Coq Alternatives
Similar projects and alternatives to coq

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coq reviews and mentions

Doing theorem proving with Haskell
I you want to do proof with a similar and more dedicated language, you can give Coq a try: https://coq.inria.fr/

what if say that set is a function which takes in any object and spits out yes or no.
Sure we can. That's a common way to do it if your foundational theory is some version of type theory. For example, when you want to talk about sets in the Coq proof assistant (wich uses type theory as its foundational theory), this is exactly what you would do. Your "set of values of type T" would be something of the type T → Prop.

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!

Introducing the Ferrocene Language Specification
Is this similar to the Coq language system?

Ask HN: What developer tools would you like to see?
 A build system like Nix [1] but with a better user experience / more straightforward commandline tooling.
 A dependently typed programming language like Coq [2] (or Agda, Idris, Lean, etc.) that is sufficiently approachable to gain enough mindshare that companies start adopting it for missioncritical work.
 A version control system which scales to petabytes or more. Something that I could put large video files in without thinking twice about it. Something a large company could use for their monorepo—or even their data warehouse.
 A notetaking tool that allows me to organize notes in a graph with links between them (like a wiki), not as files and folders in a tree, which enforces the invariant that every note is transitively reachable from some "root" so I never lose a note.
 Something like Toast [3] but which is also designed for running services in production, not just local development and continuous integration. A unified way to run code in dev, test, and prod environments. A new k8s.
[3] https://github.com/stepchowfun/toast (shameless plug)

I solved collatz, but I have no idea how to write a paper.
Learn how to use a formal proof assistant. Coq and Agda are the most popular. Both allow you to write a proof as a program instead of as a paper, and provide various tools for formally checking your proof.
 An automatic theorem proving project

Proving the Validity of a Proof or Proof Method
If you're interested in learning about how to formalize proofs, you can to a certain extent handwave a formal argument of correctness or validity, but for a serious treatment, in the 21st century, you should be using a formal proof assistant such as Coq or Lean, that is to say, a computer program specifically written for the express purpose of formalizing mathematical proofs.
 ne vais pas mentir  ils ont une longueur d'avance sur nous les Incultes bouffeurs de cheetos

Are all programming languages Turing complete? What are the necessary features for a programming language to be turing complete?
Are there any useful Turingincomplete programming languages? Probably yes. Definitely no general purpose one, but there ought to some domainspecific programming language which is not TC. Depending on the definition, some present Coq to meet the criteria (apparently you can write a C compiler in it!)
 ¿Qué debería estudiar para alcanzar mi meta como investigador?
 Coq: The world’s best macro assembler? (2013)
 How does a proof assistant like Coq work?

Machine Readable Specifications at Scale
Systems I've used for this include https://agda.readthedocs.io/en/v2.6.0.1/gettingstarted/what... https://coq.inria.fr https://www.idrislang.org and https://isabelle.in.tum.de
An easier alternative is to try disproving the statement, by executing it on thousands of examples and seeing if any fail. That gives us less confidence than a full proof, but can still be better than traditional "there exists" tests. This is called property checking or propertybased testing. Systems I've used for this include https://hypothesis.works https://hackage.haskell.org/package/QuickCheck https://scalacheck.org and https://jsverify.github.io
 Ask HN: What technology is “cutting edge” in 2022?
Stats
coq/coq is an open source project licensed under GNU Lesser General Public License v3.0 only which is an OSI approved license.
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