From: "Jon Sterling" <firstname.lastname@example.org>
To: "'Martin Escardo' via Homotopy Type Theory"
Subject: Re: [HoTT] New theorem prover Arend is released
Date: Thu, 08 Aug 2019 08:20:23 -0400 [thread overview]
Message-ID: <email@example.com> (raw)
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.
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
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next prev 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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