CoqGym
Idris2
CoqGym | Idris2 | |
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2 | 39 | |
370 | 2,401 | |
0.8% | 1.3% | |
3.6 | 9.5 | |
10 months ago | 6 days ago | |
Coq | Idris | |
GNU Lesser General Public License v3.0 only | GNU General Public License v3.0 or later |
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CoqGym
- Lean4 helped Terence Tao discover a small bug in his recent paper
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Discussion Thread
This has been an active area of research for a few years. See for example https://arxiv.org/abs/1905.09381. It's still immature as a field, and most results are essentially "we got basic stuff down but it hasn't gotten powerful enough to prove anything truly challenging" but it definitely exists and is being developed.
Idris2
- Idris2: A purely functional programming language with first class types
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Lean4 helped Terence Tao discover a small bug in his recent paper
Have you looked into Idris2 at all. While looking into these theorum provers, it always felt like they had an impedance mismatch with normal programming.
Idris2 portends to a general purpose language that also has a more advanced type system for the theorum proving.
https://github.com/idris-lang/Idris2
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How to Keep Lambda Calculus Simple
The original paper also does plain STLC first in section 2, and then adds dependent types in section 3. (And finally it adds the naturals in section 4.)
In the Idris2 github repository, Guillaume Allais goes a step further and shows a well-named version. There the types of terms and values are indexed by the list of names in the environment and the compiler checks that the manipulation of deBruin levels and indices is correct:
https://github.com/idris-lang/Idris2/blob/main/libs/papers/L...
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What are the current hot topics in type theory and static analysis?
Most of the proof assistants out there: Lean, Coq, Dafny, Isabelle, F*, Idris 2, and Agda. And the main concepts are dependent types, Homotopy Type Theory AKA HoTT, and Category Theory. Warning: HoTT and Category Theory are really dense, you're going to really need to research them.
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New video! 2022 in Programming Languages
Here's the full tab list: - https://tjpalmer.github.io/languish/ - https://blog.python.org/2022/10/python-3110-is-now-available.html - https://devblogs.microsoft.com/python/python-311-faster-cpython-team/ - https://github.com/tc39/proposals/blob/main/finished-proposals.md - https://devblogs.microsoft.com/typescript/ten-years-of-typescript/ - https://devblogs.microsoft.com/typescript/announcing-typescript-4-6/#cfa-destructured-discriminated-unions - https://devblogs.microsoft.com/typescript/announcing-typescript-4-9/#the-satisfies-operator - https://devblogs.microsoft.com/typescript/announcing-typescript-4-7/#go-to-source-definition - https://devblogs.microsoft.com/typescript/announcing-typescript-4-8/#build-watch-incremental-improvements - https://openjdk.org/projects/jdk/18/ - https://openjdk.org/projects/jdk/19/ - https://blog.jetbrains.com/clion/2022/07/july-2022-iso-cpp/ - https://en.wikipedia.org/wiki/C%2B%2B23 - https://en.cppreference.com/w/cpp/23 - https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2021/p2128r6.pdf - https://devblogs.microsoft.com/dotnet/announcing-dotnet-7/ - https://devblogs.microsoft.com/dotnet/welcome-to-csharp-11/ - https://devblogs.microsoft.com/dotnet/announcing-fsharp-7/ - https://learn.microsoft.com/en-us/dotnet/core/deploying/native-aot/ - https://go.dev/blog/go1.19 - https://go.dev/blog/go1.18 - https://thephd.dev/c23-is-coming-here-is-what-is-on-the-menu - https://thephd.dev/c23-is-coming-here-is-what-is-on-the-menu#n3017---embed - https://thephd.dev/c23-is-coming-here-is-what-is-on-the-menu#n3006--n3007---type-inference-for-object-definitions - https://www.php.net/archive/2022.php#2022-12-08-1 - https://wiki.php.net/rfc/dnf_types - https://blog.rust-lang.org/ - https://blog.rust-lang.org/2022/01/13/Rust-1.58.0.html#captured-identifiers-in-format-strings - https://blog.rust-lang.org/2022/02/24/Rust-1.59.0.html#inline-assembly - https://blog.rust-lang.org/2022/05/19/Rust-1.61.0.html#more-capabilities-for-const-fn - https://blog.rust-lang.org/2022/08/11/Rust-1.63.0.html#scoped-threads - https://blog.rust-lang.org/2022/11/03/Rust-1.65.0.html#generic-associated-types-gats - https://blog.jetbrains.com/kotlin/2022/06/kotlin-1-7-0-released/ - https://stat.ethz.ch/pipermail/r-announce/2022/000683.html - https://dart.dev/guides/whats-new - https://medium.com/dartlang/dart-2-18-f4b3101f146c - https://medium.com/dartlang/the-road-to-dart-3-afdd580fbefa - https://www.swift.org/blog/swift-5.6-released/ - https://www.swift.org/blog/swift-5.7-released/ - https://www.swift.org/blog/swift-language-updates-from-wwdc22/ - https://www.ruby-lang.org/en/news/2022/12/25/ruby-3-2-0-released/ - https://www.lua.org/news.html - https://www.scala-lang.org/blog/2022/09/05/scala-3.2.0-released.html - https://tjpalmer.github.io/languish/#y=mean&weights=issues%3D1%26pulls%3D0%26stars%3D1%26soQuestions%3D1&names=solidity%2Chaskell%2Cjulia%2Celixir%2Cclojure%2Cperl%2Cgroovy%2Cocaml%2Cgdscript%2Ccmake%2Cnix%2Cvisual+basic+.net - https://blog.soliditylang.org/ - https://downloads.haskell.org/~ghc/9.4.1/docs/users_guide/9.4.1-notes.html - https://julialang.org/blog/2022/08/julia-1.8-highlights/ - https://discourse.julialang.org/t/julia-v1-9-0-beta2-is-fast/92290 - https://elixir-lang.org/blog/2022/09/01/elixir-v1-14-0-released/ - https://elixir-lang.org/blog/2022/10/05/my-future-with-elixir-set-theoretic-types/ - https://clojure.org/news/2022/03/22/clojure-1-11-0 - https://godotengine.org/en/news/default/1 - https://ocaml.org/news/ocaml-5.0 - https://tjpalmer.github.io/languish/#y=mean&weights=issues%3D1%26pulls%3D0%26stars%3D1%26soQuestions%3D1&names=gdscript%2Czig%2Cpascal%2Cfortran%2Cnim%2Cf%23%2Ccommon+lisp%2Cwebassembly%2Ccrystal%2Ccython%2Cvala%2Cerlang%2Chaxe%2Cv%2Cd - https://ziglang.org/download/0.10.0/release-notes.html - https://ziglang.org/news/goodbye-cpp/ - https://nim-lang.org/blog.html - https://nim-lang.org/blog/2022/12/21/version-20-rc.html - https://www.erlang.org/news/157 - https://github.com/WebAssembly/proposals/commits/main - https://github.com/crystal-lang/crystal/releases - https://dlang.org/changelog/2.099.0.html - https://dlang.org/changelog/2.100.0.html - https://dlang.org/changelog/2.101.0.html - https://github.com/odin-lang/Odin/releases - https://gleam.run/news/ - https://gleam.run/news/gleam-v0.22-released/ - https://gleam.run/news/gleam-v0.24-released/ - https://github.com/idris-lang/Idris2/blob/102d7ebc18a9e881021ed4b05186cccda5274cbe/CHANGELOG.md - https://github.com/diku-dk/futhark/blob/master/CHANGELOG.md#02111 - https://grain-lang.org/blog/2022/06/06/new-release-grain-v0.5-durum/ - https://rescript-lang.org/blog/release-10-0-0 - https://www.roc-lang.org/ - https://simon.peytonjones.org/assets/pdfs/haskell-exchange-22.pdf - https://vale.dev/ - https://www.val-lang.dev/
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How to avoid right intendation?
Idris2 has a great syntax for this, see e.g. node018:
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Data types with Negation
I asked because it just baffles me any time I see a dependently typed language using unary numbers. I think to myself, "are these people even educated? Do they know about number systems?" I mean, cavemen were the last group using unary number system as their mainstay, and that was during the Paleolithic. Then they have issues open like this when they discuss optimizing those damn unaries. But this shouldn't even have been a problem for anyone even remotely related to programming! It's giving a terrible impression of dependently-typed languages. Getting rid of those should be the first step of popularizing them.
- I've learned this from Conor McBride on an SPLV'19 bus ride. A literary reference would be welcome.
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Altering behavior of runElab and macros outside of source code
addOne : Int -> EitherT String IO Int addOne x = pure $ x + 1 add : Int -> Int -> EitherT String IO Int add x y = pure $ x + y main : IO () main = do exportFn `{add} the (IO ()) $ exportFn `{addOne} -- `the (IO ())` is needed due to issue https://github.com/idris-lang/Idris2/issues/2851
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Managing world state for a imperative language with pure functions
The idea of world state is an attraction of the state that side effects change. I got the idea from Idris internals: https://github.com/idris-lang/Idris2/blob/main/libs/prelude/PrimIO.idr
What are some alternatives?
lean - Lean Theorem Prover
purescript - A strongly-typed language that compiles to JavaScript
coq - Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
rust-ordered-float
trepplein - Lean type-checker written in Scala.
lang-team - Home of the Rust lang team
mathlib - Lean 3's obsolete mathematical components library: please use mathlib4
idris - A Dependently Typed Functional Programming Language
lean-chat
rust - Empowering everyone to build reliable and efficient software.
symmetric_project
genType - Auto generation of idiomatic bindings between Reason and JavaScript: either vanilla or typed with TypeScript/FlowType.