From: Vladimir Voevodsky <vlad...@ias.edu>
To: Michael Shulman <shu...@sandiego.edu>
Cc: "Prof. Vladimir Voevodsky" <vlad...@ias.edu>,
Andrej Bauer <andrej...@andrej.com>,
Homotopy Type Theory <homotopyt...@googlegroups.com>
Subject: Re: [HoTT] a new transport rule
Date: Tue, 26 Jul 2016 11:07:27 +0300 [thread overview]
Message-ID: <92AF5F3E-2770-457F-A2DA-65C9A784660D@ias.edu> (raw)
In-Reply-To: <CAOvivQyborM0Dc6wWEdVCEVUC+yCTWsqtGZGgu-W=A28T61yzQ@mail.gmail.com>
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The semantics is the strict equality.
> On Jul 22, 2016, at 2:08 PM, Michael Shulman <shu...@sandiego.edu> wrote:
>
> Thanks! I see.
>
> But I must admit I don't immediately see a use for such a transport
> rule (or how to give it any semantics).
>
> On Fri, Jul 22, 2016 at 7:00 AM, Andrej Bauer <andrej...@andrej.com> wrote:
>> On Wed, Jul 20, 2016 at 11:10 AM, Michael Shulman <shu...@sandiego.edu> wrote:
>>> Can you give an example of such a P which becomes well-formed when A
>>> and B are substituted for X but is not well-formed with X as a
>>> variable?
>>
>> Let
>>
>> T := Universe
>>
>> nat : Universe
>> Nat type
>> El nat = Nat
>> 42 : Nat
>>
>> P(X) := Id (El X) 42 42
>>
>> Then P(nat) is well-formed, but P(X) is not. Or, if you dislike universes:
>>
>> T := bool
>>
>> P(X) := Id (match X with true => Nat | false => (Nat -> Nat) end) 42 42
>>
>> Now P(true) is well formed, but P(X) is not.
>>
>> With kind regards,
>>
>> Andrej
>>
>> --
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next prev parent reply other threads:[~2016-07-26 8:07 UTC|newest]
Thread overview: 11+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-07-19 17:18 FOMUS slides Vladimir Voevodsky
2016-07-19 18:16 ` [HoTT] " Michael Shulman
2016-07-19 19:28 ` Vladimir Voevodsky
2016-07-19 19:29 ` Michael Shulman
[not found] ` <7DACC421-37E7-43CC-B61F-D6C5F99921DF@ias.edu>
[not found] ` <CAOvivQzSs5=e=EEfP42nmDJUogkx7TjrAtYJqAEOFHetcPSZtA@mail.gmail.com>
[not found] ` <1B8618C8-0499-4D96-BACF-9AA4623061B9@ias.edu>
[not found] ` <CAOvivQzg_saqj7re-OCTFUFJceKab_eBR+X+OckFYe6fmkuVsQ@mail.gmail.com>
2016-07-20 8:44 ` a new transport rule Vladimir Voevodsky
2016-07-20 9:10 ` [HoTT] " Michael Shulman
2016-07-22 10:00 ` Andrej Bauer
2016-07-22 11:08 ` Michael Shulman
2016-07-26 8:07 ` Vladimir Voevodsky [this message]
2016-07-22 12:22 ` andré hirschowitz
2016-07-20 6:07 ` [HoTT] FOMUS slides Andrew Polonsky
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