From: Bas Spitters <email@example.com> To: Jon Sterling <firstname.lastname@example.org> 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: <email@example.com> 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 <firstname.lastname@example.org> 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 HomotopyTypeTheoryemail@example.com. > > 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 HomotopyTypeTheoryfirstname.lastname@example.org. > 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. 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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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