Idris2 VS dafny

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

Code correctness is a lost art. I requirement to think in abstractions is what scares a lot of devs to avoid it. The higher abstraction language (formal specs) focus on a dedicated language to describe code, whereas lower abstractions (code contracts) basically replace validation logic with a better model.

C# once had Code Contracts[1]; a simple yet powerful way to make formal specifications. The contracts was checked at compile time using the Z3 SMT solver[2]. It was unfortunately deprecated after a few years[3] and once removed from the .NET Runtime it was declared dead.

The closest thing C# now have is probably Dafny[4] while the C# dev guys still try to figure out how to implement it directly in the language[5].

[1] https://www.microsoft.com/en-us/research/project/code-contra...

[2] https://github.com/Z3Prover/z3

[3] https://github.com/microsoft/CodeContracts

[4] https://github.com/dafny-lang/dafny

[5] https://github.com/dotnet/csharplang/issues/105

I don't think something that specific exists. There are a very large number of formal methods tools, each with different specialties / domains.

For verification with proof assistants, [Software Foundations](https://softwarefoundations.cis.upenn.edu/) and [Concrete Semantics](http://concrete-semantics.org/) are both solid.

For verification via model checking, you can check out [Learn TLA+](https://learntla.com/), and the more theoretical [Specifying Systems](https://lamport.azurewebsites.net/tla/book-02-08-08.pdf).

For more theory, check out [Formal Reasoning About Programs](http://adam.chlipala.net/frap/).

And for general projects look at [F*](https://www.fstar-lang.org/) and [Dafny](https://dafny.org/).

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

> I think we can assume it won't be as efficient has hand written code

Actually, surprisingly, not necessarily the case!

If you'll refer to the discussion in https://github.com/dafny-lang/dafny/issues/601 and in https://github.com/dafny-lang/dafny/issues/547, Dafny can statically prove that certain compiler branches are not possible and will never be taken (such as out-of-bounds on index access, logical assumptions about whether a value is greater than or less than some other value, etc). This lets you code in the assumptions (__assume in C++ or unreachable_unchecked() under rust) that will allow the compiler to optimize the codegen using this information.

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.