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What language features are needed in order to implement dependent types? Can you implement it on top of existing features of say Rust or Swift?

• krapht 6y ago
  I'm not sure that this question even makes sense. It's like asking: "What language features are needed in order to implement a borrow checker?" You don't bolt this functionality on to an existing language; it requires changes to your whole compiler pipeline to be useful.
  • drcode 6y ago
    Don't be so certain, some languages allow a lot of flexibility within libraries. For instance, Clojure has an excellent library implementing Go-style channels with green threads (core.async) all built without any modifications to the core system.
    • krapht 6y ago
      Sure. Linear types and borrow checking is possible in Lisp too, but I wouldn't take that as evidence that it's super easy to make Clojure behave like Rust. What is possible and what is practical are two different things.
    • zelphirkalt 6y ago
      Good point, Lispy languages with sufficiently powerful macro systems can do this. This is part of the reason, why no language committee deciding on backwards compatible changes to the language is needed to develop such a library. I don't know enough to say whether this would be possible in Rust.
• zitterbewegung 6y ago
  You can implement any language in any language that is Turing complete. Or practically anything with conditionals, looping and recursion. So yes to all of your questions.
  • chongli 6y ago
    You mean you could write a compiler for Idris (or any other dependent typed language) in a Turing complete language. That’s fine but it’s not a very useful statement. If you want dependent types IN Rust or Swift then Turing-completeness won’t help you, because neither of them have Turing-complete type checkers. You’d have to modify the compiler for them (and thus change the language itself).
    • dependenttypes 6y ago
      > because neither of them have Turing-complete type checkers https://sdleffler.github.io/RustTypeSystemTuringComplete/ https://sdleffler.github.io/RustTypeSystemTuringComplete/
      • chongli 6y ago
        That's almost certainly a bug. At any rate, a proper language with dependent types does not have a Turing-complete type checker and that's what makes it magical. You get incredible power without having to worry about non-termination in your type checker.
        • devit 6y ago
          It's not a bug, it's due to the trait (aka typeclass) system. Apparently Haskell has some restrictions that make typeclasses decidable (if -XUndecidableInstances is not set), but Rust has no such mechanism other than numeric iteration limits.
        • mokus 6y ago
          Guaranteed termination of a sound dependent type system is only useful as a mathematical property, not a practical one (yes, I know the mathematical consequences have practical benefit but I mean directly it doesn’t say anything about what a typical user thinks of as “termination”). You could still trivially write an algorithm at the type level which is Turing-complete in a practical sense. For example, write a type that implements a Turing machine parameterized by a program and a natural number N of evaluation steps to take. Apply that type to Graham’s number or some suitably large natural number. You now have a type that is, for all practical purposes, Turing-complete, even though it is theoretically guaranteed to terminate.
• rscho 6y ago
  He does it on top of scheme. Have a look at https://mitpress.mit.edu/books/little-typer https://mitpress.mit.edu/books/little-typer
• dan-robertson 6y ago
  A first feature is the ability to define “interesting” types. By interesting I mean “generic” types which do things depending on the types of their arguments. In other words, a way to have functions at the type level. In Haskell you can do this with type families. I don’t know if you can do something similar in rust (have a type in a trait and then implement that trait in certain cases to get your function from input type to the type in the trait implementation for the input type) A second feature that I think is needed is a way to go between types and values which I don’t think rust or swift can do. Two fundamental dependent types are the dependent sum and dependent product. The dependent product is the type of a function whose output type depends on its input value. This is a generalisation of the product type: the product type (a,b) is like the dependent product type (x:{1,2}) -> T x where T 1 = a and T 2 = b. The dependent sum type consists of a tag value of some type and a value whose type depends on the tag. For example a vector of arbitrary length Of floats could be written with a type something like: Sum(n:Nat)(Vec n Float) And a value like (2,[1,2]) Sometimes you see online that every pair can be represented as a dependent sum and this is true but completely misses the point because it implies that you should think of it like a generalised product which you should not do.
  • pittma 6y ago
    You can, in fact, use traits to do type-level programming in Rust[1], but this is type-level programming; it isn't /dependent/ types. The biggest "blocker" for using dependent types is that programs must be /total/, because that program has to be evaluated for it to typecheck! If a program is not total, the typechecker has the potential of getting stuck. The two dependently-typed languages I've programmed in, Mostly Agda and a tiny bit of Idris, have totality checkers to aid in this. Generally this means that recursion is only allowed if its structural, and there can be no run-forever loops, i.e., no servers. I think instead, for one of these languages, the ideal would be opt in should you need it. Dependent types are, by their nature, proof carrying[2], and there are times when you want this, but for a general-purpose programming language, also times that you do not. You can't be total over IO (or any effect for that matter), so, yeah, skip it when arg-parsing, but then opt-in when you're processing your financial transactions or actuating your robot. [1] https://dpitt.me/talks/tt-for-rust/ https://dpitt.me/talks/tt-for-rust/ [2] http://www.cs.nott.ac.uk/~psztxa/publ/ydtm.pdf http://www.cs.nott.ac.uk/~psztxa/publ/ydtm.pdf
• heinrich-lunge 6y ago
  Dependent types are a language feature, simply adding two types --- the dependent product / exponential / function type, and the dependent sum / product / tuple type. You can definitely add dependent types to Rust, but I see at least the following problems. 1. Rust compile times and dependent typing compile times are both really long. Combining the two sounds like it'd be unacceptably long. 2. Rust promises full type erasure when you're not using "dyn". Predictably erasing dependent types seems to be a hard problem. Heck, even ergonomically giving low-level control over the layout of a dependent sum sounds hard. 3. Dependent types give you a whole bunch of new ways to do things that you can already do in Rust, which is probably a bad thing. I think "bolt-on" approaches, as Hoare logic is to imperative pseudocode, or SPARK is to Ada, are something that Rust could easily employ, which are more well-tested, and would solve all of the use cases of dependent types in industry.
  • kibwen 6y ago
    > Rust promises full type erasure when you're not using "dyn" I don't know if "type erasure" is the accurate term to use with the generic-specialization scheme that Rust uses; one can trivially write a generic Rust function that demonstrates that types, while inaccessible at runtime, still semantically affect the generated code: use std::mem::size_of; fn foo<T>(t: T) { dbg!(size_of::<T>()); } fn main() { foo(1); // prints 4 foo("bar"); // prints 16 }
    • TeMPOraL 6y ago
      Isn't this just compile-time dispatching? I think types 'inaccessible at runtime but still affecting generating code' are table stakes, and basically half of the point of doing these types of generics. Equivalent C++ code (admittedly, C++ templates aren't really generics) would have enough information to shove literal 4 and 16 into the binary there.
      • kibwen 6y ago
        This is kind of my point, I've never heard the term "type erasure" used with static dispatch (and Rust code, for better or worse, overwhelmingly prefers static dispatch to dynamic dispatch). Rust does guarantee type erasure on lifetimes, but lifetimes are only used for semantic analysis, and are completely separate from and unrelated to code generation/type layout.
• mvcccccc 6y ago
  IMO, it would be easy to create a new dependently typed language with on a subset of the Rust or Swift syntax. Here's a tutorial written by an Idris contributor. http://davidchristiansen.dk/tutorials/nbe/ http://davidchristiansen.dk/tutorials/nbe/ Following the guide, you can build a dependently typed language with Racket syntax in two hours. But it is not easy to plug dependent types to existing compilers of Rust or Swift. In general, a dependently typed language is not Turing-complete so that the type checking (which now requires running programs) is decidable. That means you have to rule out features like general recursion and arbitrary loops. That could mean reconnecting the wires in the existing compiler. From an engineering aspect, it should be easier to plug dependent types on a functional programming language, e.g., dependent Haskell, than imperative languages.
• contravariant 6y ago
  With no restriction on what kind of dependent types are allowed the type system should at least be Turing complete.
  • deleted 6y ago
    [deleted]
• lmm 6y ago
  You might like to read https://serokell.io/blog/why-dependent-haskell https://serokell.io/blog/why-dependent-haskell , which describes a roadmap for making dependent types practical in Haskell. Useful steps on the road: singleton types (needed to make it easy to represent basic values as types), higher-kinded types (needed to implement functions at the type level), kind polymorphism (needed to be able to reuse the same functions at the type and the value level). Rust is I think getting the first, is gradually implementing little subsets of the second, and is nowhere near the third. The other thing you need to worry about is how dependent types interact with existing language features. In particular, if not implemented carefully then they may break type inference, and I imagine Rust's lifetime inference might have similar issues.
• anentropic 6y ago
  https://dl.acm.org/doi/10.1145/3371071 https://dl.acm.org/doi/10.1145/3371071 Dependent Types via macros, in Racket somewhere near the end of the paper is a table of the macro features used, which gives the impression it was only possible in Racket, but the lack of a common terminology for these things makes it hard to compare other languages' macro systems unless you are deeply familiar with them, so maybe it could be adapted