Discussion of Homotopy Type Theory and Univalent Foundations
 help / color / mirror / Atom feed
From: Niels van der Weide <nnmvdw@gmail.com>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: [HoTT] Re: (Beginner's question) Uses of HITs beyond homotopy theory
Date: Thu, 8 Aug 2019 11:52:48 -0700 (PDT)	[thread overview]
Message-ID: <bc0fb45d-fe21-4380-bfcb-70cc58fbeef2@googlegroups.com> (raw)
In-Reply-To: <CAJGt_zG+04Rfbs_py=PYkubbwzeYb0TRhhfek-RT663uVUo=-A@mail.gmail.com>

[-- Attachment #1.1: Type: text/plain, Size: 1803 bytes --]

Some established applications of HITs outside of synthetic homotopy theory:
- Partiality monad, see "Partiality Revisited" by Altenkirch, Danielsson, 
and Kraus
- Type Theory in Type Theory, see 'Type Theory in Type Theory with Quotient 
Inductive Inductive Types' and 'Normalization by evaluation for dependent 
types' by Altenkirch and Kaposi
- Free algebraic structures, see HoTT book 6.11 and the paper "Finite Sets 
in Homotopy Type Theory" by Frumin, Geuvers, Gondelman, Van der Weide
- Patch theory, see 'Homotopical Patch Theory' by Angiuli, Morehouse, 
Licata, and Harper

On Thursday, August 8, 2019 at 8:33:06 PM UTC+2, Timothy Carstens wrote:
> Sorry for the broad & naive question. I'm a geometer by training but have 
> been working in compsci for most of my career (with lots of time spent in 
> Coq verifying programs).
> I've got a naive question that I hope isn't too inappropriate for this 
> list: can anyone suggest some papers that show applications of HITs? I'm 
> embarrassed to admit it, but I don't know any applications outside of 
> synthetic homotopy theory and higher categories.
> Perhaps categorical semantics? But even still I'm not personally aware of 
> any applied results from that domain (contrast with operational semantics; 
> but I am extremely ignorant, so please correct me!)
> All my best and apologies in advance if this is off-topic for this list,
> -t

You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group.
To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/bc0fb45d-fe21-4380-bfcb-70cc58fbeef2%40googlegroups.com.

[-- Attachment #1.2: Type: text/html, Size: 2446 bytes --]

  reply	other threads:[~2019-08-08 18:52 UTC|newest]

Thread overview: 6+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2019-08-08 18:32 [HoTT] " Timothy Carstens
2019-08-08 18:52 ` Niels van der Weide [this message]
2019-08-08 20:18 ` Steve Awodey
2019-08-08 21:49   ` Michael Shulman
2019-08-08 22:09     ` Timothy Carstens
2019-08-09 10:36       ` Thorsten Altenkirch

Reply instructions:

You may reply publicly to this message via plain-text email
using any one of the following methods:

* Save the following mbox file, import it into your mail client,
  and reply-to-all from there: mbox

  Avoid top-posting and favor interleaved quoting:

* Reply using the --to, --cc, and --in-reply-to
  switches of git-send-email(1):

  git send-email \
    --in-reply-to=bc0fb45d-fe21-4380-bfcb-70cc58fbeef2@googlegroups.com \
    --to=nnmvdw@gmail.com \
    --cc=HomotopyTypeTheory@googlegroups.com \


* If your mail client supports setting the In-Reply-To header
  via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).