dafny
lean4
dafny | lean4 | |
---|---|---|
38 | 62 | |
3,116 | 5,941 | |
1.4% | 5.6% | |
9.5 | 10.0 | |
1 day ago | 6 days ago | |
C# | Lean | |
GNU General Public License v3.0 or later | Apache License 2.0 |
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For example, an activity of 9.0 indicates that a project is amongst the top 10% of the most actively developed projects that we are tracking.
dafny
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Long division verified via Hoare logic
Automation of Hoare logic is quite good these days. Dafny, from MS Research (https://dafny.org), is probably the most friendly formal language. Dafny has been used to verify large systems, including many components of AWS. I am hoping that LLMs make more advanced languages, such as Liquid Haskell or Agda, much easier to write. Ideally, lots of code should be autocompleted once a human provides a type signature. The advantage of formal verification is that we are sure the generated code is correct.
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Automated reasoning and generative AI: Harness creativity with formal verifications
Modern software verification employs various approaches, each offering different trade-offs between ease of use and strength of guarantees. AWS contributes to the open source program verification tools used in the previous examples. Dafny and Kani represent two powerful approaches to program verification. Let's see how they work in practice before connecting the dots between automated reasoning and generative AI.
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Playing Chess with 84,688 Regular Expressions
On that note, I discovered Dafny[1] recently, as a more accessible way to program with proofs. There's a companion book[2] that seems very accessible and down-to-earth (and, unfortunately, quite expensive). I didn't have the time to play with it yet, but it looks like it does what Ada/SPARK does (and more), but with less verbose syntax and more options for compilation targets. It seems to be actively developed, too. Personally, I had a very hard time getting into Coq, which is a proof assistant more than a programming environment - Dafny seems much more welcoming for a "working programmer" :)
[1] https://dafny.org/
[2] https://mitpress.mit.edu/9780262546232/program-proofs
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F*: A proof oriented general purpose programming language
https://dafny.org/ also allows proof checking and allows do write real programs with it. It has a java like syntax and is also from MS I believe
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Safer with Google: Advancing Memory Safety
> I do think there's a bit of the Ignaz Semmelweis[1] issue at hand here, where developers want to believe in their inherent quality and refuse processes that improve safety if it goes against their worldview
I think the problem is that other variables (not only safety) must be assessed beyond the pure "better". Haskell is very good also. Very correct. Who uses that, and where? And why? Why not everyone uses https://dafny.org/ ?
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Verified Rust for low-level systems code
For those that are interested but perhaps not aware in this similar project, Dafny is a "verification-aware programming language" that can compile to rust: https://github.com/dafny-lang/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
lean4
- Lean 4, Release v4.17.0
- Programming Language and Theorem Prover
- Lean: Programming Language and Theorem Prover
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LLMs don't do formal reasoning – and that is a problem
Correction, Lean4 [1] is sponsored by Amazon, the lead developer, Leonardo de Moura is at AWS now [2]. He was previously at Microsoft Research [3]. Meeting him is a real ride, I only had the chance to talk with him once.
[1] https://lean-lang.org/
[2] https://leodemoura.github.io/about.html
[3] https://www.microsoft.com/en-us/research/blog/the-inner-magi...
- Quantum Advantage for NP Approximation
- AI Will Become Mathematicians' 'Co-Pilot'
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The Fermat's Last Theorem Project
Lean is free and open source and nothing to do with MS. Check out https://lean-lang.org/ and https://github.com/leanprover/lean4 -- no mention of MS or MSR (where de Moura was where he developed Lean 3 and started on Lean 4).
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Dafny is a verification-aware programming language
Recently replaced by Lean, though.
https://github.com/cedar-policy/cedar-spec
https://lean-lang.org
- The Mechanics of Proof
- Natural Deduction in Logic (2015)
What are some alternatives?
tlaplus - TLC is a model checker for specifications written in TLA+. The TLA+Toolbox is an IDE for TLA+.
rocq - The Rocq Prover is an interactive theorem prover, or proof assistant. 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.
FStar - A Proof-oriented Programming Language
Agda - Agda is a dependently typed programming language / interactive theorem prover.
Rust-for-Linux - Adding support for the Rust language to the Linux kernel.
z3_tutorial - Jupyter notebooks for tutorial on the Z3 SMT solver