cakeml
FStar
cakeml | FStar | |
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14 | 42 | |
915 | 2,570 | |
1.1% | 0.6% | |
9.8 | 9.9 | |
7 days ago | 1 day ago | |
Standard ML | F* | |
GNU General Public License v3.0 or later | Apache License 2.0 |
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cakeml
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The Deep Link Equating Math Proofs and Computer Programs
If I understand what you are asking about correctly, then I do think you are mistaken.
As a sibling comment observed, you would be proving something about a program, but proving things about programs is both possible and done.
This ranges from things like CakeML (https://cakeml.org/) and CompCert (compilers with verified correctness proofs of their optimizations) to something simple like absence of runtime type errors in statically strongly soundly-typed languages.
Of note is that you are proving properties of your program, not proving them perfect in every way. The properties of your program that you prove can vary wildly in both difficulty and usefulness. A sufficiently advanced formally verified compiler like CakeML can transfer a high-level proof about your source code to a corresponding proof about the behavior of the generated machine-executable code.
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The future of Clang-based tooling
> A single IR with multiple passes is a good way to build a compiler
https://mlir.llvm.org/, which is using, is largely claiming the opposite. Most passes more naturally are not "a -> a", but "a -> b". data structures and data structures work hand in hand, it is very nice to produce "evidence" for what is done in the output data structure.
This is why https://cakeml.org/, which "can't cheat" with partial functions, has so many IRs!
Using just a single IR was historically done for cost-control, the idea being that having many IRs was a disaster in repetitive boilerplate. MLIR seeks to solve that exact problem!
- CakeML – A Verified Implementation of ML
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Tools for Verifying a Language and its Semantics
You may want to look at [CakeML](https://cakeml.org) done in HOL4, there is also a nice proof pearl about a more .. minimalistic verified bootstrapped compiler also in HOL4.
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old languages compilers
CakeML
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Is there a formally-proven real-time language/computing env. or operating system?
There is also Cake ML which is a formally verified functional programming language compiler and runtime.
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CakeML: A Verified Implementation of ML
There is also a CakeML -> Standard ML compiler though it seems to have been built to translate benchmarks and sort of old so I'm not sure how comprehensive it is: https://github.com/CakeML/cakeml/tree/master/unverified/front-end
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The λ-Cube
> One guess is that lisps cope with being minimal through use of macros and metaprogramming, it's difficult for a typed language to support that level of metaprogramming while maintaining the various guarantees that one wants from such a system.
Difficult, but certainly not impossible [0].
[0] https://cakeml.org/
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Two Mechanisations of WebAssembly 1.0
If this interests you, I'd highly recommend checking out CompCert (docs here) and CakeML.
- VLISP: A Verified Implementation of Scheme [pdf]
FStar
- Lean4 helped Terence Tao discover a small bug in his recent paper
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The Deep Link Equating Math Proofs and Computer Programs
I don't think something that specific exists. There are a very large number of formal methods tools, each with different specialties / domains.
For verification with proof assistants, [Software Foundations](https://softwarefoundations.cis.upenn.edu/) and [Concrete Semantics](http://concrete-semantics.org/) are both solid.
For verification via model checking, you can check out [Learn TLA+](https://learntla.com/), and the more theoretical [Specifying Systems](https://lamport.azurewebsites.net/tla/book-02-08-08.pdf).
For more theory, check out [Formal Reasoning About Programs](http://adam.chlipala.net/frap/).
And for general projects look at [F*](https://www.fstar-lang.org/) and [Dafny](https://dafny.org/).
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If You've Got Enough Money, It's All 'Lawful'
Don't get me wrong, there are times when Microsoft got it right the first time that was technically far superior to their competitors. Windows IOCP was theoretically capable of doing C10K as far back in 1994-95 when there wasn't any hardware support yet and UNIX world was bickering over how to do asynchronous I/O. Years later POSIX came up with select which was a shoddy little shit in comparison. Linux caved in finally only as recently as 2019 and implemented io_uring. Microsoft research has contributed some very interesting things to computer science like Z3 SAT solver and in collaboration with INRIA made languages like F* and Low* for formal specification and verification. But all this dwarfs in comparison to all the harm they did.
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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.
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Why is there no simple C-like functional programming language?
F* is a dependently typed language that can be transpiled to idiomatic C via the KReMLin compiler. It’s very ML-ish to write and you can leave out some proofs. It also has the benefit of being used to write a formally verified TLS implementation that’s in wide use throughout industry.
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[Media] Genetic algorithm simulation - Smart rockets (code link in comments)
As I said, dependent types attempt to solve this problem. F* is a language where you can express complex logic as a type. The catch is, these types are checked by an SMT solver. If the solver can satisfy the type checking, then great, and you move on. If it can’t, you have no idea why, and either have to guess or manually write the proof anyway. Contrast this with Standard ML which has a proof of the soundness of its type system.
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Prop v0.42 released! Don't panic! The answer is... support for dependent types :)
So kind of like F*? https://www.fstar-lang.org/
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old languages compilers
F*
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Pegasus spyware was used to hack reporters’ phones. I’m suing its creators; When you’re infected by Pegasus, spies effectively hold a clone of your phone – we’re fighting back.
Nevermind that academia has come up with far safer ways to do a few things but social norms & inertia prevent their wider adoption (well okay, it also has a barrier to entry in the education required to use it but I don't think someone with the knowledge to meaningfully contribute to an OS kernel can be considered uneducated nor unable to learn).
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[Hobby] Amateur Generalist Programmer Seeking to Put Bugfixing Skills to Good Use
Maybe that's a little off topic here, but if you like fixing bugs, i suspect you might also enjoy showing that there are no bugs at all. Check out languages like F* https://www.fstar-lang.org/ It's a proof-oriented programming language. You can use it to write code that has no bugs at all. And you once you're done, can convert F* to C or other languages.
What are some alternatives?
Daikon - Dynamic detection of likely invariants
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.
hardware - Verilog development and verification project for HOL4
lean - Lean Theorem Prover
mpl - The MaPLe compiler for efficient and scalable parallel functional programming
dafny - Dafny is a verification-aware programming language
CompCert - The CompCert formally-verified C compiler
koka - Koka language compiler and interpreter
Checker Framework - Pluggable type-checking for Java
VisualFSharp - The F# compiler, F# core library, F# language service, and F# tooling integration for Visual Studio
checkedc - Checked C is an extension to C that lets programmers write C code that is guaranteed by the compiler to be type-safe. The goal is to let people easily make their existing C code type-safe and eliminate entire classes of errors. Checked C does not address use-after-free errors. This repo has a wiki for Checked C, sample code, the specification, and test code.
stepmania - Advanced rhythm game for Windows, Linux and OS X. Designed for both home and arcade use.