Type refinements can be used as a mechanism to capture the depedent types within the same implicit declaration. ?=> in line 2 Its result type, e.Key refers to its parameter e (we also say, e.Key depends on e). The properties we are interested in modeling are Scala’s path-dependent types and abstract type … This change would let us program path-dependent types on a new level. Its compiler is a new design intended to reflect the lessons we learned from work with the Scala compiler. The Scala and Dotty teams are working closely toward convergence for Scala 2.x and Dotty, and they’ve indicated that they take continuity very seriously. metaprogramming extension-methods shapeless macros scala typelevel-programming code-generation scalafix typeclass scalameta typeclasses simulacrum semanticdb dependent-types 21 2 … Whilst type inference in Scala is not fully specified, section 6.26.4 Local Type Inference contains language which explicitly excludes the inference of singleton types (see cases 2 and 3, “None of the inferred types Ti is a singleton type”). Scala already has dependent methods, i.e. I Goals I simplify Scala’s type system by desugaring to DOT I simplify Scala’s type inference by relying on DOT I prove that DOT is type-safe 2. The discussion naturally leads to the new ability to parameterize the types of functions, which was previously only supported for methods. basically a pattern to derive output type In addition, Scala 3 works on new compiler which is also called Dotty that support DOT and which is more powerful that current version of Scala compiler. The type of the extractor value above is. This is a core feature in the new Scala, Dotty, and these two calculi are supposed to model the behavior of path dependent types. to me or anyone interested to learn some new functional programming features that Scala 3 is bringing to us. Dotty uses the Scala Code of Conduct for all communication and discussion. Its result type, e.Key refers to its parameter e (we also say, e.Key depends on e). While I’m at it, I’ll mention another method feature that’s now supported for functions, dependent function types. the type above would be represented as Function1[C, C#T] { def apply(x: C): x.T } For the moment, dependent function types cannot be implicit. Captured types can be used by other type classes to place constraints on types; Type Level "if" Statement Stainless is a tool for verifying Scala programs. the future Scala 3). This post explores them. Try it online at Scastie: https://scastie.scala-lang.org/fyxXSR3ASj6rSkkERnUK7g, Or clone the repo and sbt test: https://github.com/jcouyang/meow, basically a pattern to derive output type, https://dotty.epfl.ch/docs/reference/new-types/dependent-function-types.html, https://dotty.epfl.ch/docs/reference/contextual/context-bounds.html, Author: Jichao Ouyang For instance, you might have a type alias. Method extractKey is an example. I … a value of list has length 2 will result in type Vector [Nat2, Int], where Nat2 is actually calculated based on value of length. In addition to path-dependent types, types in DOT are built from refinements, inter-sections and unions. But, what if we wanted to specify these conditions without givinteg them a name? methods where the result type refers to some of the parameters of the method. DOT: Dependent Object Types I DOT is a core calculus for path-dependent types. In Scala 3 this is now possible. Dependent function types … dotty is a new, experimental Scala compiler based on DOT, the calculus of Dependent Object Types. We can call it dependent type because the type of Vector actually depends on the vector length, e.g. Scala 3), that allows to verify the code in Fig.1 against its specification,at compile time. (Scala version used: 3.0.0-M3) As long as such types are just partial applications of generic classes, A refinement extends a type by (re-)declaring members, which can be types, values or methods. Method extractKey is an example. A dependent function type is a function type whose result depends on the function's parameters. Recall that a normal function type A => B is represented as an instance of the Function1 trait (i.e. Lean for Scala programmers - Part 3 April 16, 2021. You are not restricted to a single abstract type when using dependent types. Lean for Scala programmers - Part 2 March 14, 2021. methods where the result type refers to some of the parameters of the method. You want to say Sum[A, B] => Sum[A, B]#Out but you can't at the moment. Type lambdas are the type analog of “value lambdas”, also known as functions . We refer to this characteristic of connecting two arbitrary types with a path dependent type (or path in short), bad bounds. Inductive types and pattern matching. Abstract. (Dependent Object Types) Nada Amin Scala Days June 18, 2014 1. DOT • Dependent Object Types • A calculus aimed as a new foundation of Scala • Featured path-dependent types, refinement types, and abstract type members DOTはScalaの基礎となる計算モデルです。 5. Alas, Scala has struggled for years with type soundness issues and ad-hoc fixes. We propose DOT as a new type-theoretic foundation of Scala and languages like it. We know, that in math a class is a collection of objects, that fulfill some conditions and programming borrowed the idea. Dependent methods could not be turned into functions simply because there was no type that could describe them. What is Dotty? With this path dependent function types feature, it seems we would be able to abstract over that pattern. If we add the type for the function it will be like: Ok, there is another problem though, so why do we need Aux pattern anymore if dependent method can solve the problem already? In JavaScript, you can define a Sponsor Starting from a simple calculus D \(_{<:}\) of dependent functions, it adds records, intersections and recursion to arrive at DOT, a calculus for dependent object types. But so far it was not possible to turn such methods into function values, so that they can be passed as parameters to other functions, or returned as results. object calculus with path-dependent types. Exploring dependent types with Lean and Scala. But so far it was not possible to turn such methods into function values, so that they can be passed as parameters to other functions, or returned as results. Furthermore, path-dependent types allow Scala to unify modules and objects, so that the same language constructs can be used to specify the overall structure of a program as well as its imple- mentation details. Focusing on path-dependent types, the paper develops foundations for Scala from first principles. Dependent Object Types (DOT) “DOT normalizes Scala’s type system by unifying the constructs for type members and by providing classical intersection and union types which simplify greatest lower bound and least upper bound computations.” • Started 6+ years ago “as a research project to explore what a new Scala could As was argued in the previous blog post, the danger a path-dependent type system like Scala’s faces is inconsistent bounds or aliases. This includes both GitHub, Gitter chat and other more direct lines of communication such as email. For example, what's the type of foo? Maybe we can lift that restriction in the future. Finally, note that thanks to Scala’s path-dependent types, foo1.Bar is actually a different type than foo2.Bar, although they are both subtypes of Foo#Bar. This type describes function values that take any argument e of type Entry and return a result of type e.Key. Scala 2.12 and 2.13 have language flags that unlock features being incubated in Dotty (e.g., existential types), and the Dotty compiler has a Scala 2 compatibility mode. Dotty (a.k.a. Notes on Category Theory in Scala 3 (Dotty) December 23, 2019 Captured types do not count as a "free" type parameter. It is my opinion that observing dependently typed constructions in a “native” environment such as Lean can help to understand and demystify some features of Scala’s type system. https://dotty.epfl.ch/docs/reference/contextual/context-bounds.html Therefore, In Scala 3, DOT – Dependent Object Type, has been implemented as foundation of Scala and DOTTY is a project for the development of Scala 3 with DOT. A clean redesign today will let us iterate faster with new ideas in … Follow @oyanglulu, Generated by: Emacs 26.3 (Org mode 9.3.6) × OrgPress, https://scastie.scala-lang.org/fyxXSR3ASj6rSkkERnUK7g, Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. E.g. They give us a stable basis on which we can study richer languages that resemble Scala more closely. About Dotty • A next generation compiler for Scala • Formalized in DOT • Implemented new features Dottyは次世代のScalaコンパイラです 4. Scala 2 There is a very common pattern in Shapeless, Aux pattern basically a pattern to derive output type : This is achieved by replacing the rightmost “_” (line 1) with a behavioural type: Forever[ In[Pay, (p: Pay)=> // Dependent function type [16] Out[p.replyTo.type, Rejected] | ( Out[aud.type, Audit[p.type]] >>: Out[p.replyTo.type, Accepted] ) ] ] We can call it dependent type because the type of Vector actually depends on the vector length, e.g. where the actual type of Vector depends on the actual value. This includes both GitHub, Gitter chat and other more direct lines of communication such as email. Coincidentally the almost-here Scala 3 release made dramatic simplifications to some form of dependently typed programming. You probably already noticed what dependent type looks like in Vector example for Phantom Types, The inst1D depends on the input type L, inst2D now depends on the inst1D return type R, so the whole method return type R2 depends on R. See what happen if we try to transform this to dependent method: Since it is a dependent type, we don't have any chance to tell compiler that inst1D.Out must be a HList. I'm recently migrating some libs and projects to Scala 3, I guess it would be very helpful The Dotty project is a platform to develop new technology for Scala tooling and to try out concepts of future Scala language versions. Follow https://dotty.epfl.ch/docs/reference/new-types/dependent-function-types.html https://medium.com/@sinisalouc/whats-new-in-scala-3-28d9c11eec30 Dependent functions are also represented as instances of these traits, but they get an additional refinement. The Wadlerfest paper contains examples that show how one can express classes for standard types such as Boolean and List in DOT. There is a very common pattern in Shapeless, Aux pattern In Scala, types cannot be passed into function, but in Scala 3, there is a new feature called Match Types https://dotty.epfl.ch/docs/reference/new-types/match-types.html. Nat2 is actually calculated based on value of length. Assuming class C { type T } a dependent function type is written like this: (x: C) => x.T It gets represented as a normal function type that approximates the result type together with a refinement that adds an apply method with the precise type. now. Dependent … Source code https://github.com/jcouyang/meow. The Scala language has an expressive type system that supports, among other features, first-class recursive modules, path dependent types, impredicative type members, and subtyping, achieving strong information hiding. Projecting Other Nested Types Here, it gets slightly more tricky: in Scala, one can define type members (i.e., type aliases) inside classes, and these type members can be left abstract and only be given a concrete definition in subclasses. In fact, the dependent function type above is just syntactic sugar for, Scala 3.0.0-RC3 â bug fixes for 3.0.0 stable, Scala 3.0.0-RC2 â getting ready for 3.0.0, Scala 3.0.0-RC1 â first release candidate is here, Scala 3.0.0-M3: developer's preview before RC1, Announcing Dotty 0.27.0-RC1 - ScalaJS, performance, stability, Announcing Dotty 0.26.0-RC1 - unified extension methods and more, Announcing Dotty 0.25.0-RC2 - speed-up of givens and change in the tuple API, Announcing Dotty 0.24.0-RC1 - 2.13.2 standard library, better error messages and more, Announcing Dotty 0.23.0-RC1 - safe initialization checks, type-level bitwise operations and more, Announcing Dotty 0.22.0-RC1 - syntactic enhancements, type-level arithmetic and more, Announcing Dotty 0.21.0-RC1 - explicit nulls, new syntax for `match` and conditional givens, and more, Announcing Dotty 0.20.0-RC1 â `with` starting indentation blocks, inline given specializations and more, Announcing Dotty 0.19.0-RC1 â further refinements of the syntax and the migration to 2.13.1 standard library, Announcing Dotty 0.18.1-RC1 â switch to the 2.13 standard library, indentation-based syntax and other experiments, Announcing Dotty 0.17.0-RC1 â new implicit scoping rules and more, Announcing Dotty 0.16.0-RC3 â the Scala Days 2019 Release, Announcing Dotty 0.15.0-RC1 â the fully bootstrapped compiler, Announcing Dotty 0.14.0-RC1 with export, immutable arrays, creator applications and more, Announcing Dotty 0.13.0-RC1 with Spark support, top level definitions and redesigned implicits, Announcing Dotty 0.2.0-RC1, with new optimizations, improved stability and IDE support, Announcing Dotty 0.1.2-RC1, a major step towards Scala 3, Dropped: private[this] and protected[this], Dotty Internals 1: Trees & Symbols (Meeting Notes). 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