lean4
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lean4 | souper | |
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52 | 12 | |
3,714 | 2,069 | |
4.7% | 0.7% | |
9.9 | 3.4 | |
1 day ago | 15 days ago | |
Lean | C++ | |
Apache License 2.0 | Apache License 2.0 |
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lean4
- The Mechanics of Proof
- Natural Deduction in Logic (2015)
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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
- 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
souper
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Original Age of Empires 2 dev talks about its usage of assembly code
https://github.com/google/souper
It looks like it only supports Linux and macOS - no Windows, but no other things too like mobile.
It seems it exists for ten years, I wonder what optimizations aren't still picked by the recent compilers.
- Minotaur: A SIMD-Oriented Synthesizing Superoptimizer
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My First Superoptimizer
The pruning part can do a lot of heavy lifting to make it a practical tool.
Related: I work on Souper (https://github.com/google/souper).
Feel free to reach out if anyone has questions!
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Superoptimisation
Compile to LLVM IR and you can try Souper: https://github.com/google/souper
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Ryan Levick: The new pass manager in LLVM 13 (now in nightly) leads to significantly better compile times..
These exist, they are called superoptimizers. The most known superoptimizer for LLVM is caller SOUPER
- A Superoptimizer for LLVM IR
- A superoptimizer for LLVM IR
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Software Verification and Analysis Using Z3
Google's one step ahead of you there :)
What are some alternatives?
z3_tutorial - Jupyter notebooks for tutorial on the Z3 SMT solver
rust - Empowering everyone to build reliable and efficient software.
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.
minotaur - A description of Minotaur can be found in https://arxiv.org/abs/2306.00229.
ATS-Postiats - ATS2: Unleashing the Potentials of Types and Templates
ts-sql - A SQL database implemented purely in TypeScript type annotations.
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.