ATS-Postiats
Agda
ATS-Postiats | Agda | |
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18 | 27 | |
349 | 2,378 | |
- | 0.6% | |
0.0 | 9.8 | |
about 1 year ago | 6 days ago | |
ATS | Haskell | |
GNU General Public License v3.0 or later | MIT License |
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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?
Agda
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Types versus sets (and what about categories?)
This was recently deemed inappropriate:
"Bye bye Set"
"Set and Prop are removed as keywords"
https://github.com/agda/agda/pull/4629
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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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What can Category Theory do?
Haskell and Agda are probably the most obvious examples. Ocaml too, but it is much older, so its type system is not as categorical. There is also Idris, which is not as well-known but is very cool.
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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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Amendmend proposal: Changed syntax for Or patterns
Does this come with plans to separately unify the body with each of the contexts induced by matching on each of the respective patterns (similar to what’s discussed here), or will it behave like the _ pattern and use only the most general context?
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Functional Programming and Maths <|> How can a code monkey learn Agda?
That's absolutely untrue. From the horse's mouth:
- Doom emacs and agda-mode
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FP language idea - would this is possible to infer and type check?
Agda has the so-called mixfix operators (which are powerful enough to cover pre/in/postfix cases with an arbitrary number of arguments), check that out: - https://agda.readthedocs.io/en/v2.6.1/language/mixfix-operators.html - https://github.com/agda/agda/blob/master/examples/Introduction/Operators.agda - https://github.com/agda/agda-stdlib/blob/master/src/Data/Product/Base.agda
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Best Programming Language for Computational Proof
Coq, Agda, Lean, Isabelle, and probably some others which are not coming to my mind at the moment, but those would be considered the major ones.
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Do you use Idris or Coq, and why?
Funny that you say this, because there are some obvious long standing open feature requests with looking up the type of the term under cursor — № 4295 and № 516. I am not blaming anyone in particular — this is the way it is. I wish I could find time to rewrite the proof search engine (how hard can it be), but I am already buried under a pile of other commitments and a good chunk of overwhelming sadness.
What are some alternatives?
lean4 - Lean 4 programming language and theorem prover
lean - Lean Theorem Prover
chapel - a Productive Parallel Programming Language
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.
cicada - An old-school bash-like Unix shell written in Rust
open-typerep - Open type representations and dynamic types
c3c - Compiler for the C3 language
HoleyMonoid - Automatically exported from code.google.com/p/monoid-cont
virgil - A fast and lightweight native programming language
distributive - Dual Traversable
HVM - A massively parallel, optimal functional runtime in Rust