Discussion of Homotopy Type Theory and Univalent Foundations
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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)
Message-ID: <bc0fb45d-fe21-4380-bfcb-70cc58fbeef2@googlegroups.com> (raw)
In-Reply-To: <CAJGt_zG+04Rfbs_py=PYkubbwzeYb0TRhhfek-RT663uVUo=-A@mail.gmail.com>

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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
>
>

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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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Discussion of Homotopy Type Theory and Univalent Foundations

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