Agda VS lean4

Compare Agda vs lean4 and see what are their differences.

Agda

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

lean4

Lean 4 programming language and theorem prover (by leanprover)
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Agda lean4
27 56
2,399 3,951
1.2% 5.4%
9.8 10.0
7 days ago 6 days ago
Haskell Lean
MIT License Apache License 2.0
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.

lean4

Posts with mentions or reviews of lean4. We have used some of these posts to build our list of alternatives and similar projects. The last one was on 2024-06-12.
  • AI Will Become Mathematicians' 'Co-Pilot'
    5 projects | news.ycombinator.com | 12 Jun 2024
  • The Fermat's Last Theorem Project
    2 projects | news.ycombinator.com | 1 May 2024
    Lean is free and open source and nothing to do with MS. Check out https://lean-lang.org/ and https://github.com/leanprover/lean4 -- no mention of MS or MSR (where de Moura was where he developed Lean 3 and started on Lean 4).
  • Dafny is a verification-aware programming language
    4 projects | news.ycombinator.com | 23 Apr 2024
    Recently replaced by Lean, though.

    https://github.com/cedar-policy/cedar-spec

    https://lean-lang.org

  • The Mechanics of Proof
    2 projects | news.ycombinator.com | 20 Mar 2024
  • Natural Deduction in Logic (2015)
    1 project | news.ycombinator.com | 11 Jan 2024
  • The Wizardry Frontier
    2 projects | /r/rust | 10 Dec 2023
    Nice read! Rust has pushed, and will continue to push, the limits of practical, bare metal, memory safe languages. And it's interesting to think about what's next, maybe eventually there will be some form of practical theorem proving "for the masses". Lean 4 looks great and has potential, but it's still mostly a language for mathematicians. There has been some research on AI constructed proofs, which could be the best of both worlds because then the type checker can verify that the AI generated code/proof is indeed correct. Tools like Kani are also a step forward in program correctness.
  • Lean4 helped Terence Tao discover a small bug in his recent paper
    10 projects | news.ycombinator.com | 27 Oct 2023
    Yeah, I believe they said intend for it to be used as a general purpose programming language. I used it to complete Advent of Code last year.

    There are some really interesting features for general purpose programming in there. For example: you can code updates to arrays in a functional style (change a value, get a new array back), but if the refcount is 1, it updates in place. This works for inductive types and structures, too. So I was able to efficiently use C-style arrays (O(1) update/lookup) while writing functional code. (paper: https://arxiv.org/abs/1908.05647 )

    Another interesting feature is that the "do" blocks include mutable variables and for loops (with continue / break / return), that gets compiled down to monad operations. (paper: https://dl.acm.org/doi/10.1145/3547640 )

    And I'm impressed that you can add to the syntax of the language, in the same way that the language is implemented, and then use that syntax in the next line of code. (paper: https://lmcs.episciences.org/9362/pdf ). There is an example in the source repository that adds and then uses a JSX-like syntax. (https://github.com/leanprover/lean4/blob/master/tests/playgr... )

  • A Linguagem Lua completa 30 anos!
    3 projects | dev.to | 17 Oct 2023
  • Lean 4.0
    1 project | /r/hypeurls | 9 Sep 2023
  • Lean 4.0.0, first official lean4 release
    10 projects | news.ycombinator.com | 7 Sep 2023

What are some alternatives?

When comparing Agda and lean4 you can also consider the following projects:

lean - Lean Theorem Prover

z3_tutorial - Jupyter notebooks for tutorial on the Z3 SMT solver

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.

open-typerep - Open type representations and dynamic types

ATS-Postiats - ATS2: Unleashing the Potentials of Types and Templates

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

ts-sql - A SQL database implemented purely in TypeScript type annotations.

distributive - Dual Traversable

roc - A fast, friendly, functional language.

agda-vim - Agda interaction in vim

oil - Oils is our upgrade path from bash to a better language and runtime. It's also for Python and JavaScript users who avoid shell!

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