Coq Alternatives

coq reviews and mentions

• Coq will be renamed into 'The Rocq Prover'
  1 project | news.ycombinator.com | 7 Aug 2024
• Change of Name: Coq –> The Rocq Prover
  3 projects | news.ycombinator.com | 26 Dec 2023

  The page summarizing the considered new names and their pros/cons is interesting: https://github.com/coq/coq/wiki/Alternative-names

  Naming is hard...

• The First Stable Release of a Rust-Rewrite Sudo Implementation
  7 projects | news.ycombinator.com | 6 Nov 2023

  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).

• Why Mathematical Proof Is a Social Compact
  1 project | news.ycombinator.com | 31 Aug 2023

  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...

  [0] https://github.com/coq/coq/issues/4294

• In Which I Claim Rich Hickey Is Wrong
  5 projects | news.ycombinator.com | 24 Jul 2023

  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+.

  https://dafny.org/

  https://whiley.org/

  https://www.idris-lang.org/

  https://isabelle.in.tum.de/

  https://leanprover.github.io/

  https://coq.inria.fr/

  http://lamport.azurewebsites.net/tla/tla.html

• If given a list of properties/definitions and relationship between them, could a machine come up with (mostly senseless, but) true implications?
  5 projects | /r/math | 11 Jul 2023

  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.

• Functional Programming in Coq
  2 projects | news.ycombinator.com | 21 Jun 2023

  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...

• Mark Petruska has requested 250000 Algos for the development of a Coq-avm library for AVM version 8
  3 projects | /r/AlgorandOfficial | 21 May 2023

  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?
  1 project | /r/math | 17 May 2023
• Basic SAT model of x86 instructions using Z3, autogenerated from Intel docs
  5 projects | news.ycombinator.com | 15 May 2023

  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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