From: Peter LeFanu Lumsdaine <p.l.lu...@gmail.com>
To: Andrew Polonsky <andrew....@gmail.com>
Cc: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Re: Meta-conjecture about MLTT
Date: Mon, 12 Sep 2016 12:16:30 +0200 [thread overview]
Message-ID: <CAAkwb-nwqMiR3apOWZY-3kZF=gckguzZ6qQhdLHU5LrZrJFBng@mail.gmail.com> (raw)
In-Reply-To: <ca38369f-7691-46f7-8d00-2c944ec6e489@googlegroups.com>
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On Mon, Sep 12, 2016 at 7:20 AM, Andrew Polonsky <andrew....@gmail.com>
wrote:
> The meta-task is to either produce two isomorphic types in an empty
>> context, together with a property that one of them provably has but the
>> other doesn't, or to show that this is impossible.
>>
>
> What do you mean by a "property", exactly?
>
There’s also a difference in what you mean by a “type”, which is I think
the key difference between the argument I gave, and Andrew’s counterexample
(and others’).
The counterexamples show that there can be properties of *small* types,
i.e. type families [ X : U |— P(X) Type ], which can distinguish isomorphic
(small) types.
The construction I described shows that no property of *all* types — i.e.
no type [ . |— P(X) Type ], where X is a new base type, so any closed type
can be substituted for X — can distinguish isomorphic types.
–p.
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next prev parent reply other threads:[~2016-09-12 10:16 UTC|newest]
Thread overview: 17+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-09-11 20:47 Martin Escardo
2016-09-11 22:08 ` [HoTT] " Peter LeFanu Lumsdaine
2016-09-11 22:26 ` Martin Escardo
2016-09-12 9:11 ` Thomas Streicher
2016-09-12 5:20 ` Andrew Polonsky
2016-09-12 5:59 ` [HoTT] " Jason Gross
2016-09-12 9:55 ` Andrew Polonsky
2016-09-12 10:07 ` Andrew Polonsky
2016-09-12 10:35 ` Nicolai Kraus
2016-09-12 10:16 ` Peter LeFanu Lumsdaine [this message]
2016-09-12 10:44 ` [HoTT] " Nicolai Kraus
2016-09-12 11:02 ` Andrej Bauer
2016-09-12 11:14 ` Thomas Streicher
2016-09-12 11:23 ` Andrew Polonsky
2016-09-12 11:41 ` Thomas Streicher
2016-09-12 12:47 ` Thomas Streicher
2016-09-12 13:01 ` Martin Escardo
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