From: Bas Spitters <firstname.lastname@example.org> To: Jon Sterling <email@example.com> Cc: "'Martin Escardo' via Homotopy Type Theory" <HomotopyTypeTheory@googlegroups.com> Subject: Re: [HoTT] New theorem prover Arend is released Date: Thu, 8 Aug 2019 14:29:23 +0200 Message-ID: <CAOoPQuSLoX8gKy54NQM6SNoi43wVA0A1Ad59qKs6prULkh6zBw@mail.gmail.com> (raw) In-Reply-To: <firstname.lastname@example.org> I imagine it could be related to earlier discussions, but Valery will correct me: https://groups.google.com/forum/#!topic/homotopytypetheory/N8jw_5h2Qjs https://valis.github.io/doc.pdf On Thu, Aug 8, 2019 at 2:20 PM Jon Sterling <email@example.com> wrote: > > 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>. > > > > -- > > 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 HomotopyTypeTheoryfirstname.lastname@example.org. > > To view this discussion on the web visit > > https://groups.google.com/d/msgid/HomotopyTypeTheory/9d23061c-4b7a-4d69-9c22-f28261ad3b33%40googlegroups.com <https://groups.google.com/d/msgid/HomotopyTypeTheory/9d23061c-4b7a-4d69-9c22-f28261ad3b33%40googlegroups.com?utm_medium=email&utm_source=footer>. > > -- > 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 HomotopyTypeTheoryemail@example.com. > To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/06e24c98-7409-4e75-88ee-a6e1bb891e1e%40www.fastmail.com. -- 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 HomotopyTypeTheoryfirstname.lastname@example.org. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/CAOoPQuSLoX8gKy54NQM6SNoi43wVA0A1Ad59qKs6prULkh6zBw%40mail.gmail.com.
next prev parent reply index 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 2019-08-08 12:29 ` Bas Spitters [this message] 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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