From: Thorsten Altenkirch <Thorsten.Altenkirch@nottingham.ac.uk>
To: "Thomas Streicher" <streicher@mathematik.tu-darmstadt.de>,
"Martín Hötzel Escardó" <escardo.martin@gmail.com>
Cc: Homotopy Type Theory <homotopytypetheory@googlegroups.com>
Subject: Re: [HoTT] Re: Why do we need judgmental equality?
Date: Sat, 9 Feb 2019 13:29:25 +0000 [thread overview]
Message-ID: <FA7148AD-49C2-4E35-85C7-1BD450FAB679@nottingham.ac.uk> (raw)
In-Reply-To: <20190209113816.GA17951@mathematik.tu-darmstadt.de>
Even LF included beta eta hence has a non-trivial judgemental equality. Not to mention the equations for substitution.
Thorsten
On 09/02/2019, 11:38, "homotopytypetheory@googlegroups.com on behalf of Thomas Streicher" <homotopytypetheory@googlegroups.com on behalf of streicher@mathematik.tu-darmstadt.de> wrote:
Working without any judgemental equality was the aim of the original
LF where elements of a type A correspond to formal derivations of A in
abstract syntax. Also Isabelle works a bit like that.
So with a modicum of judgemental equality one uses dependent types for
having a syntax for formal derivations. But, of course, this is
absolutely useless when you want to execute your proofs!
Thomas
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next prev parent reply other threads:[~2019-02-09 13:29 UTC|newest]
Thread overview: 71+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-01-30 11:54 [HoTT] " Felix Rech
2019-02-05 23:00 ` [HoTT] " Matt Oliveri
2019-02-06 4:13 ` Anders Mörtberg
2019-02-09 11:55 ` Felix Rech
2019-02-16 15:59 ` Thorsten Altenkirch
2019-02-17 1:25 ` Michael Shulman
2019-02-17 7:56 ` Thorsten Altenkirch
2019-02-17 9:14 ` Matt Oliveri
2019-02-17 9:18 ` Michael Shulman
2019-02-17 10:52 ` Thorsten Altenkirch
2019-02-17 11:35 ` streicher
2019-02-17 11:44 ` Thorsten Altenkirch
2019-02-17 14:24 ` Bas Spitters
2019-02-17 19:36 ` Thomas Streicher
2019-02-17 21:41 ` Thorsten Altenkirch
2019-02-17 12:08 ` Matt Oliveri
2019-02-17 12:13 ` Matt Oliveri
2019-02-20 0:22 ` Michael Shulman
2019-02-17 14:22 ` [Agda] " Andreas Abel
2019-02-17 9:05 ` Matt Oliveri
2019-02-17 13:29 ` Nicolai Kraus
2019-02-08 21:19 ` Martín Hötzel Escardó
2019-02-08 23:31 ` Valery Isaev
2019-02-09 1:41 ` Nicolai Kraus
2019-02-09 8:04 ` Valery Isaev
2019-02-09 1:58 ` Jon Sterling
2019-02-09 8:16 ` Valery Isaev
2019-02-09 1:30 ` Nicolai Kraus
2019-02-09 11:38 ` Thomas Streicher
2019-02-09 13:29 ` Thorsten Altenkirch [this message]
2019-02-09 13:40 ` Théo Winterhalter
2019-02-09 11:57 ` Felix Rech
2019-02-09 12:39 ` Martín Hötzel Escardó
2019-02-11 6:58 ` Matt Oliveri
2019-02-18 17:37 ` Martín Hötzel Escardó
2019-02-18 19:22 ` Licata, Dan
2019-02-18 20:23 ` Martín Hötzel Escardó
2019-02-09 11:53 ` Felix Rech
2019-02-09 14:04 ` Nicolai Kraus
2019-02-09 14:26 ` Gabriel Scherer
2019-02-09 14:44 ` Jon Sterling
2019-02-09 20:34 ` Michael Shulman
2019-02-11 12:17 ` Matt Oliveri
2019-02-11 13:04 ` Michael Shulman
2019-02-11 15:09 ` Matt Oliveri
2019-02-11 17:20 ` Michael Shulman
2019-02-11 18:17 ` Thorsten Altenkirch
2019-02-11 18:45 ` Alexander Kurz
2019-02-11 22:58 ` Thorsten Altenkirch
2019-02-12 2:09 ` Jacques Carette
2019-02-12 11:03 ` Matt Oliveri
2019-02-12 15:36 ` Thorsten Altenkirch
2019-02-12 15:59 ` Matt Oliveri
2019-02-11 19:27 ` Matt Oliveri
2019-02-11 21:49 ` Michael Shulman
2019-02-12 9:01 ` Matt Oliveri
2019-02-12 17:54 ` Michael Shulman
2019-02-13 6:37 ` Matt Oliveri
2019-02-13 10:01 ` Ansten Mørch Klev
2019-02-11 20:11 ` Matt Oliveri
2019-02-11 8:23 ` Matt Oliveri
2019-02-11 13:03 ` Jon Sterling
2019-02-11 13:22 ` Matt Oliveri
2019-02-11 13:37 ` Jon Sterling
2019-02-11 6:51 ` Matt Oliveri
2019-02-09 12:30 ` [HoTT] " Thorsten Altenkirch
2019-02-11 7:01 ` Matt Oliveri
2019-02-11 8:04 ` Valery Isaev
2019-02-11 8:28 ` Matt Oliveri
2019-02-11 8:37 ` Matt Oliveri
2019-02-11 9:32 ` Rafaël Bocquet
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