From: Ambrus Kaposi <kaposi...@gmail.com>
To: Altenkirch Thorsten <Thorsten....@nottingham.ac.uk>
Cc: shu...@sandiego.edu, homotopyt...@googlegroups.com
Subject: Re: [HoTT] Where is the problem with initiality?
Date: Thu, 24 May 2018 11:53:17 +0200 [thread overview]
Message-ID: <CACSS4jkJHOO9frDMCTmjELf8Lsnote3isPPbEN2NFhgErj+qXA@mail.gmail.com> (raw)
In-Reply-To: <D72C2F89.ABB6D%psztxa@exmail.nottingham.ac.uk>
On Thu, May 24, 2018 at 10:11 AM Thorsten Altenkirch <
Thorsten....@nottingham.ac.uk> wrote:
> >>(5) and (7) introduce preterms which I think shouldn't be considered
> >> fundamental in the definition of type theory.
> >
> >I have to disagree here. In my view, we have to eventually connect
> >things back to untyped syntax, because untyped syntax is what we write
> >on the page, and what we enter into a proof assistant. (We don't need
> >to go all the way back to character strings -- parsing and lexing are
> >essentially solved problems in any language -- but we do need to get
> >back to some kind of untyped *abstract* syntax such as in (5).) The
> >various kinds of typed syntax are useful and important intermediate
> >objects, but at some point there has to be a step that formally
> >explains how to produce "typed syntax" from untyped syntax.
> Indeed but also type checking and scoping are solved problems.
Just to clarify this: you don't need to go through preterms and typing
relations to do type checking. You can write an algorithm which takes
untyped terms (without explicit substitutions) and returns intrinsic
(well-typed) terms. It only needs conversion checking for intrinsic terms
which is also a solved problem. Here is an example implementation:
https://bitbucket.org/akaposi/tt-in-tt/src/HEAD/Typecheck.agda
next prev parent reply other threads:[~2018-05-24 9:53 UTC|newest]
Thread overview: 57+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-05-22 5:46 Michael Shulman
2018-05-22 16:47 ` Ambrus Kaposi
2018-05-23 16:26 ` [HoTT] " Thorsten Altenkirch
2018-05-24 5:52 ` Michael Shulman
2018-05-24 8:11 ` Thorsten Altenkirch
2018-05-24 9:53 ` Ambrus Kaposi [this message]
2018-05-24 17:26 ` Michael Shulman
2018-05-26 9:21 ` Thomas Streicher
2018-05-26 11:47 ` Michael Shulman
2018-05-26 16:47 ` stre...
2018-05-27 5:14 ` Bas Spitters
2018-05-28 22:39 ` Michael Shulman
2018-05-29 9:15 ` [HoTT] " Thorsten Altenkirch
2018-05-29 15:15 ` Michael Shulman
2018-05-30 9:33 ` Thomas Streicher
2018-05-30 9:37 ` Thorsten Altenkirch
2018-05-30 10:10 ` Thomas Streicher
2018-05-30 12:08 ` Thorsten Altenkirch
2018-05-30 13:40 ` Thomas Streicher
2018-05-30 14:38 ` Thorsten Altenkirch
2018-05-30 10:53 ` Alexander Kurz
2018-05-30 12:05 ` Thorsten Altenkirch
2018-05-30 19:07 ` Michael Shulman
2018-05-31 10:06 ` Thorsten Altenkirch
2018-05-31 11:05 ` Michael Shulman
2018-05-31 19:02 ` Alexander Kurz
2018-06-01 9:55 ` Martin Escardo
2018-06-01 17:07 ` Martín Hötzel Escardó
2018-06-01 17:43 ` Eric Finster
2018-06-01 19:55 ` Martín Hötzel Escardó
2018-06-01 20:59 ` András Kovács
2018-06-01 21:06 ` Martín Hötzel Escardó
2018-06-01 21:23 ` Michael Shulman
2018-06-01 21:53 ` Eric Finster
2018-06-01 22:09 ` Michael Shulman
2018-06-02 15:06 ` Eric Finster
2018-06-05 20:04 ` Michael Shulman
2018-06-02 5:13 ` Thomas Streicher
2018-06-01 21:52 ` Jasper Hugunin
2018-06-01 22:00 ` Eric Finster
2018-06-01 21:27 ` Matt Oliveri
2018-06-02 5:21 ` Ambrus Kaposi
2018-06-02 6:01 ` Thomas Streicher
2018-06-02 14:35 ` Thorsten Altenkirch
2018-05-30 13:30 ` Jon Sterling
2018-06-05 7:52 ` Andrej Bauer
2018-06-05 8:37 ` David Roberts
2018-06-05 9:46 ` Gabriel Scherer
2018-06-05 22:19 ` Martín Hötzel Escardó
2018-06-05 22:54 ` Martín Hötzel Escardó
2018-06-05 22:12 ` Richard Williamson
2018-06-06 15:05 ` Thorsten Altenkirch
2018-06-06 19:25 ` Richard Williamson
2018-05-29 14:00 ` Jon Sterling
2018-05-30 22:35 ` Michael Shulman
2018-05-31 10:48 ` Martín Hötzel Escardó
2018-05-31 11:09 ` Michael Shulman
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