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FStar | dafny | |
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42 | 31 | |
2,562 | 2,665 | |
1.2% | 1.5% | |
9.9 | 9.7 | |
7 days ago | 4 days ago | |
F* | C# | |
Apache License 2.0 | GNU General Public License v3.0 or later |
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FStar
- Lean4 helped Terence Tao discover a small bug in his recent paper
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The Deep Link Equating Math Proofs and Computer Programs
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/).
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If You've Got Enough Money, It's All 'Lawful'
Don't get me wrong, there are times when Microsoft got it right the first time that was technically far superior to their competitors. Windows IOCP was theoretically capable of doing C10K as far back in 1994-95 when there wasn't any hardware support yet and UNIX world was bickering over how to do asynchronous I/O. Years later POSIX came up with select which was a shoddy little shit in comparison. Linux caved in finally only as recently as 2019 and implemented io_uring. Microsoft research has contributed some very interesting things to computer science like Z3 SAT solver and in collaboration with INRIA made languages like F* and Low* for formal specification and verification. But all this dwarfs in comparison to all the harm they did.
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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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Why is there no simple C-like functional programming language?
F* is a dependently typed language that can be transpiled to idiomatic C via the KReMLin compiler. It’s very ML-ish to write and you can leave out some proofs. It also has the benefit of being used to write a formally verified TLS implementation that’s in wide use throughout industry.
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[Media] Genetic algorithm simulation - Smart rockets (code link in comments)
As I said, dependent types attempt to solve this problem. F* is a language where you can express complex logic as a type. The catch is, these types are checked by an SMT solver. If the solver can satisfy the type checking, then great, and you move on. If it can’t, you have no idea why, and either have to guess or manually write the proof anyway. Contrast this with Standard ML which has a proof of the soundness of its type system.
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Prop v0.42 released! Don't panic! The answer is... support for dependent types :)
So kind of like F*? https://www.fstar-lang.org/
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old languages compilers
F*
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Pegasus spyware was used to hack reporters’ phones. I’m suing its creators; When you’re infected by Pegasus, spies effectively hold a clone of your phone – we’re fighting back.
Nevermind that academia has come up with far safer ways to do a few things but social norms & inertia prevent their wider adoption (well okay, it also has a barrier to entry in the education required to use it but I don't think someone with the knowledge to meaningfully contribute to an OS kernel can be considered uneducated nor unable to learn).
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[Hobby] Amateur Generalist Programmer Seeking to Put Bugfixing Skills to Good Use
Maybe that's a little off topic here, but if you like fixing bugs, i suspect you might also enjoy showing that there are no bugs at all. Check out languages like F* https://www.fstar-lang.org/ It's a proof-oriented programming language. You can use it to write code that has no bugs at all. And you once you're done, can convert F* to C or other languages.
dafny
- Dafny is a verification-aware programming language
- Candy – a minimalistic functional programming language
- Dafny – a verification-aware programming language
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Lean4 helped Terence Tao discover a small bug in his recent paper
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
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The Deep Link Equating Math Proofs and Computer Programs
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
- The Dafny Programming and Verification Language
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In Which I Claim Rich Hickey Is Wrong
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
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Programming Languages Going Above and Beyond
> 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.
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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.
What are some alternatives?
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.
tlaplus - TLC is a model checker for specifications written in TLA+. The TLA+Toolbox is an IDE for TLA+.
lean - Lean Theorem Prover
rust - Rust for the xtensa architecture. Built in targets for the ESP32 and ESP8266
koka - Koka language compiler and interpreter
VisualFSharp - The F# compiler, F# core library, F# language service, and F# tooling integration for Visual Studio
Rust-for-Linux - Adding support for the Rust language to the Linux kernel.
stepmania - Advanced rhythm game for Windows, Linux and OS X. Designed for both home and arcade use.
interactive - .NET Interactive combines the power of .NET with many other languages to create notebooks, REPLs, and embedded coding experiences. Share code, explore data, write, and learn across your apps in ways you couldn't before.
SharpLab - .NET language playground
rust - Empowering everyone to build reliable and efficient software.