lean4 VS Idris2

Recently replaced by Lean, though.

https://github.com/cedar-policy/cedar-spec

https://lean-lang.org

Nice read! Rust has pushed, and will continue to push, the limits of practical, bare metal, memory safe languages. And it's interesting to think about what's next, maybe eventually there will be some form of practical theorem proving "for the masses". Lean 4 looks great and has potential, but it's still mostly a language for mathematicians. There has been some research on AI constructed proofs, which could be the best of both worlds because then the type checker can verify that the AI generated code/proof is indeed correct. Tools like Kani are also a step forward in program correctness.

Yeah, I believe they said intend for it to be used as a general purpose programming language. I used it to complete Advent of Code last year.

There are some really interesting features for general purpose programming in there. For example: you can code updates to arrays in a functional style (change a value, get a new array back), but if the refcount is 1, it updates in place. This works for inductive types and structures, too. So I was able to efficiently use C-style arrays (O(1) update/lookup) while writing functional code. (paper: https://arxiv.org/abs/1908.05647 )

Another interesting feature is that the "do" blocks include mutable variables and for loops (with continue / break / return), that gets compiled down to monad operations. (paper: https://dl.acm.org/doi/10.1145/3547640 )

And I'm impressed that you can add to the syntax of the language, in the same way that the language is implemented, and then use that syntax in the next line of code. (paper: https://lmcs.episciences.org/9362/pdf ). There is an example in the source repository that adds and then uses a JSX-like syntax. (https://github.com/leanprover/lean4/blob/master/tests/playgr... )

My latest inspiration to use code to a) replace my video editor, b) learn the basics of EDM production and c) understand a few topics in higher maths. This might sound very strange given there are specialised tools for these jobs. There's iMovie / Adobe Premier for video, there's GarageBand and FL studio for music and old good pen and pencil for math proofs. But these tools have three big limitations. First they have a lot of idiosyncratic learning, you have to spend quite some time getting used to these tools and my experience is that this time is quite upsetting. In contrast, you only have to learn to code one, maybe spend a few hours getting used to the syntax of another language. I'm not sure if that's true for most people but it was true for me using the tools mentioned above and wanted a place to discuss and see other people ideas and experiments. The second issue is that all these custom-made tools, are not composing easily. I can't search for all math proofs that used a single theorem. I can't create a plugin for iMovie and apply it to all my videos. I can't pick easily pick a rhythm from the internet and build upon for fun. There's also the issue of costs and version control, all tools I'm using today are open source and my work is stored in my repositories. This way I can create branches and test my ideas and I'm also confident that I can work in these projects in years.

Dafny and Whiley are two examples with explicit verification support. Idris and other dependently typed languages should all be rich enough to express the required predicate but might not necessarily be able to accept a reasonable implementation as proof. Isabelle, Lean, Coq, and other theorem provers definitely can express the capability but aren't going to churn out much in the way of executable programs; they're more useful to guide an implementation in a more practical functional language but then the proof is separated from the implementation, and you could also use tools like TLA+.

https://dafny.org/

https://whiley.org/

https://www.idris-lang.org/

https://isabelle.in.tum.de/

https://leanprover.github.io/

https://coq.inria.fr/

http://lamport.azurewebsites.net/tla/tla.html

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

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...

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.

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/

Idris2 has a great syntax for this, see e.g. node018:

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.

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

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