ATS-Postiats
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ATS-Postiats | coq | |
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18 | 87 | |
349 | 4,602 | |
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about 1 year ago | 3 days ago | |
ATS | OCaml | |
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ATS-Postiats
- What is the most feature-rich programming language
- 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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Does Rust have any design mistakes?
Not being ATS
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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".
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ESPOL, NEWP, Mesa, Cedar, Modula-2, Modula-2+, Modula-3, Oberon, Oberon-2, Component Pascal, Active Oberon, D, C#, F#, VB, Ada, Go, Swift, just a few examples.
In SPARK's case, you have to state your invariants in even greater precision than in Rust, and naturally it has worse inference. That's okay, the same happens in a certain language with Atrocious Type Syntax.
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What are all the situations you can't do compile time type-checking when building a programming language?
Yes, things like mentioned in the post can be expressed and checked statically, as demonstrated by languages like Idris and ATS. ATS might be even more relevant as it's an imperative language too, it can get rather low-level (like talking about properties of C runtime functions) while proving required properties statically, and it includes a solver for certain amount of arithmetics so that you don't need to prove obvious mathematical identities to the compiler. http://www.ats-lang.org/
- Is it possible to make a functional programming language that is equivalent of Rust in terms of performance and resource efficiency?
coq
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Change of Name: Coq –> The Rocq Prover
The page summarizing the considered new names and their pros/cons is interesting: https://github.com/coq/coq/wiki/Alternative-names
Naming is hard...
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The First Stable Release of a Rust-Rewrite Sudo Implementation
Are those more important than, say:
- Proven with Coq, a formal proof management system: https://coq.inria.fr/
See in the real world: https://aws.amazon.com/security/provable-security/
And check out Computer-Aided Verification (CAV).
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Why Mathematical Proof Is a Social Compact
To be ruthlessly, uselessly pedantic - after all, we're mathematicians - there's reasonable definitions of "academic" where logical unsoundness is still academic if it never interfered with the reasoning behind any proofs of interest ;)
But: so long as we're accepting that unsoundness in your checker or its underlying theory are intrinsically deal breakers, there's definitely a long history of this, perhaps more somewhat more relevant than the HM example, since no proof checkers of note, AFAIK, have incorporated mutation into their type theory.
For one thing, the implementation can very easily have bugs. Coq itself certainly has had soundness bugs occasionally [0]. I'm sure Agda, Lean, Idris, etc. have too, but I've followed them less closely.
But even the underlying mathematics have been tricky. Girard's Paradox broke Martin-Löf's type theory, which is why in these dependently typed proof assistants you have to deal with the bizarre "Tower of Universes"; and Girard's Paradox is an analogue of Russell's Paradox which broke more naive set theories. And then Russell himself and his system of universal mathematics was very famously struck down by Gödel.
But we've definitely gotten it right this time...
[0] https://github.com/coq/coq/issues/4294
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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+.
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
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If given a list of properties/definitions and relationship between them, could a machine come up with (mostly senseless, but) true implications?
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.
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Functional Programming in Coq
What ever happened to the effort [1] to rename Coq in order to make it less offensive? There were a number of excellent proposals [2] that seemed to die on the vine.
[1] https://github.com/coq/coq/wiki/Alternative-names
[2] https://github.com/coq/coq/wiki/Alternative-names#c%E1%B5%A3...
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Mark Petruska has requested 250000 Algos for the development of a Coq-avm library for AVM version 8
Information about the Coq proof assistant: https://coq.inria.fr/ , https://en.wikipedia.org/wiki/Coq
- How are people like Andrew Wiles and Grigori Perelman able to work on popular problems for years without others/the research community discovering the same breakthroughs? Is it just luck?
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Basic SAT model of x86 instructions using Z3, autogenerated from Intel docs
This type of thing can help you formally verify code.
So, if your proof is correct, and your description of the (language/CPU) is correct, you can prove the code does what you think it does.
Formal proof systems are still growing up, though, and they are still pretty hard to use. See Coq for an introduction: https://coq.inria.fr/
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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.
What are some alternatives?
lean4 - Lean 4 programming language and theorem prover
coc.nvim - Nodejs extension host for vim & neovim, load extensions like VSCode and host language servers.
chapel - a Productive Parallel Programming Language
kok.nvim - Fast as FUCK nvim completion. SQLite, concurrent scheduler, hundreds of hours of optimization.
cicada - An old-school bash-like Unix shell written in Rust
FStar - A Proof-oriented Programming Language
c3c - Compiler for the C3 language
Agda - Agda is a dependently typed programming language / interactive theorem prover.
virgil - A fast and lightweight native programming language
HVM - A massively parallel, optimal functional runtime in Rust
tlaplus - TLC is a model checker for specifications written in TLA+. The TLA+Toolbox is an IDE for TLA+.