Agda VS lean

Compare Agda vs lean and see what are their differences.

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Agda lean
27 4
2,421 1,915
1.2% -
9.8 0.0
1 day ago almost 4 years ago
Haskell C++
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.

lean

Posts with mentions or reviews of lean. We have used some of these posts to build our list of alternatives and similar projects. The last one was on 2021-03-26.
  • Paper from 2021 claims P=NP with poorly specified algorithm for maximum clique using dynamical systems theory
    1 project | /r/computerscience | 12 Jan 2023
    Apparently, it even still segfaulted in 2018 https://github.com/leanprover/lean/issues/1958. I don't expect my tools to segfault.
  • Low-level format file of mathlib
    1 project | /r/leanprover | 21 Dec 2022
    Does anyone happen to have the mathlib library in the [low-level format](https://github.com/leanprover/lean/blob/master/doc/export_format.md)? I've been trying to run lean --export to obtain it, but I keep getting various errors.
  • Mathematics: our overlooked ability
    1 project | /r/agi | 30 Apr 2021
    I have spent a good deal of time trying to formalize elementary mathematics and computer science textbooks in the Lean Theorem Prover, and in trying to extend and improve Lean to make the process easier. I have been able to translate entire chapters of several textbooks into Lean in a natural way, with every line of Lean seemingly isomorphic to the informal presentation. However, once in a while I will hit a statement or proof step that may seem simple to me but that requires a major refactor, or adding new features to Lean itself, or just seems like a brick wall. My brain is able to perform massive refactorings of mathematical knowledge and abstractions, synthesize the equivalent of tens of thousands of lines of tricky and performance-critical software, and maybe even expand the logic I am effectively operating in, all in the blink of an eye.
  • How do I get back into math?
    3 projects | /r/math | 26 Mar 2021
    However, mathlib makes some weird design choices. For example, (semi)groups are defined using multiplicative notation -- and then immediately followed by an entire section giving the exact same definitions using additive notation! The claimed reason for this is that the more abstract approach is inconvenient for automation. I did it in Coq using the abstract approach, and indeed, noticed that doing so broke automation, which I then worked around in various ways. But it's just weird to me as a mathematician to have additive and multiplicative groups be different objects, so I wouldn't want to do it the Lean way come hell or high water. The Lean approach causes practical difficulties as well: you have to prove every theorem about groups twice. In some cases (e.g. product groups), you have to prove every theorem FOUR times. Ugh.

What are some alternatives?

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

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.

FStar - A Proof-oriented Programming Language

open-typerep - Open type representations and dynamic types

Coq-HoTT - A Coq library for Homotopy Type Theory

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

CoqGym - A Learning Environment for Theorem Proving with the Coq proof assistant

lean4 - Lean 4 programming language and theorem prover

arend-lib

distributive - Dual Traversable

ttlite - A SuperCompiler for Martin-Löf's Type Theory

agda-vim - Agda interaction in vim

daisy-nfsd - DaisyNFS is an NFS server verified using Dafny and Perennial.

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