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FStar | lean | |
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42 | 4 | |
2,562 | 1,915 | |
1.2% | - | |
9.9 | 0.0 | |
5 days ago | over 3 years ago | |
F* | C++ | |
Apache License 2.0 | Apache License 2.0 |
Stars - the number of stars that a project has on GitHub. Growth - month over month growth in stars.
Activity is a relative number indicating how actively a project is being developed. Recent commits have higher weight than older ones.
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.
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.
lean
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Paper from 2021 claims P=NP with poorly specified algorithm for maximum clique using dynamical systems theory
Apparently, it even still segfaulted in 2018 https://github.com/leanprover/lean/issues/1958. I don't expect my tools to segfault.
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Low-level format file of mathlib
Does anyone happen to have the mathlib library in the [low-level format](https://github.com/leanprover/lean/blob/master/doc/export_format.md)? I've been trying to run lean --export to obtain it, but I keep getting various errors.
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Mathematics: our overlooked ability
I have spent a good deal of time trying to formalize elementary mathematics and computer science textbooks in the Lean Theorem Prover, and in trying to extend and improve Lean to make the process easier. I have been able to translate entire chapters of several textbooks into Lean in a natural way, with every line of Lean seemingly isomorphic to the informal presentation. However, once in a while I will hit a statement or proof step that may seem simple to me but that requires a major refactor, or adding new features to Lean itself, or just seems like a brick wall. My brain is able to perform massive refactorings of mathematical knowledge and abstractions, synthesize the equivalent of tens of thousands of lines of tricky and performance-critical software, and maybe even expand the logic I am effectively operating in, all in the blink of an eye.
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How do I get back into math?
However, mathlib makes some weird design choices. For example, (semi)groups are defined using multiplicative notation -- and then immediately followed by an entire section giving the exact same definitions using additive notation! The claimed reason for this is that the more abstract approach is inconvenient for automation. I did it in Coq using the abstract approach, and indeed, noticed that doing so broke automation, which I then worked around in various ways. But it's just weird to me as a mathematician to have additive and multiplicative groups be different objects, so I wouldn't want to do it the Lean way come hell or high water. The Lean approach causes practical difficulties as well: you have to prove every theorem about groups twice. In some cases (e.g. product groups), you have to prove every theorem FOUR times. Ugh.
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.
Agda - Agda is a dependently typed programming language / interactive theorem prover.
dafny - Dafny is a verification-aware programming language
Coq-HoTT - A Coq library for Homotopy Type Theory
koka - Koka language compiler and interpreter
CoqGym - A Learning Environment for Theorem Proving with the Coq proof assistant
VisualFSharp - The F# compiler, F# core library, F# language service, and F# tooling integration for Visual Studio
arend-lib
stepmania - Advanced rhythm game for Windows, Linux and OS X. Designed for both home and arcade use.
ttlite - A SuperCompiler for Martin-Löf's Type Theory
SharpLab - .NET language playground
daisy-nfsd - DaisyNFS is an NFS server verified using Dafny and Perennial.