Agda VS Coq

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... Source: 10 months ago

Haskell and Agda are probably the most obvious examples. Ocaml too, but it is much older, so its type system is not as categorical. There is also Idris, which is not as well-known but is very cool. Source: 10 months ago

Coq, Agda, Lean, Isabelle, and probably some others which are not coming to my mind at the moment, but those would be considered the major ones. Source: over 1 year ago

Safer doesn't mean better. You could proof program correctness, and get proven program with tools like Coq (https://news.ycombinator.com/) and Agda (https://wiki.portal.chalmers.se/agda/pmwiki.php). However, it leads to much higher cost of creating software than both C++ and Rust. It's a trade-off. A great thing about Rust is that the safety costs very little compared to Coq and Agda. Source: over 1 year ago

At the most extreme level, you disappear into a meditative solitary retreat for a couple of years to seek enlightenment, and when you emerge you're no longer a programmer who writes programs, you're a theorist who proves theorems in Agda, and you have transcended above things that are tainted by the inherent evil of the material plane like "side effects" and "business needs" and "delivery timelines" and "could you... Source: almost 2 years ago

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). - Source: Hacker News / 6 months ago

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;... - Source: Hacker News / 9 months ago

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... Source: 10 months ago

Information about the Coq proof assistant: https://coq.inria.fr/ , https://en.wikipedia.org/wiki/Coq. Source: 11 months ago

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/. - Source: Hacker News / 12 months ago