Agda VS coq

Compare Agda vs coq and see what are their differences.

Agda

Agda is a dependently typed programming language / interactive theorem prover. (by agda)

coq

Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs. (by coq)
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Agda coq
27 87
2,403 4,676
1.3% 1.4%
9.8 10.0
4 days ago 4 days ago
Haskell OCaml
MIT License GNU Lesser General Public License v3.0 only
The number of mentions indicates the total number of mentions that we've tracked plus the number of user suggested alternatives.
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.
For example, an activity of 9.0 indicates that a project is amongst the top 10% of the most actively developed projects that we are tracking.

Agda

Posts with mentions or reviews of Agda. We have used some of these posts to build our list of alternatives and similar projects. The last one was on 2023-07-11.
  • Types versus sets (and what about categories?)
    1 project | news.ycombinator.com | 31 Aug 2023
    This was recently deemed inappropriate:

    "Bye bye Set"

    "Set and Prop are removed as keywords"

    https://github.com/agda/agda/pull/4629

  • 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.
  • What can Category Theory do?
    2 projects | /r/askmath | 22 Jun 2023
    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.
  • What are the current hot topics in type theory and static analysis?
    15 projects | /r/ProgrammingLanguages | 8 May 2023
    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.
  • Amendmend proposal: Changed syntax for Or patterns
    2 projects | /r/haskell | 14 Apr 2023
    Does this come with plans to separately unify the body with each of the contexts induced by matching on each of the respective patterns (similar to what’s discussed here), or will it behave like the _ pattern and use only the most general context?
  • Functional Programming and Maths <|> How can a code monkey learn Agda?
    1 project | /r/functionalprogramming | 26 Mar 2023
    That's absolutely untrue. From the horse's mouth:
  • Doom emacs and agda-mode
    2 projects | /r/emacs | 22 Mar 2023
  • FP language idea - would this is possible to infer and type check?
    1 project | /r/haskell | 26 Jan 2023
    Agda has the so-called mixfix operators (which are powerful enough to cover pre/in/postfix cases with an arbitrary number of arguments), check that out: - https://agda.readthedocs.io/en/v2.6.1/language/mixfix-operators.html - https://github.com/agda/agda/blob/master/examples/Introduction/Operators.agda - https://github.com/agda/agda-stdlib/blob/master/src/Data/Product/Base.agda
  • Best Programming Language for Computational Proof
    3 projects | /r/math | 21 Jan 2023
    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.
  • Do you use Idris or Coq, and why?
    3 projects | /r/haskell | 16 Nov 2022
    Funny that you say this, because there are some obvious long standing open feature requests with looking up the type of the term under cursor — № 4295 and № 516. I am not blaming anyone in particular — this is the way it is. I wish I could find time to rewrite the proof search engine (how hard can it be), but I am already buried under a pile of other commitments and a good chunk of overwhelming sadness.

coq

Posts with mentions or reviews of coq. We have used some of these posts to build our list of alternatives and similar projects. The last one was on 2023-12-26.
  • 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/

  • What are the current hot topics in type theory and static analysis?
    15 projects | /r/ProgrammingLanguages | 8 May 2023
    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.

What are some alternatives?

When comparing Agda and coq you can also consider the following projects:

lean - Lean Theorem Prover

coc.nvim - Nodejs extension host for vim & neovim, load extensions like VSCode and host language servers.

open-typerep - Open type representations and dynamic types

kok.nvim - Fast as FUCK nvim completion. SQLite, concurrent scheduler, hundreds of hours of optimization.

HoleyMonoid - Automatically exported from code.google.com/p/monoid-cont

FStar - A Proof-oriented Programming Language

distributive - Dual Traversable

lean4 - Lean 4 programming language and theorem prover

tlaplus - TLC is a model checker for specifications written in TLA+. The TLA+Toolbox is an IDE for TLA+.

agda-vim - Agda interaction in vim

coq.vim - Pathogen-compatible distribution of Vicent Aravantinos' vim scripts for Coq.

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