lean4

Lean 4 programming language and theorem prover (by leanprover)

Lean4 Alternatives

Similar projects and alternatives to lean4

  • coq

    8 lean4 VS 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.

  • Agda

    2 lean4 VS Agda

    Agda is a dependently typed programming language / interactive theorem prover.

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    - lean4 VS z3_tutorial

    Jupyter notebooks for tutorial on the Z3 SMT solver

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    - lean4 VS ts-sql

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  • mathlib4

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  • dafny

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NOTE: The number of mentions on this list indicates mentions on common posts plus user suggested alternatives. Hence, a higher number means a better lean4 alternative or higher similarity.

lean4 reviews and mentions

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 2024-03-20.
  • The Mechanics of Proof
    2 projects | news.ycombinator.com | 20 Mar 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 4.0.0, first official lean4 release
    10 projects | news.ycombinator.com | 7 Sep 2023
  • Looking to start a new community for people who want to use code for everything
    2 projects | /r/finality | 15 Aug 2023
    My latest inspiration to use code to a) replace my video editor, b) learn the basics of EDM production and c) understand a few topics in higher maths. This might sound very strange given there are specialised tools for these jobs. There's iMovie / Adobe Premier for video, there's GarageBand and FL studio for music and old good pen and pencil for math proofs. But these tools have three big limitations. First they have a lot of idiosyncratic learning, you have to spend quite some time getting used to these tools and my experience is that this time is quite upsetting. In contrast, you only have to learn to code one, maybe spend a few hours getting used to the syntax of another language. I'm not sure if that's true for most people but it was true for me using the tools mentioned above and wanted a place to discuss and see other people ideas and experiments. The second issue is that all these custom-made tools, are not composing easily. I can't search for all math proofs that used a single theorem. I can't create a plugin for iMovie and apply it to all my videos. I can't pick easily pick a rhythm from the internet and build upon for fun. There's also the issue of costs and version control, all tools I'm using today are open source and my work is stored in my repositories. This way I can create branches and test my ideas and I'm also confident that I can work in these projects in years.
  • 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

  • Macro-ts: TypeScript compiler with typesafe syntactic macros (2022)
    2 projects | news.ycombinator.com | 30 May 2023
    Lean4 manages to pull off changing the parser on the fly at compile time. You can add new productions, add new syntax node types, and add new tokens. Then define macros or code to process the additional syntax. Here is a sample I found that adds a simple JSX-like syntax starting around line 93 and then uses it at line 169:

    https://github.com/leanprover/lean4/blob/master/tests/playgr...

    I believe most of the language is defined this way, although it is pre-compiled.

    For more details see the lean4 metaprogramming book: https://github.com/arthurpaulino/lean4-metaprogramming-book

  • is dependent haskell still a thing?
    4 projects | /r/haskell | 19 May 2023
    Lean is another alternative. Very fast, built by Microsoft. Dependent types, proof tactics, type classes, monads, nice macro system.
  • 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.
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    www.influxdata.com | 16 Apr 2024
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Stats

Basic lean4 repo stats
52
3,687
9.9
6 days ago

leanprover/lean4 is an open source project licensed under Apache License 2.0 which is an OSI approved license.

The primary programming language of lean4 is Lean.

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