Discussion of Homotopy Type Theory and Univalent Foundations
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From: "Jon Sterling" <jon@jonmsterling.com>
To: "'Martin Escardo' via Homotopy Type Theory"
	<HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] New theorem prover Arend is released
Date: Thu, 08 Aug 2019 08:20:23 -0400	[thread overview]
Message-ID: <06e24c98-7409-4e75-88ee-a6e1bb891e1e@www.fastmail.com> (raw)
In-Reply-To: <9d23061c-4b7a-4d69-9c22-f28261ad3b33@googlegroups.com>

Dear Valery,

Arend looks really impressive, especially the IDE features! I look forward to trying it. I like the little screen demos on the website.

We have been curious for some time if someone could begin to explain what type theory Arend implements --- I am not necessarily looking for something super precise, but it would be great to have a high-level gloss that would help experts in the semantics of HoTT understand where Arend's type theory lies. For instance, I can see that Arend uses an interval, but this interval seems to work a bit differently from the interval in some other type theories. Is there any note or document that explains some of the mathematics behind Arend?

Nice work! And I look forward to hearing and reading more.

Best,
Jon


On Tue, Aug 6, 2019, at 6:16 PM, Валерий Исаев wrote:
> Arend is a new theorem prover that have been developed at JetBrains 
> <https://www.jetbrains.com/> for quite some time. We are proud to 
> announce that the first version of the language was released! To learn 
> more about Arend, visit our site <https://arend-lang.github.io/>.
> 
> Arend is based on a version of homotopy type theory that includes some 
> of the cubical features. In particular, it has native higher inductive 
> types, including higher inductive-inductive types. It also has other 
> features which are necessary for a theorem prover such as universe 
> polymorphism and class system. We believe that a theorem prover should 
> be convenient to use. That is why we also developed a plugin for 
> IntelliJ IDEA <https://www.jetbrains.com/idea/> that turns it into a 
> full-fledged IDE for the Arend language. It implements many standard 
> features such as syntax highlighting, completion, auto import, and auto 
> formatting. It also has some language-specific features such as 
> incremental typechecking and various refactoring tools.
> 
> To learn more about Arend, you can check out the documentation 
> <https://arend-lang.github.io/documentation>. You can also learn a lot 
> from studying the standard library 
> <https://github.com/JetBrains/arend-lib>. It implements some basic 
> algebra, including localization of rings, and homotopy theory, 
> including joins, modalities, and localization of types.
> 
> Frequently asked questions (that nobody asked):
>  * Why do we need another theorem prover? We believe that a theorem 
> prover should be convenient to use. This means that it should have an 
> IDE comparable to that of mainstream programming languages. That is why 
> we implemented IntelliJ Arend 
> <https://arend-lang.github.io/about/intellij-features>. This also means 
> that the underlying theory should be powerful and expressive. That is 
> why Arend is based on homotopy type theory and has features such as an 
> impredicative type of propositions and a powerful class system.
>  * Does Arend have tactics? Not yet, but we are working on it.
>  * Does Arend have the canonicity property, i.e. does it evaluate 
> closed expressions to their canonical forms? No, but it computes more 
> terms than ordinary homotopy type theory, which makes it more 
> convenient in many aspects.
> If you want to know about language updates, you can follow us on 
> twitter <https://twitter.com/ArendLang>. Questions, suggestions, and 
> comments are welcome at google groups 
> <https://groups.google.com/forum/#!forum/arend-lang>.
> 
>  -- 
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  parent reply	other threads:[~2019-08-08 12:20 UTC|newest]

Thread overview: 20+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2019-08-06 22:16 Валерий Исаев
2019-08-07 15:01 ` Andrej Bauer
2019-08-07 22:13 ` Nicolai Kraus
2019-08-08  9:55   ` Valery Isaev
2019-08-10  9:47     ` Michael Shulman
2019-08-10 12:30       ` Valery Isaev
2019-08-10 12:37       ` Valery Isaev
2019-08-08 12:20 ` Jon Sterling [this message]
2019-08-08 12:29   ` Bas Spitters
2019-08-08 14:44     ` Valery Isaev
2019-08-08 15:11       ` Jon Sterling
2019-08-08 15:22         ` Valery Isaev
2019-08-10  9:42           ` Michael Shulman
2019-08-10 12:24             ` Valery Isaev
2019-08-10 23:37               ` Michael Shulman
2019-08-11 10:46                 ` Valery Isaev
2019-08-11 12:39                   ` Michael Shulman
2019-08-11 16:55                     ` Michael Shulman
2019-08-12 14:44                       ` Daniel R. Grayson
2019-08-12 17:32                         ` Michael Shulman

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