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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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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
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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.
- The seven programming ur-languages
- Rosenpass – formally verified post-quantum WireGuard
CompCert
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Differ: Tool for testing and validating transformed programs
A big problem is that proving that transformations preserve semantics is very hard. Formal methods has huge potential and I believe it will be a big part of the future, but it hasn't become mainstream yet. Probably a big reason why is that right now it's simply not practical: the things you can prove are much more limited than the things you can do, and it's a lot less work to just create a large testsuite.
Example: CompCert (https://compcert.org/), a formally-verified compiler AKA formally-verified sequence of semantics-preserving transformations from C code to Assembly. It's a great accomplishment, but few people are actually compiling their code with CompCert. Because GCC and LLVM are much faster[1], and have been used so widely that >99.9% of code is going to be compiled correctly, especially code which isn't doing anything extremely weird.
But as articles like this show, no matter how large a testsuite there may always be bugs, tests will never provide the kind of guarantees formal verification does.
[1] From CompCert, "Performance of the generated code is decent but not outstanding: on PowerPC, about 90% of the performance of GCC version 4 at optimization level 1"
- So you think you know C?
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Can the language of proof assistants be used for general purpose programming?
Also a C compiler (https://compcert.org/). I did exaggerate bit in saying that anything non-trivial is "nearly impossible".
However, both CompCert and sel4 took a few years to develop, whereas it would only take months if not weeks to make versions of both which aren't formally verified but heavily tested.
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A Guide to Undefined Behavior in C and C++
From my experience, while many MCUs have settled for the big compilers (GCC and Clang), DSPs and some FPGAs (not Intel and Xilinx, those have lately settled for Clang and a combination of Clang and GCC respectively) use some pretty bespoke compilers (just running ./ --version is enough to verify this, if the compiler even offers that option). That's not necessarily bad, since many of them offer some really useful features, but error messages can be really cryptic in some cases. Also some industries require use of verified compilers, like CompCert[1], and in such cases GCC and Clang just don't cut it.
- Rosenpass – formally verified post-quantum WireGuard
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OpenAI might be training its AI technology to replace some software engineers, report says
But that's fine, because we can do even better with things like the CompCert C compiler, which is formally proven to produce correct asm output for ISO C 2011 source. It's designed for high-reliability, safety-critical applications; it's used for things like Airbus A380 avionics software, or control software for emergency generators at nuclear power plants. Software that's probably not overly sophisticated and doesn't need to be highly optimized, but does need to work ~100% correctly, ~100% of the time.
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Checked C
Does anybody know how does this compare to https://compcert.org/ ?
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Is it possible to make C as safe as Rust?
There is. They're called formally verified compilers, and are used for safety critical applications: https://compcert.org/ https://github.com/AbsInt/CompCert
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New Coq tutorial
Hi all, Coq is a "proof assistant" that allows you to write both code and proofs in the same language (thanks to the Curry–Howard correspondence). Its uses range from pure math (e.g., the Feit–Thompson theorem was proven in Coq!) to reasoning about programming languages (e.g., proving the soundness of a type system) to writing verified code (e.g., this verified C compiler!). You can "extract" your code (without the proofs) to OCaml/Haskell/Scheme for running it in production. Coq is awesome, but it's known for having a steep learning curve (it's based on type theory, which is a foundational system of mathematics). It took me several years to become proficient in it. I wanted to help people pick it up faster than I did, so I wrote this introductory tutorial. Hope you find it useful!
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The Software Foundations: mathematical underpinnings of reliable software
Not an expert but I've heard formal methods are used in Chip Design. Also https://compcert.org/ a c compiler which uses formal verifcation. I tiored some exercises in the series. Its pretty interesting thing to do, but yes I don't think its great for rapid software development.
What are some alternatives?
coc.nvim - Nodejs extension host for vim & neovim, load extensions like VSCode and host language servers.
kok.nvim - Fast as FUCK nvim completion. SQLite, concurrent scheduler, hundreds of hours of optimization.
FStar - A Proof-oriented Programming Language
Agda - Agda is a dependently typed programming language / interactive theorem prover.
lean4 - Lean 4 programming language and theorem prover
coq.vim - Pathogen-compatible distribution of Vicent Aravantinos' vim scripts for Coq.
tlaplus - TLC is a model checker for specifications written in TLA+. The TLA+Toolbox is an IDE for TLA+.
coq-serapi - Coq Protocol Playground with Se(xp)rialization of Internal Structures.
mathlib - Lean 3's obsolete mathematical components library: please use mathlib4
CoqGym - A Learning Environment for Theorem Proving with the Coq proof assistant
seL4 - The seL4 microkernel
learn-you-a-haskell - “Learn You a Haskell for Great Good!” by Miran Lipovača