lean4
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lean4 | ATS-Postiats | |
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52 | 18 | |
3,646 | 349 | |
5.6% | - | |
9.9 | 0.0 | |
about 23 hours ago | about 1 year ago | |
Lean | ATS | |
Apache License 2.0 | GNU General Public License v3.0 or later |
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.
lean4
- The Mechanics of Proof
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The Wizardry Frontier
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.
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Lean4 helped Terence Tao discover a small bug in his recent paper
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!
- Lean 4.0.0, first official lean4 release
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Looking to start a new community for people who want to use code for everything
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.
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In Which I Claim Rich Hickey Is Wrong
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+.
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Macro-ts: TypeScript compiler with typesafe syntactic macros (2022)
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
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is dependent haskell still a thing?
Lean is another alternative. Very fast, built by Microsoft. Dependent types, proof tactics, type classes, monads, nice macro system.
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What are the current hot topics in type theory and static analysis?
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.
ATS-Postiats
- Evolutie limbaje in industrie
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The Little Typer – The Beauty of Dependent Type Systems, One Step at a Time
This is one of my two favorite books in The Little ...er series. The other is The Rational Schemer. These are two of the most advanced books in the series.
The Little Typer provides an introduction to dependent types. These can by used to guarantee things like "applying 'concat' to a list of length X and list of length Y returns a list of X+Y". It is also possible, to some extent, to use dependent types to replace proof tools like Coq. Two interesting languages using dependent types are:
- Idris. This is basically "strict Haskell plus dependent types": https://www.idris-lang.org/)
- ATS. This is a complex systems-level language with dependent types: http://www.ats-lang.org/
The Rational Schemer shows how to build a Prolog-like logic language as a Scheme library. This is a very good introduction to logic programming and the implementation of backtracking and unification is fascinating.
This is an excellent series overall, but these two books are especially good for people who are interested in unusual programming language designs. I don't expect dependent types or logic programming to become widely-used in the next couple generations of mainstream languages, but they're still fascinating.
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The case against an alternative to C
> any safety checks put into the competing language will have a runtime cost, which often is unacceptable
This is completely wrong. The best counterexample is probably ATS http://www.ats-lang.org which is compatible with C, yet also features dependent types (allowing us to prove arbitrary statements about our programs, and check them at compile time) and linear type (allowing us to precisely track resource usage; similar to Rust)
A good example is http://ats-lang.sourceforge.net/DOCUMENT/ATS2CAIRO/HTML/c36.... which uses the Cairo graphics library, and ends with the following:
> It may seem that using cairo functions in ATS is nearly identical to using them in C (modulo syntatical difference). However, what happens at the level of typechecking in ATS is far more sophisticated than in C. In particular, linear types are assigned to cairo objects (such as contexts, surfaces, patterns, font faces, etc.) in ATS to allow them to be tracked statically, that is, at compile-time, preventing potential mismanagement of such objects. For instance, if the following line:
val () = cairo_surface_destroy (sf) // a type error if omitted
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Security advisory: malicious crate rustdecimal | Rust Blog
For a low level language in which you actually need to prove that your code doesn't cause UB, see http://www.ats-lang.org/
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Why is ATS not considered in the design of modern system languages?
Here's the homepage fo the language: http://www.ats-lang.org/. The trick to finding results about with google is to search "ATS programming language".
- Is it possible to make a functional programming language that is equivalent of Rust in terms of performance and resource efficiency?
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Ask HN: What technology is “cutting edge” in 2022?
Another language I would add to this list is the ATS Language¹. First released in 2013, it tries to follow closer to performance and minimalism of C which can make it a good candidate for systems level programming.
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Why Static Languages Suffer From Complexity
There is the ATS programming language. Though it is not very user-friendly :)
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Are there any other programming languages that use a similar memory architecture?
ATS language and Pony are similar in that regard.
- Are there any ML style languages with no runtime?
What are some alternatives?
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.
Agda - Agda is a dependently typed programming language / interactive theorem prover.
ts-sql - A SQL database implemented purely in TypeScript type annotations.
chapel - a Productive Parallel Programming Language
cicada - An old-school bash-like Unix shell written in Rust
roc - A fast, friendly, functional language. Work in progress!
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!
typeshed - Collection of library stubs for Python, with static types
ivy - IVy is a research tool intended to allow interactive development of protocols and their proofs of correctness and to provide a platform for developing and experimenting with automated proof techniques. In particular, IVy provides interactive visualization of automated proofs, and supports a use model in which the human protocol designer and the automated tool interact to expose errors and prove correctness.
c3c - Compiler for the C3 language
wuffs - Wrangling Untrusted File Formats Safely