@sandiego.edu>
To: Nils Anders Danielsson <nad@cse.gu.se>
Cc: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] doing "all of pure mathematics" in type theory
Date: Tue, 28 May 2019 03:22:48 -0700 [thread overview]
Message-ID: <CAOvivQyPDzzjLEQfB=C5jQSH8wzFpr=gG8E_4BSWaBtb95mg3w@mail.gmail.com> (raw)
In-Reply-To: <9232f85a-6d64-84dc-a2d0-290c0fc6e760@cse.gu.se>
Of course Agda is a real-world proof assistant, but its cubical mode
is still new and experimental, so I was counting it as a "prototype".
But I suppose that's not really fair, since unlike a custom-developed
prototype it presumably benefits from all the usability superstructure
of Agda. Sorry!
On Tue, May 28, 2019 at 3:13 AM Nils Anders Danielsson <nad@cse.gu.se> wrote:
>
> On 28/05/2019 11.50, Michael Shulman wrote:
> > More modern homotopy type theories, which are generally based on
> > cubical structures, allow univalence to be "executed" by the system.
> > However, these systems lack (so far) all the intended categorical
> > semantics (see below), and haven't yet been implemented in "real
> > world" proof assistants (though there are prototypes now in use and
> > development).
>
> The latest release of Agda can be used in cubical mode, and supports
> both univalence and higher inductive types. (As well as things like
> higher inductive-coinductive-recursive types that may not have a proper
> explanation.)
>
> --
> /NAD
>
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next prev parent reply other threads:[~2019-05-28 10:23 UTC|newest]
Thread overview: 31+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-05-25 10:12 Kevin Buzzard
2019-05-25 10:22 ` Steve Awodey
2019-05-25 12:23 ` Kevin Buzzard
[not found] ` <B7D67BBA-5E0B-4438-908D-4EF316C8C1F1@chalmers.se>
[not found] ` <CAH52Xb1Y=Xq=012v_-KSDUuwgnKpEp5qjrxgtUJf+qc_0RWJUg@mail.gmail.com>
2019-05-25 13:13 ` Fwd: " Kevin Buzzard
2019-05-25 13:34 ` Juan Ospina
2019-05-25 14:50 ` Noah Snyder
2019-05-25 15:36 ` Kevin Buzzard
2019-05-25 16:41 ` Noah Snyder
2019-05-26 5:50 ` Bas Spitters
2019-05-26 11:41 ` Kevin Buzzard
2019-05-26 12:09 ` Bas Spitters
2019-05-26 17:00 ` Kevin Buzzard
2019-05-27 2:33 ` Daniel R. Grayson
2019-06-02 16:30 ` Bas Spitters
2019-06-02 17:55 ` Kevin Buzzard
2019-06-02 20:46 ` Nicola Gambino
2019-06-02 20:59 ` Valery Isaev
2019-06-04 20:32 ` Michael Shulman
2019-06-04 20:58 ` Kevin Buzzard
2019-06-06 16:30 ` Matt Oliveri
2019-05-27 13:09 ` Assia Mahboubi
2019-05-28 9:50 ` Michael Shulman
2019-05-28 10:13 ` Nils Anders Danielsson
2019-05-28 10:22 ` Michael Shulman [this message]
2019-05-29 19:04 ` Martín Hötzel Escardó
2019-05-30 17:14 ` Michael Shulman
2019-06-02 17:49 ` Kevin Buzzard
2019-06-04 20:50 ` Martín Hötzel Escardó
2019-06-05 17:11 ` Thorsten Altenkirch
2019-05-28 15:20 ` Joyal, André
2019-05-27 8:41 ` Nils Anders Danielsson
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