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coq | FStar | |
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87 | 42 | |
4,594 | 2,558 | |
1.2% | 1.0% | |
10.0 | 9.9 | |
3 days ago | 7 days ago | |
OCaml | F* | |
GNU Lesser General Public License v3.0 only | 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.
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coq
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Change of Name: Coq –> The Rocq Prover
The page summarizing the considered new names and their pros/cons is interesting: https://github.com/coq/coq/wiki/Alternative-names
Naming is hard...
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The First Stable Release of a Rust-Rewrite Sudo Implementation
Are those more important than, say:
- Proven with Coq, a formal proof management system: https://coq.inria.fr/
See in the real world: https://aws.amazon.com/security/provable-security/
And check out Computer-Aided Verification (CAV).
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Why Mathematical Proof Is a Social Compact
To be ruthlessly, uselessly pedantic - after all, we're mathematicians - there's reasonable definitions of "academic" where logical unsoundness is still academic if it never interfered with the reasoning behind any proofs of interest ;)
But: so long as we're accepting that unsoundness in your checker or its underlying theory are intrinsically deal breakers, there's definitely a long history of this, perhaps more somewhat more relevant than the HM example, since no proof checkers of note, AFAIK, have incorporated mutation into their type theory.
For one thing, the implementation can very easily have bugs. Coq itself certainly has had soundness bugs occasionally [0]. I'm sure Agda, Lean, Idris, etc. have too, but I've followed them less closely.
But even the underlying mathematics have been tricky. Girard's Paradox broke Martin-Löf's type theory, which is why in these dependently typed proof assistants you have to deal with the bizarre "Tower of Universes"; and Girard's Paradox is an analogue of Russell's Paradox which broke more naive set theories. And then Russell himself and his system of universal mathematics was very famously struck down by Gödel.
But we've definitely gotten it right this time...
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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+.
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If given a list of properties/definitions and relationship between them, could a machine come up with (mostly senseless, but) true implications?
Still, there are many useful tools based on these ideas, used by programmers and mathematicians alike. What you describe sounds rather like Datalog (e.g. Soufflé Datalog), where you supply some rules and an initial fact, and the system repeatedly expands out the set of facts until nothing new can be derived. (This has to be finite, if you want to get anywhere.) In Prolog (e.g. SWI Prolog) you also supply a set of rules and facts, but instead of a fact as your starting point, you give a query containing some unknown variables, and the system tries to find an assignment of the variables that proves the query. And finally there is a rich array of theorem provers and proof assistants such as Agda, Coq, Lean, and Twelf, which can all be used to help check your reasoning or explore new ideas.
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Functional Programming in Coq
What ever happened to the effort [1] to rename Coq in order to make it less offensive? There were a number of excellent proposals [2] that seemed to die on the vine.
[1] https://github.com/coq/coq/wiki/Alternative-names
[2] https://github.com/coq/coq/wiki/Alternative-names#c%E1%B5%A3...
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Mark Petruska has requested 250000 Algos for the development of a Coq-avm library for AVM version 8
Information about the Coq proof assistant: https://coq.inria.fr/ , https://en.wikipedia.org/wiki/Coq
- How are people like Andrew Wiles and Grigori Perelman able to work on popular problems for years without others/the research community discovering the same breakthroughs? Is it just luck?
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Basic SAT model of x86 instructions using Z3, autogenerated from Intel docs
This type of thing can help you formally verify code.
So, if your proof is correct, and your description of the (language/CPU) is correct, you can prove the code does what you think it does.
Formal proof systems are still growing up, though, and they are still pretty hard to use. See Coq for an introduction: https://coq.inria.fr/
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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.
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.
What are some alternatives?
coc.nvim - Nodejs extension host for vim & neovim, load extensions like VSCode and host language servers.
lean - Lean Theorem Prover
kok.nvim - Fast as FUCK nvim completion. SQLite, concurrent scheduler, hundreds of hours of optimization.
dafny - Dafny is a verification-aware programming language
Agda - Agda is a dependently typed programming language / interactive theorem prover.
koka - Koka language compiler and interpreter
lean4 - Lean 4 programming language and theorem prover
stepmania - Advanced rhythm game for Windows, Linux and OS X. Designed for both home and arcade use.
tlaplus - TLC is a model checker for specifications written in TLA+. The TLA+Toolbox is an IDE for TLA+.
VisualFSharp - The F# compiler, F# core library, F# language service, and F# tooling integration for Visual Studio
coq.vim - Pathogen-compatible distribution of Vicent Aravantinos' vim scripts for Coq.
SharpLab - .NET language playground