From: Niels van der Weide <email@example.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: <firstname.lastname@example.org> (raw)
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Some established applications of HITs outside of synthetic homotopy theory:
- Partiality monad, see "Partiality Revisited" by Altenkirch, Danielsson,
- 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,
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next prev parent 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
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