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Generics: Details

Table of contents

Overview

This document goes into the details of the design of generic type parameters.

Imagine we want to write a function parameterized by a type argument. Maybe our function is PrintToStdout and let's say we want to operate on values that have a type for which we have an implementation of the ConvertibleToString interface. The ConvertibleToString interface has a ToString method returning a string. To do this, we give the PrintToStdout function two parameters: one is the value to print, let's call that val, the other is the type of that value, let's call that T. The type of val is T, what is the type of T? Well, since we want to let T be any type implementing the ConvertibleToString interface, we express that in the "interfaces are type-of-types" model by saying the type of T is ConvertibleToString.

Since we can figure out T from the type of val, we don't need the caller to pass in T explicitly, so it can be a deduced parameter (also see deduced parameters in the Generics overview doc). Basically, the user passes in a value for val, and the type of val determines T. T still gets passed into the function though, and it plays an important role -- it defines the key used to look up interface implementations.

We can think of the interface as defining a struct type whose members are function pointers, and an implementation of an interface as a value of that struct with actual function pointer values. An implementation is a table mapping the interface's functions to function pointers. For more on this, see the implementation model section.

In addition to function pointer members, interfaces can include any constants that belong to a type. For example, the type's size (represented by an integer constant member of the type) could be a member of an interface and its implementation. There are a few cases why we would include another interface implementation as a member:

The function expresses that the type argument is passed in statically, basically generating a separate function body for every different type passed in, by using the "generic argument" syntax :!, see the generics section below. The interface contains enough information to type and definition check the function body -- you can only call functions defined in the interface in the function body. Contrast this with making the type a template argument, where you could just use Type instead of an interface and it will work as long as the function is only called with types that allow the definition of the function to compile. The interface bound has other benefits:

  • allows the compiler to deliver clearer error messages,
  • documents expectations, and
  • expresses that a type has certain semantics beyond what is captured in its member function names and signatures.

The last piece of the puzzle is calling the function. For a value of type Song to be printed using the PrintToStdout function, Song needs to implement the ConvertibleToString interface. Interface implementations will usually be defined either with the type or with the interface. They may also be defined somewhere else as long as Carbon can be guaranteed to see the definition when needed. For more on this, see the implementing interfaces section below.

Unless the implementation of ConvertibleToString for Song is defined as external, every member of ConvertibleToString is also a member of Song. This includes members of ConvertibleToString that are not explicitly named in the impl definition but have defaults. Whether the implementation is defined as internal or external, you may access the ToString function for a Song value s by a writing function call using a qualified member access expression, like s.(ConvertibleToString.ToString)().

If Song doesn't implement an interface or we would like to use a different implementation of that interface, we can define another type that also has the same data representation as Song that has whatever different interface implementations we want. However, Carbon won't implicitly convert to that other type, the user will have to explicitly cast to that type in order to select those alternate implementations. For more on this, see the adapting type section below.

Interfaces

An interface, defines an API that a given type can implement. For example, an interface capturing a linear-algebra vector API might have two methods:

interface Vector {
  // Here `Self` means "the type implementing this interface".
  fn Add[me: Self](b: Self) -> Self;
  fn Scale[me: Self](v: f64) -> Self;
}

The syntax here is to match how the same members would be defined in a type. Each declaration in the interface defines an associated entity. In this example, Vector has two associated methods, Add and Scale.

An interface defines a type-of-type, that is a type whose values are types. The values of an interface are any types implementing the interface, and so provide definitions for all the functions (and other members) declared in the interface.

Implementing interfaces

Carbon interfaces are "nominal", which means that types explicitly describe how they implement interfaces. An "impl" defines how one interface is implemented for a type. Every associated entity is given a definition. Different types satisfying Vector can have different definitions for Add and Scale, so we say their definitions are associated with what type is implementing Vector. The impl defines what is associated with the type for that interface.

Impls may be defined inline inside the type definition:

class Point {
  var x: f64;
  var y: f64;
  impl as Vector {
    // In this scope, "Self" is an alias for "Point".
    fn Add[me: Self](b: Self) -> Self {
      return {.x = a.x + b.x, .y = a.y + b.y};
    }
    fn Scale[me: Self](v: f64) -> Self {
      return {.x = a.x * v, .y = a.y * v};
    }
  }
}

Interfaces that are implemented inline contribute to the type's API:

var p1: Point = {.x = 1.0, .y = 2.0};
var p2: Point = {.x = 2.0, .y = 4.0};
Assert(p1.Scale(2.0) == p2);
Assert(p1.Add(p1) == p2);

Note: A type may implement any number of different interfaces, but may provide at most one implementation of any single interface. This makes the act of selecting an implementation of an interface for a type unambiguous throughout the whole program.

Comparison with other languages: Rust defines implementations lexically outside of the class definition. This Carbon approach means that a type's API is described by declarations inside the class definition and doesn't change afterwards.

References: This interface implementation syntax was accepted in proposal #553. In particular, see the alternatives considered.

Implementing multiple interfaces

To implement more than one interface when defining a type, simply include an impl block per interface.

class Point {
  var x: f64;
  var y: f64;
  impl as Vector {
    fn Add[me: Self](b: Self) -> Self { ... }
    fn Scale[me: Self](v: f64) -> Self { ... }
  }
  impl as Drawable {
    fn Draw[me: Self]() { ... }
  }
}

In this case, all the functions Add, Scale, and Draw end up a part of the API for Point. This means you can't implement two interfaces that have a name in common (unless you use an external impl for one or both, as described below).

class GameBoard {
  impl as Drawable {
    fn Draw[me: Self]() { ... }
  }
  impl as EndOfGame {
    // ❌ Error: `GameBoard` has two methods named
    // `Draw` with the same signature.
    fn Draw[me: Self]() { ... }
    fn Winner[me: Self](player: i32) { ... }
  }
}

Open question: Should we have some syntax for the case where you want both names to be given the same implementation? It seems like that might be a common case, but we won't really know if this is an important case until we get more experience.

class Player {
  var name: String;
  impl as Icon {
    fn Name[me: Self]() -> String { return me.name; }
    // ...
  }
  impl as GameUnit {
    // Possible syntax options for defining
    // `GameUnit.Name` as the same as `Icon.Name`:
    alias Name = Icon.Name;
    fn Name[me: Self]() -> String = Icon.Name;
    // ...
  }
}

External impl

Interfaces may also be implemented for a type externally, by using the external impl construct. An external impl does not add the interface's methods to the type.

class Point2 {
  var x: f64;
  var y: f64;

  external impl as Vector {
    // In this scope, `Self` is an alias for `Point2`.
    fn Add[me: Self](b: Self) -> Self {
      return {.x = a.x + b.x, .y = a.y + b.y};
    }
    fn Scale[me: Self](v: f64) -> Self {
      return {.x = a.x * v, .y = a.y * v};
    }
  }
}

var a: Point2 = {.x = 1.0, .y = 2.0};
// `a` does *not* have `Add` and `Scale` methods:
// ❌ Error: a.Add(a.Scale(2.0));

An external impl may be defined out-of-line, by including the name of the existing type before as, which is otherwise optional:

class Point3 {
  var x: f64;
  var y: f64;
}

external impl Point3 as Vector {
  // In this scope, `Self` is an alias for `Point3`.
  fn Add[me: Self](b: Self) -> Self {
    return {.x = a.x + b.x, .y = a.y + b.y};
  }
  fn Scale[me: Self](v: f64) -> Self {
    return {.x = a.x * v, .y = a.y * v};
  }
}

var a: Point3 = {.x = 1.0, .y = 2.0};
// `a` does *not* have `Add` and `Scale` methods:
// ❌ Error: a.Add(a.Scale(2.0));

References: The external interface implementation syntax was decided in proposal #553. In particular, see the alternatives considered.

The external impl statement is allowed to be defined in a different library from Point3, restricted by the coherence/orphan rules that ensure that the implementation of an interface can't change based on imports. In particular, the external impl statement is allowed in the library defining the interface (Vector in this case) in addition to the library that defines the type (Point3 here). This (at least partially) addresses the expression problem.

Carbon requires impls defined in a different library to be external so that the API of Point3 doesn't change based on what is imported. It would be particularly bad if two different libraries implemented interfaces with conflicting names that both affected the API of a single type. As a consequence of this restriction, you can find all the names of direct members (those available by simple member access) of a type in the definition of that type. The only thing that may be in another library is an impl of an interface.

You might also use external impl to implement an interface for a type to avoid cluttering the API of that type, for example to avoid a name collision. A syntax for reusing method implementations allows us to do this selectively when needed. In this case, the external impl may be declared lexically inside the class scope.

class Point4a {
  var x: f64;
  var y: f64;
  fn Add[me: Self](b: Self) -> Self {
    return {.x = a.x + b.x, .y = a.y + b.y};
  }
  external impl as Vector {
    alias Add = Point4a.Add;  // Syntax TBD
    fn Scale[me: Self](v: f64) -> Self {
      return {.x = a.x * v, .y = a.y * v};
    }
  }
}

// OR:

class Point4b {
  var x: f64;
  var y: f64;
  external impl as Vector {
    fn Add[me: Self](b: Self) -> Self {
      return {.x = a.x + b.x, .y = a.y + b.y};
    }
    fn Scale[me: Self](v: f64) -> Self {
      return {.x = a.x * v, .y = a.y * v};
    }
  }
  alias Add = Vector.Add;  // Syntax TBD
}

// OR:

class Point4c {
  var x: f64;
  var y: f64;
  fn Add[me: Self](b: Self) -> Self {
    return {.x = a.x + b.x, .y = a.y + b.y};
  }
}

external impl Point4c as Vector {
  alias Add = Point4c.Add;  // Syntax TBD
  fn Scale[me: Self](v: f64) -> Self {
    return {.x = a.x * v, .y = a.y * v};
  }
}

Being defined lexically inside the class means that implementation is available to other members defined in the class. For example, it would allow implementing another interface or method that requires this interface to be implemented.

Open question: Do implementations need to be defined lexically inside the class to get access to private members, or is it sufficient to be defined in the same library as the class?

Rejected alternative: We could allow types to have different APIs in different files based on explicit configuration in that file. For example, we could support a declaration that a given interface or a given method of an interface is "in scope" for a particular type in this file. With that declaration, the method could be called using simple member access. This avoids most concerns arising from name collisions between interfaces. It has a few downsides though:

  • It increases variability between files, since the same type will have different APIs depending on these declarations. This makes it harder to copy-paste code between files.
  • It makes reading code harder, since you have to search the file for these declarations that affect name lookup.

Comparison with other languages: Both Rust and Swift support external implementation. Swift's syntax does this as an "extension" of the original type. In Rust, all implementations are external as in this example. Unlike Swift and Rust, we don't allow a type's API to be modified outside its definition. So in Carbon a type's API is consistent no matter what is imported, unlike Swift and Rust.

Qualified member names and compound member access

Given a value of type Point3 and an interface Vector implemented for that type, you can access the methods from that interface using a qualified member access expression whether or not the implementation is done externally with an external impl declaration. The qualified member access expression writes the member's qualified name in the parentheses of the compound member access syntax:

var p1: Point3 = {.x = 1.0, .y = 2.0};
var p2: Point3 = {.x = 2.0, .y = 4.0};
Assert(p1.(Vector.Scale)(2.0) == p2);
Assert(p1.(Vector.Add)(p1) == p2);

Note that the name in the parens is looked up in the containing scope, not in the names of members of Point3. So if there was another interface Drawable with method Draw defined in the Plot package also implemented for Point3, as in:

package Plot;
import Points;

interface Drawable {
  fn Draw[me: Self]();
}

external impl Points.Point3 as Drawable { ... }

You could access Draw with a qualified name:

import Plot;
import Points;

var p: Points.Point3 = {.x = 1.0, .y = 2.0};
p.(Plot.Drawable.Draw)();

Comparison with other languages: This is intended to be analogous to, in C++, adding ClassName:: in front of a member name to disambiguate, such as names defined in both a parent and child class.

Access

An impl must be visible to all code that can see both the type and the interface being implemented:

  • If either the type or interface is private to a single file, then since the only way to define the impl is to use that private name, the impl must be defined private to that file as well.
  • Otherwise, if the type or interface is private but declared in an API file, then the impl must be declared in the same file so the existence of that impl is visible to all files in that library.
  • Otherwise, the impl must be defined in the public API file of the library, so it is visible in all places that might use it.

No access control modifiers are allowed on impl declarations, an impl is always visible to the intersection of the visibility of all names used in the declaration of the impl.

Generics

Here is a function that can accept values of any type that has implemented the Vector interface:

fn AddAndScaleGeneric[T:! Vector](a: T, b: T, s: f64) -> T {
  return a.Add(b).Scale(s);
}
var v: Point = AddAndScaleGeneric(a, w, 2.5);

Here T is a type whose type is Vector. The :! syntax means that T is a generic parameter. That means it must be known to the caller, but we will only use the information present in the signature of the function to type check the body of AddAndScaleGeneric's definition. In this case, we know that any value of type T implements the Vector interface and so has an Add and a Scale method.

References: The :! syntax was accepted in proposal #676.

Names are looked up in the body of AddAndScaleGeneric for values of type T in Vector. This means that AddAndScaleGeneric is interpreted as equivalent to adding a Vector qualification to replace all simple member accesses of T:

fn AddAndScaleGeneric[T:! Vector](a: T, b: T, s: Double) -> T {
  return a.(Vector.Add)(b).(Vector.Scale)(s);
}

With these qualifications, the function can be type-checked for any T implementing Vector. This type checking is equivalent to type checking the function with T set to an archetype of Vector. An archetype is a placeholder type considered to satisfy its constraint, which is Vector in this case, and no more. It acts as the most general type satisfying the interface. The effect of this is that an archetype of Vector acts like a supertype of any T implementing Vector.

For name lookup purposes, an archetype is considered to have implemented its constraint internally. The only oddity is that the archetype may have different names for members than specific types T that implement interfaces from the constraint externally. This difference in names can also occur for supertypes in C++, for example members in a derived class can hide members in the base class with the same name, though it is not that common for it to come up in practice.

The behavior of calling AddAndScaleGeneric with a value of a specific type like Point is to set T to Point after all the names have been qualified.

// AddAndScaleGeneric with T = Point
fn AddAndScaleForPoint(a: Point, b: Point, s: Double) -> Point {
  return a.(Vector.Add)(b).(Vector.Scale)(s);
}

This qualification gives a consistent interpretation to the body of the function even when the type supplied by the caller implements the interface externally, as Point2 does:

// AddAndScaleGeneric with T = Point2
fn AddAndScaleForPoint2(a: Point2, b: Point2, s: Double) -> Point2 {
  // ✅ This works even though `a.Add(b).Scale(s)` wouldn't.
  return a.(Vector.Add)(b).(Vector.Scale)(s);
}

Return type

From the caller's perspective, the return type is the result of substituting the caller's values for the generic parameters into the return type expression. So AddAndScaleGeneric called with Point values returns a Point and called with Point2 values returns a Point2. So looking up a member on the resulting value will look in Point or Point2 rather than Vector.

This is part of realizing the goal that generic functions can be used in place of regular functions without changing the return type that callers see. In this example, AddAndScaleGeneric can be substituted for AddAndScaleForPoint and AddAndScaleForPoint2 without affecting the return types. This requires the return value to be converted to the type that the caller expects instead of the erased type used inside the generic function.

A generic caller of a generic function performs the same substitution process to determine the return type, but the result may be generic. In this example of calling a generic from another generic,

fn DoubleThreeTimes[U:! Vector](a: U) -> U {
  return AddAndScaleGeneric(a, a, 2.0).Scale(2.0);
}

the return type of AddAndScaleGeneric is found by substituting in the U from DoubleThreeTimes for the T from AddAndScaleGeneric in the return type expression of AddAndScaleGeneric. U is an archetype of Vector, and so implements Vector internally and therefore has a Scale method.

If U had a more specific type, the return value would have the additional capabilities of U. For example, given a parameterized type GeneralPoint implementing Vector, and a function that takes a GeneralPoint and calls AddAndScaleGeneric with it:

class GeneralPoint(C:! Numeric) {
  external impl as Vector { ... }
  fn Get[me: Self](i: i32) -> C;
}

fn CallWithGeneralPoint[C:! Numeric](p: GeneralPoint(C)) -> C {
  // `AddAndScaleGeneric` returns `T` and in these calls `T` is
  // deduced to be `GeneralPoint(C)`.

  // ❌ Illegal: AddAndScaleGeneric(p, p, 2.0).Scale(2.0);
  //    `GeneralPoint(C)` implements `Vector` externally, and so
  //    does not have a `Scale` method.

  // ✅ Allowed: `GeneralPoint(C)` has a `Get` method
  AddAndScaleGeneric(p, p, 2.0).Get(0);

  // ✅ Allowed: `GeneralPoint(C)` implements `Vector`
  //    externally, and so has a `Vector.Scale` method.
  //    `Vector.Scale` returns `Self` which is `GeneralPoint(C)`
  //    again, and so has a `Get` method.
  return AddAndScaleGeneric(p, p, 2.0).(Vector.Scale)(2.0).Get(0);
}

The result of the call to AddAndScaleGeneric from CallWithGeneralPoint has type GeneralPoint(C) and so has a Get method and a Vector.Scale method. But, in contrast to how DoubleThreeTimes works, since Vector is implemented externally the return value in this case does not directly have a Scale method.

Implementation model

A possible model for generating code for a generic function is to use a witness table to represent how a type implements an interface:

Type checking is done with just the interface. The impl is used during code generation time, possibly using monomorphization to have a separate instantiation of the function for each combination of the generic argument values. The compiler is free to use other implementation strategies, such as passing the witness table for any needed implementations, if that can be predicted.

For the example above, the Vector interface could be thought of defining a witness table type like:

class Vector {
  // `Self` is the representation type, which is only
  // known at compile time.
  var Self:! Type;
  // `fnty` is **placeholder** syntax for a "function type",
  // so `Add` is a function that takes two `Self` parameters
  // and returns a value of type `Self`.
  var Add: fnty(a: Self, b: Self) -> Self;
  var Scale: fnty(a: Self, v: f64) -> Self;
}

The impl of Vector for Point would be a value of this type:

var VectorForPoint: Vector  = {
    .Self = Point,
    // `lambda` is **placeholder** syntax for defining a
    // function value.
    .Add = lambda(a: Point, b: Point) -> Point {
      return {.x = a.x + b.x, .y = a.y + b.y};
    },
    .Scale = lambda(a: Point, v: f64) -> Point {
      return {.x = a.x * v, .y = a.y * v};
    },
};

Since generic arguments (where the parameter is declared using :!) are passed at compile time, so the actual value of VectorForPoint can be used to generate the code for functions using that impl. This is the static-dispatch witness table approach.

Interfaces recap

Interfaces have a name and a definition.

The definition of an interface consists of a set of declarations. Each declaration defines a requirement for any impl that is in turn a capability that consumers of that impl can rely on. Typically those declarations also have names, useful for both saying how the impl satisfies the requirement and accessing the capability.

Interfaces are "nominal", which means their name is significant. So two interfaces with the same body definition but different names are different, just like two classes with the same definition but different names are considered different types. For example, lets say we define another interface, say LegoFish, with the same Add and Scale method signatures. Implementing Vector would not imply an implementation of LegoFish, because the impl definition explicitly refers to the name Vector.

An interface's name may be used in a few different contexts:

While interfaces are examples of type-of-types, type-of-types are a more general concept, for which interfaces are a building block.

Type-of-types

A type-of-type consists of a set of requirements and a set of names. Requirements are typically a set of interfaces that a type must satisfy, though other kinds of requirements are added below. The names are aliases for qualified names in those interfaces.

An interface is one particularly simple example of a type-of-type. For example, Vector as a type-of-type has a set of requirements consisting of the single interface Vector. Its set of names consists of Add and Scale which are aliases for the corresponding qualified names inside Vector as a namespace.

The requirements determine which types are values of a given type-of-type. The set of names in a type-of-type determines the API of a generic type value and define the result of member access into the type-of-type.

This general structure of type-of-types holds not just for interfaces, but others described in the rest of this document.

Named constraints

If the interfaces discussed above are the building blocks for type-of-types, generic named constraints describe how they may be composed together. Unlike interfaces which are nominal, the name of a named constraint is not a part of its value. Two different named constraints with the same definition are equivalent even if they have different names. This is because types don't explicitly specify which named constraints they implement, types automatically implement any named constraints they can satisfy.

A named constraint definition can contain interface requirements using impl declarations and names using alias declarations. Note that this allows us to declare the aspects of a type-of-type directly.

constraint VectorLegoFish {
  // Interface implementation requirements
  impl as Vector;
  impl as LegoFish;
  // Names
  alias Scale = Vector.Scale;
  alias VAdd = Vector.Add;
  alias LFAdd = LegoFish.Add;
}

We don't expect developers to directly define many named constraints, but other constructs we do expect them to use will be defined in terms of them. For example, we can define the Carbon builtin Type as:

constraint Type { }

That is, Type is the type-of-type with no requirements (so matches every type), and defines no names.

fn Identity[T:! Type](x: T) -> T {
  // Can accept values of any type. But, since we know nothing about the
  // type, we don't know about any operations on `x` inside this function.
  return x;
}

var i: i32 = Identity(3);
var s: String = Identity("string");

Aside: We can define auto as syntactic sugar for (template _:! Type). This definition allows you to use auto as the type for a local variable whose type can be statically determined by the compiler. It also allows you to use auto as the type of a function parameter, to mean "accepts a value of any type, and this function will be instantiated separately for every different type." This is consistent with the use of auto in the C++20 Abbreviated function template feature.

In general, the declarations in constraint definition match a subset of the declarations in an interface. Named constraints used with generics, as opposed to templates, should only include required interfaces and aliases to named members of those interfaces.

To declare a named constraint that includes other declarations for use with template parameters, use the template keyword before constraint. Method, associated type, and associated function requirements may only be declared inside a template constraint. Note that a generic constraint ignores the names of members defined for a type, but a template constraint can depend on them.

There is an analogy between declarations used in a constraint and in an interface definition. If an interface I has (non-alias) declarations X, Y, and Z, like so:

interface I {
  X;
  Y;
  Z;
}

Then a type implementing I would have impl as I with definitions for X, Y, and Z, as in:

class ImplementsI {
  // ...
  impl as I {
    X { ... }
    Y { ... }
    Z { ... }
  }
}

But the corresponding constraint or template constraint, S:

// or template constraint S {
constraint S {
  X;
  Y;
  Z;
}

would match any type with definitions for X, Y, and Z directly:

class ImplementsS {
  // ...
  X { ... }
  Y { ... }
  Z { ... }
}

TODO: Move the template constraint and auto content to the template design document, once it exists.

Subtyping between type-of-types

There is a subtyping relationship between type-of-types that allows calls of one generic function from another as long as it has a subset of the requirements.

Given a generic type variable T with type-of-type I1, it satisfies a type-of-type I2 as long as the requirements of I1 are a superset of the requirements of I2. This means a value x of type T may be passed to functions requiring types to satisfy I2, as in this example:

interface Printable { fn Print[me: Self](); }
interface Renderable { fn Draw[me: Self](); }

constraint PrintAndRender {
  impl as Printable;
  impl as Renderable;
}
constraint JustPrint {
  impl as Printable;
}

fn PrintIt[T2:! JustPrint](x2: T2) {
  x2.(Printable.Print)();
}
fn PrintDrawPrint[T1:! PrintAndRender](x1: T1) {
  // x1 implements `Printable` and `Renderable`.
  x1.(Printable.Print)();
  x1.(Renderable.Draw)();
  // Can call `PrintIt` since `T1` satisfies `JustPrint` since
  // it implements `Printable` (in addition to `Renderable`).
  PrintIt(x1);
}

Combining interfaces by anding type-of-types

In order to support functions that require more than one interface to be implemented, we provide a combination operator on type-of-types, written &. This operator gives the type-of-type with the union of all the requirements and the union of the names minus any conflicts.

interface Printable {
  fn Print[me: Self]();
}
interface Renderable {
  fn Center[me: Self]() -> (i32, i32);
  fn Draw[me: Self]();
}

// `Printable & Renderable` is syntactic sugar for this type-of-type:
constraint {
  impl as Printable;
  impl as Renderable;
  alias Print = Printable.Print;
  alias Center = Renderable.Center;
  alias Draw = Renderable.Draw;
}

fn PrintThenDraw[T:! Printable & Renderable](x: T) {
  // Can use methods of `Printable` or `Renderable` on `x` here.
  x.Print();  // Same as `x.(Printable.Print)();`.
  x.Draw();  // Same as `x.(Renderable.Draw)();`.
}

class Sprite {
  // ...
  impl as Printable {
    fn Print[me: Self]() { ... }
  }
  impl as Renderable {
    fn Center[me: Self]() -> (i32, i32) { ... }
    fn Draw[me: Self]() { ... }
  }
}

var s: Sprite = ...;
PrintThenDraw(s);

Any conflicting names between the two types are replaced with a name that is an error to use.

interface Renderable {
  fn Center[me: Self]() -> (i32, i32);
  fn Draw[me: Self]();
}
interface EndOfGame {
  fn Draw[me: Self]();
  fn Winner[me: Self](player: i32);
}
// `Renderable & EndOfGame` is syntactic sugar for this type-of-type:
constraint {
  impl as Renderable;
  impl as EndOfGame;
  alias Center = Renderable.Center;
  // Open question: `forbidden`, `invalid`, or something else?
  forbidden Draw
    message "Ambiguous, use either `(Renderable.Draw)` or `(EndOfGame.Draw)`.";
  alias Winner = EndOfGame.Winner;
}

Conflicts can be resolved at the call site using a qualified member access expression, or by defining a named constraint explicitly and renaming the methods:

constraint RenderableAndEndOfGame {
  impl as Renderable;
  impl as EndOfGame;
  alias Center = Renderable.Center;
  alias RenderableDraw = Renderable.Draw;
  alias TieGame = EndOfGame.Draw;
  alias Winner = EndOfGame.Winner;
}

fn RenderTieGame[T:! RenderableAndEndOfGame](x: T) {
  // Calls Renderable.Draw()
  x.RenderableDraw();
  // Calls EndOfGame.Draw()
  x.TieGame();
}

Reserving the name when there is a conflict is part of resolving what happens when you combine more than two type-of-types. If x is forbidden in A, it is forbidden in A & B, whether or not B defines the name x. This makes & associative and commutative, and so it is well defined on sets of interfaces, or other type-of-types, independent of order.

Note that we do not consider two type-of-types using the same name to mean the same thing to be a conflict. For example, combining a type-of-type with itself gives itself, MyTypeOfType & MyTypeOfType == MyTypeOfType. Also, given two interface extensions of a common base interface, the sum should not conflict on any names in the common base.

Rejected alternative: Instead of using & as the combining operator, we considered using +, like Rust. See #531 for the discussion.

Future work: We may want to define another operator on type-of-types for adding requirements to a type-of-type without affecting the names, and so avoid the possibility of name conflicts. Note this means the operation is not commutative. If we call this operator [&], then A [&] B has the names of A and B [&] A has the names of B.

// `Printable [&] Renderable` is syntactic sugar for this type-of-type:
constraint {
  impl as Printable;
  impl as Renderable;
  alias Print = Printable.Print;
}

// `Renderable [&] EndOfGame` is syntactic sugar for this type-of-type:
constraint {
  impl as Renderable;
  impl as EndOfGame;
  alias Center = Renderable.Center;
  alias Draw = Renderable.Draw;
}

Note that all three expressions A & B, A [&] B, and B [&] A have the same requirements, and so you would be able to switch a function declaration between them without affecting callers.

Nothing in this design depends on the [&] operator, and having both & and [&] might be confusing for users, so it makes sense to postpone implementing [&] until we have a demonstrated need. The [&] operator seems most useful for adding requirements for interfaces used for operator overloading, where merely implementing the interface is enough to be able to use the operator to access the functionality.

Alternatives considered: See Carbon: Access to interface methods.

Comparison with other languages: This & operation on interfaces works very similarly to Rust's + operation, with the main difference being how you qualify names when there is a conflict.

Interface requiring other interfaces

Some interfaces will depend on other interfaces being implemented for the same type. For example, in C++, the Container concept requires all containers to also satisfy the requirements of DefaultConstructible, CopyConstructible, EqualityComparable, and Swappable. This is already a capability for type-of-types in general. For consistency we will use the same semantics and syntax as we do for named constraints:

interface Equatable { fn Equals[me: Self](rhs: Self) -> bool; }

interface Iterable {
  fn Advance[addr me: Self*]() -> bool;
  impl as Equatable;
}

def DoAdvanceAndEquals[T:! Iterable](x: T) {
  // `x` has type `T` that implements `Iterable`, and so has `Advance`.
  x.Advance();
  // `Iterable` requires an implementation of `Equatable`,
  // so `T` also implements `Equatable`.
  x.(Equatable.Equals)(x);
}

class Iota {
  impl as Iterable { fn Advance[me: Self]() { ... } }
  impl as Equatable { fn Equals[me: Self](rhs: Self) -> bool { ... } }
}
var x: Iota;
DoAdvanceAndEquals(x);

Like with named constraints, an interface implementation requirement doesn't by itself add any names to the interface, but again those can be added with alias declarations:

interface Hashable {
  fn Hash[me: Self]() -> u64;
  impl as Equatable;
  alias Equals = Equatable.Equals;
}

def DoHashAndEquals[T:! Hashable](x: T) {
  // Now both `Hash` and `Equals` are available directly:
  x.Hash();
  x.Equals(x);
}

Comparison with other languages: This feature is called "Supertraits" in Rust.

Note: The design for this feature is continued in a later section.

Interface extension

When implementing an interface, we should allow implementing the aliased names as well. In the case of Hashable above, this includes all the members of Equatable, obviating the need to implement Equatable itself:

class Song {
  impl as Hashable {
    fn Hash[me: Self]() -> u64 { ... }
    fn Equals[me: Self](rhs: Self) -> bool { ... }
  }
}
var y: Song;
DoHashAndEquals(y);

This allows us to say that Hashable "extends" Equatable, with some benefits:

  • This allows Equatable to be an implementation detail of Hashable.
  • This allows types implementing Hashable to implement all of its API in one place.
  • This reduces the boilerplate for types implementing Hashable.

We expect this concept to be common enough to warrant dedicated syntax:

interface Equatable { fn Equals[me: Self](rhs: Self) -> bool; }

interface Hashable {
  extends Equatable;
  fn Hash[me: Self]() -> u64;
}
// is equivalent to the definition of Hashable from before:
// interface Hashable {
//   impl as Equatable;
//   alias Equals = Equatable.Equals;
//   fn Hash[me: Self]() -> u64;
// }

No names in Hashable are allowed to conflict with names in Equatable (unless those names are marked as upcoming or deprecated as in evolution future work). Hopefully this won't be a problem in practice, since interface extension is a very closely coupled relationship, but this may be something we will have to revisit in the future.

Examples:

To write an interface extending multiple interfaces, use multiple extends declarations. For example, the BinaryInteger protocol in Swift inherits from CustomStringConvertible, Hashable, Numeric, and Stridable. The SetAlgebra protocol extends Equatable and ExpressibleByArrayLiteral, which would be declared in Carbon:

interface SetAlgebra {
  extends Equatable;
  extends ExpressibleByArrayLiteral;
}

Alternative considered: The extends declarations are in the body of the interface definition instead of the header so we can use associated types (defined below) also defined in the body in parameters or constraints of the interface being extended.

// A type can implement `ConvertibleTo` many times, using
// different values of `T`.
interface ConvertibleTo(T:! Type) { ... }

// A type can only implement `PreferredConversion` once.
interface PreferredConversion {
  let AssociatedType:! Type;
  extends ConvertibleTo(AssociatedType);
}

extends and impl with named constraints

The extends declaration makes sense with the same meaning inside a constraint definition, and so is also supported.

interface Media {
  fn Play[me: Self]();
}
interface Job {
  fn Run[me: Self]();
}

constraint Combined {
  extends Media;
  extends Job;
}

This definition of Combined is equivalent to requiring both the Media and Job interfaces being implemented, and aliases their methods.

// Equivalent
constraint Combined {
  impl as Media;
  alias Play = Media.Play;
  impl as Job;
  alias Run = Job.Run;
}

Notice how Combined has aliases for all the methods in the interfaces it requires. That condition is sufficient to allow a type to impl the named constraint:

class Song {
  impl as Combined {
    fn Play[me: Self]() { ... }
    fn Run[me: Self]() { ... }
  }
}

This is equivalent to implementing the required interfaces directly:

class Song {
  impl as Media {
    fn Play[me: Self]() { ... }
  }
  impl as Job {
    fn Run[me: Self]() { ... }
  }
}

This is just like when you get an implementation of Equatable by implementing Hashable when Hashable extends Equatable. This provides a tool useful for evolution.

Conversely, an interface can extend a constraint:

interface MovieCodec {
  extends Combined;

  fn Load[addr me: Self*](filename: String);
}

This gives MovieCodec the same requirements and names as Combined, and so is equivalent to:

interface MovieCodec {
  impl as Media;
  alias Play = Media.Play;
  impl as Job;
  alias Run = Job.Run;

  fn Load[addr me: Self*](filename: String);
}

Diamond dependency issue

Consider this set of interfaces, simplified from this example generic graph library doc:

interface Graph {
  fn Source[addr me: Self*](e: EdgeDescriptor) -> VertexDescriptor;
  fn Target[addr me: Self*](e: EdgeDescriptor) -> VertexDescriptor;
}

interface IncidenceGraph {
  extends Graph;
  fn OutEdges[addr me: Self*](u: VertexDescriptor)
    -> (EdgeIterator, EdgeIterator);
}

interface EdgeListGraph {
  extends Graph;
  fn Edges[addr me: Self*]() -> (EdgeIterator, EdgeIterator);
}

We need to specify what happens when a graph type implements both IncidenceGraph and EdgeListGraph, since both interfaces extend the Graph interface.

class MyEdgeListIncidenceGraph {
  impl as IncidenceGraph { ... }
  impl as EdgeListGraph { ... }
}

The rule is that we need one definition of each method of Graph. Each method though could be defined in the impl block of IncidenceGraph, EdgeListGraph, or Graph. These would all be valid:

  • IncidenceGraph implements all methods of Graph, EdgeListGraph implements none of them.

    class MyEdgeListIncidenceGraph {
  impl as IncidenceGraph {
    fn Source[me: Self](e: EdgeDescriptor) -> VertexDescriptor { ... }
    fn Target[me: Self](e: EdgeDescriptor) -> VertexDescriptor { ... }
    fn OutEdges[addr me: Self*](u: VertexDescriptor)
        -> (EdgeIterator, EdgeIterator) { ... }
  }
  impl as EdgeListGraph {
    fn Edges[addr me: Self*]() -> (EdgeIterator, EdgeIterator) { ... }
  }
}

  • IncidenceGraph and EdgeListGraph implement all methods of Graph between them, but with no overlap.

    class MyEdgeListIncidenceGraph {
  impl as IncidenceGraph {
    fn Source[me: Self](e: EdgeDescriptor) -> VertexDescriptor { ... }
    fn OutEdges[addr me: Self*](u: VertexDescriptor)
        -> (EdgeIterator, EdgeIterator) { ... }
  }
  impl as EdgeListGraph {
    fn Target[me: Self](e: EdgeDescriptor) -> VertexDescriptor { ... }
    fn Edges[addr me: Self*]() -> (EdgeIterator, EdgeIterator) { ... }
  }
}

  • Explicitly implementing Graph.

    class MyEdgeListIncidenceGraph {
  impl as Graph {
    fn Source[me: Self](e: EdgeDescriptor) -> VertexDescriptor { ... }
    fn Target[me: Self](e: EdgeDescriptor) -> VertexDescriptor { ... }
  }
  impl as IncidenceGraph { ... }
  impl as EdgeListGraph { ... }
}

  • Implementing Graph externally.

    class MyEdgeListIncidenceGraph {
  impl as IncidenceGraph { ... }
  impl as EdgeListGraph { ... }
}
external impl MyEdgeListIncidenceGraph as Graph {
  fn Source[me: Self](e: EdgeDescriptor) -> VertexDescriptor { ... }
  fn Target[me: Self](e: EdgeDescriptor) -> VertexDescriptor { ... }
}

This last point means that there are situations where we can only detect a missing method definition by the end of the file. This doesn't delay other aspects of semantic checking, which will just assume that these methods will eventually be provided.

Open question: We could require that the external impl of the required interface be declared lexically in the class scope in this case. That would allow earlier detection of missing definitions.

Use case: overload resolution

Implementing an extended interface is an example of a more specific match for lookup resolution. For example, this could be used to provide different implementations of an algorithm depending on the capabilities of the iterator being passed in:

interface ForwardIntIterator {
  fn Advance[addr me: Self*]();
  fn Get[me: Self]() -> i32;
}
interface BidirectionalIntIterator {
  extends ForwardIntIterator;
  fn Back[addr me: Self*]();
}
interface RandomAccessIntIterator {
  extends BidirectionalIntIterator;
  fn Skip[addr me: Self*](offset: i32);
  fn Difference[me: Self](rhs: Self) -> i32;
}

fn SearchInSortedList[IterT:! ForwardIntIterator]
    (begin: IterT, end: IterT, needle: i32) -> bool {
  ... // does linear search
}
// Will prefer the following overload when it matches
// since it is more specific.
fn SearchInSortedList[IterT:! RandomAccessIntIterator]
    (begin: IterT, end: IterT, needle: i32) -> bool {
  ... // does binary search
}

This would be an example of the more general rule that an interface A requiring an implementation of interface B means A is more specific than B.

Adapting types

Since interfaces may only be implemented for a type once, and we limit where implementations may be added to a type, there is a need to allow the user to switch the type of a value to access different interface implementations. Carbon therefore provides a way to create new types compatible with existing types with different APIs, in particular with different interface implementations, by adapting them:

interface Printable {
  fn Print[me: Self]();
}
interface Comparable {
  fn Less[me: Self](rhs: Self) -> bool;
}
class Song {
  impl as Printable { fn Print[me: Self]() { ... } }
}
adapter SongByTitle for Song {
  impl as Comparable {
    fn Less[me: Self](rhs: Self) -> bool { ... }
  }
}
adapter FormattedSong for Song {
  impl as Printable { fn Print[me: Self]() { ... } }
}
adapter FormattedSongByTitle for Song {
  impl as Printable = FormattedSong;
  impl as Comparable = SongByTitle;
}

This allows developers to provide implementations of new interfaces (as in SongByTitle), provide different implementations of the same interface (as in FormattedSong), or mix and match implementations from other compatible types (as in FormattedSongByTitle). The rules are:

  • You can add any declaration that you could add to a class except for declarations that would change the representation of the type. This means you can add methods, functions, interface implementations, and aliases, but not fields, base classes, or virtual functions.
  • The adapted type is compatible with the original type, and that relationship is an equivalence class, so all of Song, SongByTitle, FormattedSong, and FormattedSongByTitle end up compatible with each other.
  • Since adapted types are compatible with the original type, you may explicitly cast between them, but there is no implicit conversion between these types.

Inside an adapter, the Self type matches the adapter. Members of the original type may be accessed either by a cast:

adapter SongByTitle for Song {
  impl as Comparable {
    fn Less[me: Self](rhs: Self) -> bool {
      return (me as Song).Title() < (rhs as Song).Title();
    }
  }
}

or using a qualified member access expression:

adapter SongByTitle for Song {
  impl as Comparable {
    fn Less[me: Self](rhs: Self) -> bool {
      return me.(Song.Title)() < rhs.(Song.Title)();
    }
  }
}

Comparison with other languages: This matches the Rust idiom called "newtype", which is used to implement traits on types while avoiding coherence problems, see here and here. Rust's mechanism doesn't directly support reusing implementations, though some of that is provided by macros defined in libraries. Haskell has a newtype feature as well. Haskell's feature doesn't directly support reusing implementations either, but the most popular compiler provides it as an extension.

Adapter compatibility

Consider a type with a generic type parameter, like a hash map:

interface Hashable { ... }
class HashMap(KeyT:! Hashable, ValueT:! Type) {
  fn Find[me:Self](key: KeyT) -> Optional(ValueT);
  // ...
}

A user of this type will provide specific values for the key and value types:

class Song {
  impl as Hashable { ... }
  // ...
}

var play_count: HashMap(Song, i32) = ...;
var thriller_count: Optional(i32) =
    play_count.Find(Song("Thriller"));

Since the Find function is generic, it can only use the capabilities that HashMap requires of KeyT and ValueT. This allows us to evaluate when we can convert between two different arguments to a parameterized type. Consider two adapters of Song that implement Hashable:

adapter PlayableSong for Song {
  impl as Hashable = Song;
  impl as Media { ... }
}
adapter SongHashedByTitle for Song {
  impl as Hashable { ... }
}

Song and PlayableSong have the same implementation of Hashable in addition to using the same data representation. This means that it is safe to convert between HashMap(Song, i32) and HashMap(PlayableSong, i32), because the implementation of all the methods will use the same implementation of the Hashable interface. Carbon permits this conversion with an explicit cast.

On the other hand, SongHashedByTitle has a different implementation of Hashable than Song. So even though Song and SongHashedByTitle are compatible types, HashMap(Song, i32) and HashMap(SongHashedByTitle, i32) are incompatible. This is important because we know that in practice the invariants of a HashMap implementation rely on the hashing function staying the same.

Extending adapter

Frequently we expect that the adapter type will want to preserve most or all of the API of the original type. The two most common cases expected are adding and replacing an interface implementation. Users would indicate that an adapter starts from the original type's existing API by using the extends keyword instead of for:

class Song {
  impl as Hashable { ... }
  impl as Printable { ... }
}

adapter SongByArtist extends Song {
  // Add an implementation of a new interface
  impl as Comparable { ... }

  // Replace an existing implementation of an interface
  // with an alternative.
  impl as Hashable { ... }
}

The resulting type SongByArtist would:

  • implement Comparable, unlike Song,
  • implement Hashable, but differently than Song, and
  • implement Printable, inherited from Song.

Unlike the similar class B extends A notation, adapter B extends A is permitted even if A is a final class. Also, there is no implicit conversion from B to A, matching adapter...for but unlike class extension.

To avoid or resolve name conflicts between interfaces, an impl may be declared external. The names in that interface may then be pulled in individually or renamed using alias declarations.

adapter SongRenderToPrintDriver extends Song {
  // Add a new `Print()` member function.
  fn Print[me: Self]() { ... }

  // Avoid name conflict with new `Print` function by making
  // the implementation of the `Printable` interface external.
  external impl as Printable = Song;

  // Make the `Print` function from `Printable` available
  // under the name `PrintToScreen`.
  alias PrintToScreen = Printable.Print;
}

Use case: Using independent libraries together

Imagine we have two packages that are developed independently. Package CompareLib defines an interface CompareLib.Comparable and a generic algorithm CompareLib.Sort that operates on types that implement CompareLib.Comparable. Package SongLib defines a type SongLib.Song. Neither has a dependency on the other, so neither package defines an implementation for CompareLib.Comparable for type SongLib.Song. A user that wants to pass a value of type SongLib.Song to CompareLib.Sort has to define an adapter that provides an implementation of CompareLib.Comparable for SongLib.Song. This adapter will probably use the extends facility of adapters to preserve the SongLib.Song API.

import CompareLib;
import SongLib;

adapter Song extends SongLib.Song {
  impl as CompareLib.Comparable { ... }
}
// Or, to keep the names from CompareLib.Comparable out of Song's API:
adapter Song extends SongLib.Song { }
external impl Song as CompareLib.Comparable { ... }
// Or, equivalently:
adapter Song extends SongLib.Song {
  external impl as CompareLib.Comparable { ... }
}

The caller can either convert SongLib.Song values to Song when calling CompareLib.Sort or just start with Song values in the first place.

var lib_song: SongLib.Song = ...;
CompareLib.Sort((lib_song as Song,));

var song: Song = ...;
CompareLib.Sort((song,));

Use case: Defining an impl for use by other types

Let's say we want to provide a possible implementation of an interface for use by types for which that implementation would be appropriate. We can do that by defining an adapter implementing the interface that is parameterized on the type it is adapting. That impl may then be pulled in using the impl as ... = ...; syntax.

For example, given an interface Comparable for deciding which value is smaller:

interface Comparable {
  fn Less[me: Self](rhs: Self) -> bool;
}

We might define an adapter that implements Comparable for types that define another interface Difference:

interface Difference {
  fn Sub[me:Self](rhs: Self) -> i32;
}
adapter ComparableFromDifference(T:! Difference) for T {
  impl as Comparable {
    fn Less[me: Self](rhs: Self) -> bool {
      return (me as T).Sub(rhs) < 0;
    }
  }
}
class IntWrapper {
  var x: i32;
  impl as Difference {
    fn Sub[me: Self](rhs: Self) -> i32 {
      return left.x - right.x;
    }
  }
  impl as Comparable = ComparableFromDifferenceFn(IntWrapper);
}

TODO: If we support function types, we could potentially pass a function to use to the adapter instead:

adapter ComparableFromDifferenceFn
    (T:! Type, Difference:! fnty(T, T)->i32) for T {
  impl as Comparable {
    fn Less[me: Self](rhs: Self) -> bool {
      return Difference(me, rhs) < 0;
    }
  }
}
class IntWrapper {
  var x: i32;
  fn Difference(left: Self, right: Self) {
    return left.x - right.x;
  }
  impl as Comparable =
      ComparableFromDifferenceFn(IntWrapper, Difference);
}

Use case: Private impl

Adapter types can be used when a library publicly exposes a type, but only wants to say that type implements an interface as a private detail internal to the implementation of the type. In that case, instead of implementing the interface for the public type, the library can create a private adapter for that type and implement the interface on that instead. Any member of the class can cast its me parameter to the adapter type when it wants to make use of the private impl.

// Public, in API file
class Complex64 {
  // ...
  fn CloserToOrigin[me: Self](them: Self) -> bool;
}

// Private

adapter ByReal extends Complex64 {
  // Complex numbers are not generally comparable,
  // but this comparison function is useful for some
  // method implementations.
  impl as Comparable {
    fn Less[me: Self](that: Self) -> bool {
      return me.Real() < that.Real();
    }
  }
}

fn Complex64.CloserToOrigin[me: Self](them: Self) -> bool {
  var me_mag: ByReal = me * me.Conj() as ByReal;
  var them_mag: ByReal = them * them.Conj() as ByReal;
  return me_mag.Less(them_mag);
}

Use case: Accessing external names

Consider a case where a function will call several functions from an interface that is implemented externally for a type.

interface DrawingContext {
  fn SetPen[me: Self](...);
  fn SetFill[me: Self](...);
  fn DrawRectangle[me: Self](...);
  fn DrawLine[me: Self](...);
  ...
}
external impl Window as DrawingContext { ... }

An adapter can make that much more convenient by making a compatible type where the interface is implemented internally. This avoids having to qualify each call to methods in the interface.

adapter DrawInWindow for Window {
  impl as DrawingContext = Window;
}
fn Render(w: Window) {
  let d: DrawInWindow = w as DrawInWindow;
  d.SetPen(...);
  d.SetFill(...);
  d.DrawRectangle(...);
  ...
}

Adapter with stricter invariants

Future work: Rust also uses the newtype idiom to create types with additional invariants or other information encoded in the type (1, 2, 3). This is used to record in the type system that some data has passed validation checks, like ValidDate with the same data layout as Date. Or to record the units associated with a value, such as Seconds versus Milliseconds or Feet versus Meters. We should have some way of restricting the casts between a type and an adapter to address this use case.

Associated constants

In addition to associated methods, we allow other kinds of associated entities. For consistency, we use the same syntax to describe a constant in an interface as in a type without assigning a value. As constants, they are declared using the let introducer. For example, a fixed-dimensional point type could have the dimension as an associated constant.

interface NSpacePoint {
  let N:! i32;
  // The following require: 0 <= i < N.
  fn Get[addr me: Self*](i: i32) -> f64;
  fn Set[addr me: Self*](i: i32, value: f64);
  // Associated constants may be used in signatures:
  fn SetAll[addr me: Self*](value: Array(f64, N));
}

An implementation of an interface specifies values for associated constants with a where clause. For example, implementations of NSpacePoint for different types might have different values for N:

class Point2D {
  impl as NSpacePoint where .N = 2 {
    fn Get[addr me: Self*](i: i32) -> f64 { ... }
    fn Set[addr me: Self*](i: i32, value: f64) { ... }
    fn SetAll[addr me: Self*](value: Array(f64, 2)) { ... }
  }
}

class Point3D {
  impl as NSpacePoint where .N = 3 {
    fn Get[addr me: Self*](i: i32) -> f64 { ... }
    fn Set[addr me: Self*](i: i32, value: f64) { ... }
    fn SetAll[addr me: Self*](value: Array(f64, 3)) { ... }
  }
}

Multiple assignments to associated constants may be joined using the and keyword. The list of assignments is subject to two restrictions:

  • An implementation of an interface cannot specify a value for a final associated constant.
  • If an associated constant doesn't have a default value, every implementation must specify its value.

These values may be accessed as members of the type:

Assert(Point2D.N == 2);
Assert(Point3D.N == 3);

fn PrintPoint[PointT:! NSpacePoint](p: PointT) {
  for (var i: i32 = 0; i < PointT.N; ++i) {
    if (i > 0) { Print(", "); }
    Print(p.Get(i));
  }
}

fn ExtractPoint[PointT:! NSpacePoint](
    p: PointT,
    dest: Array(f64, PointT.N)*) {
  for (var i: i32 = 0; i < PointT.N; ++i) {
    (*dest)[i] = p.Get(i);
  }
}

Comparison with other languages: This feature is also called associated constants in Rust.

Aside: In general, the use of :! here means these let declarations will only have compile-time and not runtime storage associated with them.

Associated class functions

To be consistent with normal class function declaration syntax, associated class functions are written using a fn declaration:

interface DeserializeFromString {
  fn Deserialize(serialized: String) -> Self;
}

class MySerializableType {
  var i: i32;

  impl as DeserializeFromString {
    fn Deserialize(serialized: String) -> Self {
      return (.i = StringToInt(serialized));
    }
  }
}

var x: MySerializableType = MySerializableType.Deserialize("3");

fn Deserialize(T:! DeserializeFromString, serialized: String) -> T {
  return T.Deserialize(serialized);
}
var y: MySerializableType = Deserialize(MySerializableType, "4");

This is instead of declaring an associated constant using let with a function type.

Together associated methods and associated class functions are called associated functions, much like together methods and class functions are called member functions.

Associated types

Associated types are associated entities that happen to be types. These are particularly interesting since they can be used in the signatures of associated methods or functions, to allow the signatures of methods to vary from implementation to implementation. We already have one example of this: the Self type discussed in the "Interfaces" section. For other cases, we can say that the interface declares that each implementation will provide a type under a specific name. For example:

interface StackAssociatedType {
  let ElementType:! Type;
  fn Push[addr me: Self*](value: ElementType);
  fn Pop[addr me: Self*]() -> ElementType;
  fn IsEmpty[addr me: Self*]() -> bool;
}

Here we have an interface called StackAssociatedType which defines two methods, Push and Pop. The signatures of those two methods declare them as accepting or returning values with the type ElementType, which any implementer of StackAssociatedType must also define. For example, maybe DynamicArray implements StackAssociatedType:

class DynamicArray(T:! Type) {
  class IteratorType { ... }
  fn Begin[addr me: Self*]() -> IteratorType;
  fn End[addr me: Self*]() -> IteratorType;
  fn Insert[addr me: Self*](pos: IteratorType, value: T);
  fn Remove[addr me: Self*](pos: IteratorType);

  // Set the associated type `ElementType` to `T`.
  impl as StackAssociatedType where .ElementType = T {
    fn Push[addr me: Self*](value: ElementType) {
      me->Insert(me->End(), value);
    }
    fn Pop[addr me: Self*]() -> ElementType {
      var pos: IteratorType = me->End();
      Assert(pos != me->Begin());
      --pos;
      returned var ret: ElementType = *pos;
      me->Remove(pos);
      return var;
    }
    fn IsEmpty[addr me: Self*]() -> bool {
      return me->Begin() == me->End();
    }
  }
}

Alternatives considered: See other syntax options considered in #731 for specifying associated types. In particular, it was deemed that Swift's approach of inferring the associated type from method signatures in the impl was unneeded complexity.

The definition of the StackAssociatedType is sufficient for writing a generic function that operates on anything implementing that interface, for example:

fn PeekAtTopOfStack[StackType:! StackAssociatedType](s: StackType*)
    -> StackType.ElementType {
  var top: StackType.ElementType = s->Pop();
  s->Push(top);
  return top;
}

Inside the generic function PeekAtTopOfStack, the ElementType associated type member of StackType is erased. This means StackType.ElementType has the API dictated by the declaration of ElementType in the interface StackAssociatedType.

Outside the generic, associated types have the concrete type values determined by impl lookup, rather than the erased version of that type used inside a generic.

var my_array: DynamicArray(i32) = (1, 2, 3);
// PeekAtTopOfStack's `StackType` is set to `DynamicArray(i32)`
// with `StackType.ElementType` set to `i32`.
Assert(PeekAtTopOfStack(my_array) == 3);

This is another part of achieving the goal that generic functions can be used in place of regular functions without changing the return type that callers see discussed in the return type section.

Associated types can also be implemented using a member type.

interface Container {
  let IteratorType:! Iterator;
  ...
}

class DynamicArray(T:! Type) {
  ...
  impl as Container {
    class IteratorType {
      impl Iterator { ... }
    }
    ...
  }
}

For context, see "Interface type parameters and associated types" in the generics terminology document.

Comparison with other languages: Both Rust and Swift support associated types.

Implementation model

The associated type can be modeled by a witness table field in the interface's witness table.

interface Iterator {
  fn Advance[addr me: Self*]();
}

interface Container {
  let IteratorType:! Iterator;
  fn Begin[addr me: Self*]() -> IteratorType;
}

is represented by:

class Iterator(Self:! Type) {
  var Advance: fnty(this: Self*);
  ...
}
class Container(Self:! Type) {
  // Representation type for the iterator.
  let IteratorType:! Type;
  // Witness that IteratorType implements Iterator.
  var iterator_impl: Iterator(IteratorType)*;

  // Method
  var Begin: fnty (this: Self*) -> IteratorType;
  ...
}

Parameterized interfaces

Associated types don't change the fact that a type can only implement an interface at most once.

If instead you want a family of related interfaces, one per possible value of a type parameter, multiple of which could be implemented for a single type, you would use parameterized interfaces. To write a parameterized version of the stack interface, instead of using associated types, write a parameter list after the name of the interface instead of the associated type declaration:

interface StackParameterized(ElementType:! Type) {
  fn Push[addr me: Self*](value: ElementType);
  fn Pop[addr me: Self*]() -> ElementType;
  fn IsEmpty[addr me: Self*]() -> bool;
}

Then StackParameterized(Fruit) and StackParameterized(Veggie) would be considered different interfaces, with distinct implementations.

class Produce {
  var fruit: DynamicArray(Fruit);
  var veggie: DynamicArray(Veggie);
  impl as StackParameterized(Fruit) {
    fn Push[addr me: Self*](value: Fruit) {
      me->fruit.Push(value);
    }
    fn Pop[addr me: Self*]() -> Fruit {
      return me->fruit.Pop();
    }
    fn IsEmpty[addr me: Self*]() -> bool {
      return me->fruit.IsEmpty();
    }
  }
  impl as StackParameterized(Veggie) {
    fn Push[addr me: Self*](value: Veggie) {
      me->veggie.Push(value);
    }
    fn Pop[addr me: Self*]() -> Veggie {
      return me->veggie.Pop();
    }
    fn IsEmpty[addr me: Self*]() -> bool {
      return me->veggie.IsEmpty();
    }
  }
}

Unlike associated types in interfaces and parameters to types, interface parameters can't be deduced. For example, if we were to rewrite the PeekAtTopOfStack example in the "associated types" section for StackParameterized(T) it would generate a compile error:

// ❌ Error: can't deduce interface parameter `T`.
fn BrokenPeekAtTopOfStackParameterized
    [T:! Type, StackType:! StackParameterized(T)]
    (s: StackType*) -> T { ... }

This error is because the compiler can not determine if T should be Fruit or Veggie when passing in argument of type Produce*. The function's signature would have to be changed so that the value for T could be determined from the explicit parameters.

fn PeekAtTopOfStackParameterized
    [T:! Type, StackType:! StackParameterized(T)]
    (s: StackType*, _:! singleton_type_of(T)) -> T { ... }

var produce: Produce = ...;
var top_fruit: Fruit =
    PeekAtTopOfStackParameterized(&produce, Fruit);
var top_veggie: Veggie =
    PeekAtTopOfStackParameterized(&produce, Veggie);

The pattern _:! singleton_type_of(T) is a placeholder syntax for an expression that will only match T, until issue #578: Value patterns as function parameters is resolved. Using that pattern in the explicit parameter list allows us to make T available earlier in the declaration so it can be passed as the argument to the parameterized interface StackParameterized.

This approach is useful for the ComparableTo(T) interface, where a type might be comparable with multiple other types, and in fact interfaces for operator overloads more generally. Example:

interface EquatableWith(T:! Type) {
  fn Equals[me: Self](rhs: T) -> bool;
  ...
}
class Complex {
  var real: f64;
  var imag: f64;
  // Can implement this interface more than once
  // as long as it has different arguments.
  impl as EquatableWith(Complex) { ... }
  impl as EquatableWith(f64) { ... }
}

All interface parameters must be marked as "generic", using the :! syntax. This reflects these two properties of these parameters:

  • They must be resolved at compile-time, and so can't be passed regular dynamic values.
  • We allow either generic or template values to be passed in.

Note: Interface parameters aren't required to be types, but that is the vast majority of cases. As an example, if we had an interface that allowed a type to define how the tuple-member-read operator would work, the index of the member could be an interface parameter:

interface ReadTupleMember(index:! u32) {
  let T:! Type;
  // Returns me[index]
  fn Get[me: Self]() -> T;
}

This requires that the index be known at compile time, but allows different indices to be associated with different types.

Caveat: When implementing an interface twice for a type, the interface parameters are required to always be different. For example:

interface Map(FromType:! Type, ToType:! Type) {
  fn Map[addr me: Self*](needle: FromType) -> Optional(ToType);
}
class Bijection(FromType:! Type, ToType:! Type) {
  impl as Map(FromType, ToType) { ... }
  impl as Map(ToType, FromType) { ... }
}
// ❌ Error: Bijection has two impls of interface Map(String, String)
var oops: Bijection(String, String) = ...;

In this case, it would be better to have an adapting type to contain the impl for the reverse map lookup, instead of implementing the Map interface twice:

class Bijection(FromType:! Type, ToType:! Type) {
  impl as Map(FromType, ToType) { ... }
}
adapter ReverseLookup(FromType:! Type, ToType:! Type)
    for Bijection(FromType, ToType) {
  impl as Map(ToType, FromType) { ... }
}

Comparison with other languages: Rust calls traits with type parameters "generic traits" and uses them for operator overloading.

Rust uses the term "type parameters" for both interface type parameters and associated types. The difference is that interface parameters are "inputs" since they determine which impl to use, and associated types are "outputs" since they are determined by the impl, but play no role in selecting the impl.

Impl lookup

Let's say you have some interface I(T, U(V)) being implemented for some type A(B(C(D), E)). To satisfy the orphan rule for coherence, that impl must be defined in some library that must be imported in any code that looks up whether that interface is implemented for that type. This requires that impl is defined in the same library that defines the interface or one of the names needed by the type. That is, the impl must be defined with one of I, T, U, V, A, B, C, D, or E. We further require anything looking up this impl to import the definitions of all of those names. Seeing a forward declaration of these names is insufficient, since you can presumably see forward declarations without seeing an impl with the definition. This accomplishes a few goals:

  • The compiler can check that there is only one definition of any impl that is actually used, avoiding One Definition Rule (ODR) problems.
  • Every attempt to use an impl will see the exact same impl, making the interpretation and semantics of code consistent no matter its context, in accordance with the low context-sensitivity principle.
  • Allowing the impl to be defined with either the interface or the type addresses the expression problem.

Note that the rules for specialization do allow there to be more than one impl to be defined for a type, by unambiguously picking one as most specific.

References: Implementation coherence is defined in terminology, and is a goal for Carbon. More detail can be found in this appendix with the rationale and alternatives considered.

Parameterized named constraints

We should also allow the named constraint construct to support parameters. Parameters would work the same way as for interfaces.

Where constraints

So far, we have restricted a generic type parameter by saying it has to implement an interface or a set of interfaces. There are a variety of other constraints we would like to be able to express, such as applying restrictions to its associated types and associated constants. This is done using the where operator that adds constraints to a type-of-type.

The where operator can be applied to a type-of-type in a declaration context:

// Constraints on function parameters:
fn F[V:! D where ...](v: V) { ... }

// Constraints on a class parameter:
class S(T:! B where ...) {
  // Constraints on a method:
  fn G[me: Self, V:! D where ...](v: V);
}

// Constraints on an interface parameter:
interface A(T:! B where ...) {
  // Constraints on an associated type:
  let U:! C where ...;
  // Constraints on an associated method:
  fn G[me: Self, V:! D where ...](v: V);
}

We also allow you to name constraints using a where operator in a let or constraint definition. The expressions that can follow the where keyword are described in the "constraint use cases" section, but generally look like boolean expressions that should evaluate to true.

The result of applying a where operator to a type-of-type is another type-of-type. Note that this expands the kinds of requirements that type-of-types can have from just interface requirements to also include the various kinds of constraints discussed later in this section. In addition, it can introduce relationships between different type variables, such as that a member of one is equal to the member of another.

Comparison with other languages: Both Swift and Rust use where clauses on declarations instead of in the expression syntax. These happen after the type that is being constrained has been given a name and use that name to express the constraint.

Rust also supports directly passing in the values for associated types when using a trait as a constraint. This is helpful when specifying concrete types for all associated types in a trait in order to make it object safe so it can be used to define a trait object type.

Rust is adding trait aliases (RFC, tracking issue) to support naming some classes of constraints.

Constraint use cases

Set an associated constant to a specific value

We might need to write a function that only works with a specific value of an associated constant N. In this case, the name of the associated constant is written first, followed by an =, and then the value:

fn PrintPoint2D[PointT:! NSpacePoint where .N = 2](p: PointT) {
  Print(p.Get(0), ", ", p.Get(1));
}

Similarly in an interface definition:

interface Has2DPoint {
  let PointT:! NSpacePoint where .N = 2;
}

To name such a constraint, you may use a let or a constraint declaration:

let Point2DInterface:! auto = NSpacePoint where .N = 2;
constraint Point2DInterface {
  extends NSpacePoint where .N = 2;
}

This syntax is also used to specify the values of associated constants when implementing an interface for a type.

Concern: Using = for this use case is not consistent with other where clauses that write a boolean expression that evaluates to true when the constraint is satisfied.

A constraint to say that two associated constants should have the same value without specifying what specific value they should have must use == instead of =:

interface PointCloud {
  let Dim:! i32;
  let PointT:! NSpacePoint where .N == Dim;
}

Same type constraints

Set an associated type to a specific value

Functions accepting a generic type might also want to constrain one of its associated types to be a specific, concrete type. For example, we might want to have a function only accept stacks containing integers:

fn SumIntStack[T:! Stack where .ElementType = i32](s: T*) -> i32 {
  var sum: i32 = 0;
  while (!s->IsEmpty()) {
    // s->Pop() has type `T.ElementType` == i32:
    sum += s->Pop();
  }
  return sum;
}

To name these sorts of constraints, we could use let declarations or constraint definitions:

let IntStack:! auto = Stack where .ElementType = i32;
constraint IntStack {
  extends Stack where .ElementType = i32;
}

This syntax is also used to specify the values of associated types when implementing an interface for a type.

Equal generic types

Alternatively, two generic types could be constrained to be equal to each other, without specifying what that type is. This uses == instead of =. For example, we could make the ElementType of an Iterator interface equal to the ElementType of a Container interface as follows:

interface Iterator {
  let ElementType:! Type;
  ...
}
interface Container {
  let ElementType:! Type;
  let IteratorType:! Iterator where .ElementType == ElementType;
  ...
}

Given an interface with two associated types

interface PairInterface {
  let Left:! Type;
  let Right:! Type;
}

we can constrain them to be equal in a function signature:

fn F[MatchedPairType:! PairInterface where .Left == .Right]
    (x: MatchedPairType*);

or in an interface definition:

interface HasEqualPair {
  let P:! PairInterface where .Left == .Right;
}

This kind of constraint can be named:

let EqualPair:! auto =
    PairInterface where .Left == .Right;
constraint EqualPair {
  extends PairInterface where .Left == .Right;
}

Another example of same type constraints is when associated types of two different interfaces are constrained to be equal:

fn Map[CT:! Container,
       FT:! Function where .InputType == CT.ElementType]
      (c: CT, f: FT) -> Vector(FT.OutputType);
Satisfying both type-of-types

If the two types being constrained to be equal have been declared with different type-of-types, then the actual type value they are set to will have to satisfy both constraints. For example, if SortedContainer.ElementType is declared to be Comparable, then in this declaration:

fn Contains
    [SC:! SortedContainer,
     CT:! Container where .ElementType == SC.ElementType]
    (haystack: SC, needles: CT) -> bool;

the where constraint means CT.ElementType must satisfy Comparable as well. However, inside the body of Contains, CT.ElementType will only act like the implementation of Comparable is external. That is, items from the needles container won't directly have a Compare method member, but can still be implicitly converted to Comparable and can still call Compare using the compound member access syntax, needle.(Comparable.Compare)(elt). The rule is that an == where constraint between two type variables does not modify the set of member names of either type. (If you write where .ElementType = String with a = and a concrete type, then .ElementType is actually set to String including the complete String API.)

Note that == constraints are symmetric, so the previous declaration of Contains is equivalent to an alternative declaration where CT is declared first and the where clause is attached to SortedContainer:

fn Contains
    [CT:! Container,
     SC:! SortedContainer where .ElementType == CT.ElementType]
    (haystack: SC, needles: CT) -> bool;

Type bound for associated type

A where clause can express that a type must implement an interface. This is more flexible than the usual approach of including that interface in the type since it can be applied to associated type members as well.

Type bounds on associated types in declarations

In the following example, normally the ElementType of a Container can be any type. The SortContainer function, however, takes a pointer to a type satisfying Container with the additional constraint that its ElementType must satisfy the Comparable interface.

interface Container {
  let ElementType:! Type;
  ...
}

fn SortContainer
    [ContainerType:! Container where .ElementType is Comparable]
    (container_to_sort: ContainerType*);

In contrast to a same type constraint, this does not say what type ElementType exactly is, just that it must satisfy some type-of-type.

Open question: How do you spell that? Provisionally we are writing is, following Swift, but maybe we should have another operator that more clearly returns a boolean like has_type?

Note: Container defines ElementType as having type Type, but ContainerType.ElementType has type Comparable. This is because ContainerType has type Container where .ElementType is Comparable, not Container. This means we need to be a bit careful when talking about the type of ContainerType when there is a where clause modifying it.

Type bounds on associated types in interfaces

Given these definitions (omitting ElementType for brevity):

interface IteratorInterface { ... }
interface ContainerInterface {
  let IteratorType:! IteratorInterface;
  ...
}
interface RandomAccessIterator {
  extends IteratorInterface;
  ...
}

We can then define a function that only accepts types that implement ContainerInterface where its IteratorType associated type implements RandomAccessIterator:

fn F[ContainerType:! ContainerInterface
     where .IteratorType is RandomAccessIterator]
    (c: ContainerType);

We would like to be able to name this constraint, defining a RandomAccessContainer to be a type-of-type whose types satisfy ContainerInterface with an IteratorType satisfying RandomAccessIterator.

let RandomAccessContainer:! auto =
    ContainerInterface where .IteratorType is RandomAccessIterator;
// or
constraint RandomAccessContainer {
  extends ContainerInterface
      where .IteratorType is RandomAccessIterator;
}

// With the above definition:
fn F[ContainerType:! RandomAccessContainer](c: ContainerType);
// is equivalent to:
fn F[ContainerType:! ContainerInterface
     where .IteratorType is RandomAccessIterator]
    (c: ContainerType);

Combining constraints

Constraints can be combined by separating constraint clauses with the and keyword. This example expresses a constraint that two associated types are equal and satisfy an interface:

fn EqualContainers
    [CT1:! Container,
     CT2:! Container where .ElementType is HasEquality
                       and .ElementType == CT1.ElementType]
    (c1: CT1*, c2: CT2*) -> bool;

Comparison with other languages: Swift and Rust use commas , to separate constraint clauses, but that only works because they place the where in a different position in a declaration. In Carbon, the where is attached to a type in a parameter list that is already using commas to separate parameters.

Recursive constraints

We sometimes need to constrain a type to equal one of its associated types. In this first example, we want to represent the function Abs which will return Self for some but not all types, so we use an associated type MagnitudeType to encode the return type:

interface HasAbs {
  extends Numeric;
  let MagnitudeType:! Numeric;
  fn Abs[me: Self]() -> MagnitudeType;
}

For types representing subsets of the real numbers, such as i32 or f32, the MagnitudeType will match Self, the type implementing an interface. For types representing complex numbers, the types will be different. For example, the Abs() applied to a Complex64 value would produce a f32 result. The goal is to write a constraint to restrict to the first case.

In a second example, when you take the slice of a type implementing Container you get a type implementing Container which may or may not be the same type as the original container type. However, taking the slice of a slice always gives you the same type, and some functions want to only operate on containers whose slice type is the same as the container type.

To solve this problem, we think of Self as an actual associated type member of every interface. We can then address it using .Self in a where clause, like any other associated type member.

fn Relu[T:! HasAbs where .MagnitudeType == .Self](x: T) {
  // T.MagnitudeType == T so the following is allowed:
  return (x.Abs() + x) / 2;
}
fn UseContainer[T:! Container where .SliceType == .Self](c: T) -> bool {
  // T.SliceType == T so `c` and `c.Slice(...)` can be compared:
  return c == c.Slice(...);
}

Notice that in an interface definition, Self refers to the type implementing this interface while .Self refers to the associated type currently being defined.

interface Container {
  let ElementType:! Type;

  let SliceType:! Container
      where .ElementType == ElementType and
            .SliceType == .Self;

  fn GetSlice[addr me: Self*]
      (start: IteratorType, end: IteratorType) -> SliceType;
}

These recursive constraints can be named:

let RealAbs:! auto = HasAbs where .MagnitudeType == .Self;
constraint RealAbs {
  extends HasAbs where .MagnitudeType == Self;
}
let ContainerIsSlice:! auto =
    Container where .SliceType == .Self;
constraint ContainerIsSlice {
  extends Container where .SliceType == Self;
}

Note that using the constraint approach we can name these constraints using Self instead of .Self, since they refer to the same type.

Parameterized type implements interface

There are times when a function will pass a generic type parameter of the function as an argument to a parameterized type, as in the previous case, and in addition the function needs the result to implement a specific interface.

// Some parameterized type.
class Vector(T:! Type) { ... }

// Parameterized type implements interface only for some arguments.
external impl Vector(String) as Printable { ... }

// Constraint: `T` such that `Vector(T)` implements `Printable`
fn PrintThree
    [T:! Type where Vector(.Self) is Printable]
    (a: T, b: T, c: T) {
  var v: Vector(T) = (a, b, c);
  Print(v);
}

Comparison with other languages: This use case was part of the Rust rationale for adding support for where clauses.

Another type implements parameterized interface

In this case, we need some other type to implement an interface parameterized by a generic type parameter. The syntax for this case follows the previous case, except now the .Self parameter is on the interface to the right of the is. For example, we might need a type parameter T to support explicit conversion from an integer type like i32:

interface As(T:! Type) {
  fn Convert[me: Self]() -> T;
}

fn Double[T:! Mul where i32 is As(.Self)](x: T) -> T {
  return x * (2 as T);
}

Implied constraints

Imagine we have a generic function that accepts an arbitrary HashMap:

fn LookUp[KeyType:! Type](hm: HashMap(KeyType, i32)*,
                          k: KeyType) -> i32;

fn PrintValueOrDefault[KeyType:! Printable,
                       ValueT:! Printable & HasDefault]
    (map: HashMap(KeyType, ValueT), key: KeyT);

The KeyType in these declarations does not visibly satisfy the requirements of HashMap, which requires the type implement Hashable and other interfaces:

class HashMap(
    KeyType:! Hashable & EqualityComparable & Movable,
    ...) { ... }

In this case, KeyType gets Hashable and so on as implied constraints. Effectively that means that these functions are automatically rewritten to add a where constraint on KeyType attached to the HashMap type:

fn LookUp[KeyType:! Type]
    (hm: HashMap(KeyType, i32)*
        where KeyType is Hashable & EqualityComparable & Movable,
     k: KeyType) -> i32;

fn PrintValueOrDefault[KeyType:! Printable,
                       ValueT:! Printable & HasDefault]
    (map: HashMap(KeyType, ValueT)
        where KeyType is Hashable & EqualityComparable & Movable,
     key: KeyT);

In this case, Carbon will accept the definition and infer the needed constraints on the generic type parameter. This is both more concise for the author of the code and follows the "don't repeat yourself" principle. This redundancy is undesirable since it means if the needed constraints for HashMap are changed, then the code has to be updated in more locations. Further it can add noise that obscures relevant information. In practice, any user of these functions will have to pass in a valid HashMap instance, and so will have already satisfied these constraints.

This implied constraint is equivalent to the explicit constraint that each parameter and return type is legal.

Note: These implied constraints affect the requirements of a generic type parameter, but not its member names. This way you can always look at the declaration to see how name resolution works, without having to look up the definitions of everything it is used as an argument to.

Limitation: To limit readability concerns and ambiguity, this feature is limited to a single signature. Consider this interface declaration:

interface GraphNode {
  let Edge:! Type;
  fn EdgesFrom[me: Self]() -> HashSet(Edge);
}

One approach would be to say the use of HashSet(Edge) in the signature of the EdgesFrom function would imply that Edge satisfies the requirements of an argument to HashSet, such as being Hashable. Another approach would be to say that the EdgesFrom would only be conditionally available when Edge does satisfy the constraints on HashSet arguments. Instead, Carbon will reject this definition, requiring the user to include all the constraints required for the other declarations in the interface in the declaration of the Edge associated type. Similarly, a parameter to a class must be declared with all the constraints needed to declare the members of the class that depend on that parameter.

Comparison with other languages: Both Swift (1, 2) and Rust support some form of this feature as part of their type inference (and the Rust community is considering expanding support).

Must be legal type argument constraints

Now consider the case that the generic type parameter is going to be used as an argument to a parameterized type in a function body, not in the signature. If the parameterized type was explicitly mentioned in the signature, the implied constraint feature would ensure all of its requirements were met. The developer can create a trivial parameterized type implements interface where constraint to just say the type is a legal with this argument, by saying that the parameterized type implements Type, which all types do.

For example, a function that adds its parameters to a HashSet to deduplicate them, needs them to be Hashable and so on. To say "T is a type where HashSet(T) is legal," we can write:

fn NumDistinct[T:! Type where HashSet(.Self) is Type]
    (a: T, b: T, c: T) -> i32 {
  var set: HashSet(T);
  set.Add(a);
  set.Add(b);
  set.Add(c);
  return set.Size();
}

This has the same advantages over repeating the constraints on HashSet arguments in the type of T as the general implied constraints above.

Referencing names in the interface being defined

The constraint in a where clause is required to only reference earlier names from this scope, as in this example:

interface Graph {
  let E: Edge;
  let V: Vert where .E == E and .Self == E.V;
}

Manual type equality

Imagine we have some function with generic parameters:

fn F[T:! SomeInterface](x: T) {
  x.G(x.H());
}

We want to know if the return type of method T.H is the same as the parameter type of T.G in order to typecheck the function. However, determining whether two type expressions are transitively equal is in general undecidable, as has been shown in Swift.

Carbon's approach is to only allow implicit conversions between two type expressions that are constrained to be equal in a single where clause. This means that if two type expressions are only transitively equal, the user will need to include a sequence of casts or use an observe declaration to convert between them.

Given this interface Transitive that has associated types that are constrained to all be equal, with interfaces P, Q, and R:

interface P { fn InP[me:Self](); }
interface Q { fn InQ[me:Self](); }
interface R { fn InR[me:Self](); }

interface Transitive {
  let A:! P;
  let B:! Q where .Self == A;
  let C:! R where .Self == B;

  fn GetA[me: Self]() -> A;
  fn TakesC[me:Self](c: C);
}

A cast to B is needed to call TakesC with a value of type A, so each step only relies on one equality:

fn F[T:! Transitive](t: T) {
  // ✅ Allowed
  t.TakesC(t.GetA() as T.B);

  // ✅ Allowed
  let b: T.B = t.GetA();
  t.TakesC(b);

  // ❌ Not allowed: t.TakesC(t.GetA());
}

A value of type A, such as the return value of GetA(), has the API of P. Any such value also implements Q, and since the compiler can see that by way of a single where equality, values of type A are treated as if they implement Q externally. However, the compiler will require a cast to B or C to see that the type implements R.

fn TakesPQR[U:! P & Q & R](u: U);

fn G[T:! Transitive](t: T) {
  var a: T.A = t.GetA();

  // ✅ Allowed: `T.A` implements `P`.
  a.InP();

  // ✅ Allowed: `T.A` implements `Q` externally.
  a.(Q.InQ)();

  // ❌ Not allowed: a.InQ();

  // ✅ Allowed: values of type `T.A` may be cast
  // to `T.B`, which implements `Q` internally.
  (a as T.B).InQ();

  // ✅ Allowed: `T.B` implements `R` externally.
  (a as T.B).(R.InR)();

  // ❌ Not allowed: TakesPQR(a);

  // ✅ Allowed: `T.B` implements `P`, `Q`, and
  // `R`, though the implementations of `P`
  // and `R` are external.
  TakesPQR(a as T.B);
}

The compiler may have several different where clauses to consider, particularly when an interface has associated types that recursively satisfy the same interface. For example, given this interface Commute:

interface Commute {
  let X:! Commute;
  let Y:! Commute where .X == X.Y;

  fn GetX[me: Self]() -> X;
  fn GetY[me: Self]() -> Y;
  fn TakesXXY[me:Self](xxy: X.X.Y);
}

and a function H taking a value with some type implementing this interface, then the following would be legal statements in H:

fn H[C: Commute](c: C) {
  // ✅ Legal: argument has type `C.X.X.Y`
  c.TakesXXY(c.GetX().GetX().GetY());

  // ✅ Legal: argument has type `C.X.Y.X` which is equal
  // to `C.X.X.Y` following only one `where` clause.
  c.TakesXXY(c.GetX().GetY().GetX());

  // ✅ Legal: cast is legal since it matches a `where`
  // clause, and produces an argument that has type
  // `C.X.Y.X`.
  c.TakesXXY(c.GetY().GetX().GetX() as C.X.Y.X);
}

That last call would not be legal without the cast, though.

Comparison with other languages: Other languages such as Swift and Rust instead perform automatic type equality. In practice this means that their compiler can reject some legal programs based on heuristics simply to avoid running for an unbounded length of time.

The benefits of the manual approach include:

  • fast compilation, since the compiler does not need to explore a potentially large set of combinations of equality restrictions, supporting Carbon's goal of fast and scalable development;
  • expressive and predictable semantics, since there are no limitations on how complex a set of constraints can be supported; and
  • simplicity.

The main downsides are:

  • manual work for the source code author to prove to the compiler that types are equal; and
  • verbosity.

We expect that rich error messages and IDE tooling will be able to suggest changes to the source code when a single equality constraint is not sufficient to show two type expressions are equal, but a more extensive automated search can find a sequence that prove they are equal.

observe declarations

An observe declaration lists a sequence of type expressions that are equal by some same-type where constraints. These observe declarations may be included in an interface definition or a function body, as in:

interface Commute {
  let X:! Commute;
  let Y:! Commute where .X == X.Y;
  ...
  observe X.X.Y == X.Y.X == Y.X.X;
}

fn H[C: Commute](c: C) {
  observe C.X.Y.Y == C.Y.X.Y == C.Y.Y.X;
  ...
}

Every type expression after the first must be equal to some earlier type expression in the sequence by a single where equality constraint. In this example,

interface Commute {
  let X:! Commute;
  let Y:! Commute where .X == X.Y;
  ...
  // ✅ Legal:
  observe X.X.Y.Y == X.Y.X.Y == Y.X.X.Y == X.Y.Y.X;
}

the expression X.Y.Y.X is one equality away from X.Y.X.Y and so it is allowed. This is even though X.Y.X.Y isn't the type expression immediately prior to X.Y.Y.X.

After an observe declaration, all of the listed type expressions are considered equal to each other using a single where equality. In this example, the observe declaration in the Transitive interface definition provides the link between associated types A and C that allows function F to type check.

interface P { fn InP[me:Self](); }
interface Q { fn InQ[me:Self](); }
interface R { fn InR[me:Self](); }

interface Transitive {
  let A:! P;
  let B:! Q where .Self == A;
  let C:! R where .Self == B;

  fn GetA[me: Self]() -> A;
  fn TakesC[me:Self](c: C);

  // Without this `observe` declaration, the
  // calls in `F` below would not be allowed.
  observe A == B == C;
}

fn TakesPQR[U:! P & Q & R](u: U);

fn F[T:! Transitive](t: T) {
  var a: T.A = t.GetA();

  // ✅ Allowed: `T.A` == `T.C`
  t.TakesC(a);
  a.(R.InR());

  // ✅ Allowed: `T.A` implements `P`,
  // `T.A` == `T.B` that implements `Q`, and
  // `T.A` == `T.C` that implements `R`.
  TakesPQR(a);
}

Since adding an observe declaration only adds external implementations of interfaces to generic types, they may be added without breaking existing code.

Other constraints as type-of-types

There are some constraints that we will naturally represent as named type-of-types. These can either be used directly to constrain a generic type parameter, or in a where ... is ... clause to constrain an associated type.

The compiler determines which types implement these interfaces, developers can not explicitly implement these interfaces for their own types.

Open question: Are these names part of the prelude or in a standard library?

Is a derived class

Given a type T, Extends(T) is a type-of-type whose values are types that are derived from T. That is, Extends(T) is the set of all types U that are subtypes of T.

fn F[T:! Extends(BaseType)](p: T*);
fn UpCast[T:! Type](p: T*, U:! Type where T is Extends(.Self)) -> U*;
fn DownCast[T:! Type](p: T*, U:! Extends(T)) -> U*;

Open question: Alternatively, we could define a new extends operator:

fn F[T:! Type where .Self extends BaseType](p: T*);
fn UpCast[T:! Type](p: T*, U:! Type where T extends .Self) -> U*;
fn DownCast[T:! Type](p: T*, U:! Type where .Self extends T) -> U*;

Comparison to other languages: In Swift, you can add a required superclass to a type bound using &.

Type compatible with another type

Given a type U, define the type-of-type CompatibleWith(U) as follows:

CompatibleWith(U) is a type whose values are types T such that T and U are compatible. That is values of types T and U can be cast back and forth without any change in representation (for example T is an adapter for U).

To support this, we extend the requirements that type-of-types are allowed to have to include a "data representation requirement" option.

CompatibleWith determines an equivalence relationship between types. Specifically, given two types T1 and T2, they are equivalent if T1 is CompatibleWith(T2). That is, if T1 has the type CompatibleWith(T2).

Note: Just like interface parameters, we require the user to supply U, they may not be deduced. Specifically, this code would be illegal:

fn Illegal[U:! Type, T:! CompatibleWith(U)](x: T*) ...

In general there would be multiple choices for U given a specific T here, and no good way of picking one. However, similar code is allowed if there is another way of determining U:

fn Allowed[U:! Type, T:! CompatibleWith(U)](x: U*, y: T*) ...

Same implementation restriction

In some cases, we need to restrict to types that implement certain interfaces the same way as the type U.

The values of type CompatibleWith(U, TT) are types satisfying CompatibleWith(U) that have the same implementation of TT as U.

For example, if we have a type HashSet(T):

class HashSet(T:! Hashable) { ... }

Then HashSet(T) may be cast to HashSet(U) if T is CompatibleWith(U, Hashable). The one-parameter interpretation of CompatibleWith(U) is recovered by letting the default for the second TT parameter be Type.

Example: Multiple implementations of the same interface

This allows us to represent functions that accept multiple implementations of the same interface for a type.

enum CompareResult { Less, Equal, Greater }
interface Comparable {
  fn Compare[me: Self](rhs: Self) -> CompareResult;
}
fn CombinedLess[T:! Type](a: T, b: T,
                          U:! CompatibleWith(T) & Comparable,
                          V:! CompatibleWith(T) & Comparable) -> bool {
  match ((a as U).Compare(b as U)) {
    case CompareResult.Less => { return True; }
    case CompareResult.Greater => { return False; }
    case CompareResult.Equal => {
      return (a as V).Compare(b as V) == CompareResult.Less;
    }
  }
}

Used as:

class Song { ... }
adapter SongByArtist for Song { impl as Comparable { ... } }
adapter SongByTitle for Song { impl as Comparable { ... } }
var s1: Song = ...;
var s2: Song = ...;
assert(CombinedLess(s1, s2, SongByArtist, SongByTitle) == True);

We might generalize this to a list of implementations:

fn CombinedCompare[T:! Type]
    (a: T, b: T, CompareList:! List(CompatibleWith(T) & Comparable))
    -> CompareResult {
  for (let U:! auto in CompareList) {
    var result: CompareResult = (a as U).Compare(b);
    if (result != CompareResult.Equal) {
      return result;
    }
  }
  return CompareResult.Equal;
}

assert(CombinedCompare(Song(...), Song(...), (SongByArtist, SongByTitle)) ==
       CompareResult.Less);

Open question: How are compile-time lists of types declared and iterated through? They will also be needed for variadic argument support.

Example: Creating an impl out of other impls

And then to package this functionality as an implementation of Comparable, we combine CompatibleWith with type adaptation:

adapter ThenCompare(
      T:! Type,
      CompareList:! List(CompatibleWith(T) & Comparable))
    for T {
  impl as Comparable {
    fn Compare[me: Self](rhs: Self) -> CompareResult {
      for (let U:! auto in CompareList) {
        var result: CompareResult = (me as U).Compare(rhs as U);
        if (result != CompareResult.Equal) {
          return result;
        }
      }
      return CompareResult.Equal;
    }
  }
}

let SongByArtistThenTitle: auto =
    ThenCompare(Song, (SongByArtist, SongByTitle));
var s1: Song = ...;
var s2: SongByArtistThenTitle =
    Song(...) as SongByArtistThenTitle;
assert((s1 as SongByArtistThenTitle).Compare(s2) ==
       CompareResult.Less);

Sized types and type-of-types

What is the size of a type?

  • It could be fully known and fixed at compile time -- this is true of primitive types (i32, f64, and so on), most classes, and most other concrete types.
  • It could be known generically. This means that it will be known at codegen time, but not at type-checking time.
  • It could be dynamic. For example, it could be a dynamic type, a slice, variable-sized type (such as found in Rust), or you could dereference a pointer to a base class that could actually point to a derived class.
  • It could be unknown which category the type is in. In practice this will be essentially equivalent to having dynamic size.

A type is called sized if it is in the first two categories, and unsized otherwise. Note: something with size 0 is still considered "sized". The type-of-type Sized is defined as follows:

Sized is a type whose values are types T that are "sized" -- that is the size of T is known, though possibly only generically.

Knowing a type is sized is a precondition to declaring variables of that type, taking values of that type as parameters, returning values of that type, and defining arrays of that type. Users will not typically need to express the Sized constraint explicitly, though, since it will usually be a dependency of some other constraint the type will need such as Movable or Concrete.

Note: The compiler will determine which types are "sized", this is not something types will implement explicitly like ordinary interfaces.

Example:

// In the Carbon standard library
interface DefaultConstructible {
  // Types must be sized to be default constructible.
  impl as Sized;
  fn Default() -> Self;
}

// Classes are "sized" by default.
class Name {
  impl as DefaultConstructible {
    fn Default() -> Self { ... }
  }
  ...
}

fn F[T:! Type](x: T*) {  // T is unsized.
  // ✅ Allowed: may access unsized values through a pointer.
  var y: T* = x;
  // ❌ Illegal: T is unsized.
  var z: T;
}

// T is sized, but its size is only known generically.
fn G[T: DefaultConstructible](x: T*) {
  // ✅ Allowed: T is default constructible, which means sized.
  var y: T = T.Default();
}

var z: Name = Name.Default();;
// ✅ Allowed: `Name` is sized and implements `DefaultConstructible`.
G(&z);

Open question: Even if the size is fixed, it won't be known at the time of compiling the generic function if we are using the dynamic strategy. Should we automatically box local variables when using the dynamic strategy? Or should we only allow MaybeBox values to be instantiated locally? Or should this just be a case where the compiler won't necessarily use the dynamic strategy?

Open question: Should the Sized type-of-type expose an associated constant with the size? So you could say T.ByteSize in the above example to get a generic int value with the size of T. Similarly you might say T.ByteStride to get the number of bytes used for each element of an array of T.

Implementation model

This requires a special integer field be included in the witness table type to hold the size of the type. This field will only be known generically, so if its value is used for type checking, we need some way of evaluating those type tests symbolically.

TypeId

There are some capabilities every type can provide. For example, every type should be able to return its name or identify whether it is equal to another type. It is rare, however, for code to need to access these capabilities, so we relegate these capabilities to an interface called TypeId that all types automatically implement. This way generic code can indicate that it needs those capabilities by including TypeId in the list of requirements. In the case where no type capabilities are needed, for example the code is only manipulating pointers to the type, you would write T:! Type and get the efficiency of void* but without giving up type safety.

fn SortByAddress[T:! Type](v: Vector(T*)*) { ... }

In particular, the compiler should in general avoid monomorphizing to generate multiple instantiations of the function in this case.

Open question: Should TypeId be implemented externally for types to avoid name pollution (.TypeName, .TypeHash, etc.) unless the function specifically requests those capabilities?

Destructor constraints

There are four type-of-types related to the destructors of types:

  • Concrete types may be local or member variables.
  • Deletable types may be safely deallocated by pointer using the Delete method on the Allocator used to allocate it.
  • Destructible types have a destructor and may be deallocated by pointer using the UnsafeDelete method on the correct Allocator, but it may be unsafe. The concerning case is deleting a pointer to a derived class through a pointer to its base class without a virtual destructor.
  • TrivialDestructor types have empty destructors. This type-of-type may be used with specialization to unlock specific optimizations.

Note: The names Deletable and Destructible are placeholders since they do not conform to the decision on question-for-leads issue #1058: "How should interfaces for core functionality be named?".

The type-of-types Concrete, Deletable, and TrivialDestructor all extend Destructible. Combinations of them may be formed using the & operator. For example, a generic function that both instantiates and deletes values of a type T would require T implement Concrete & Deletable.

Types are forbidden from explicitly implementing these type-of-types directly. Instead they use destructor declarations in their class definition and the compiler uses them to determine which of these type-of-types are implemented.

Generic let

A let statement inside a function body may be used to get the change in type behavior of calling a generic function without having to introduce a function call.

fn F(...) {
  ...
  let T:! C = U;
  X;
  Y;
  Z;
}

gets rewritten to:

fn F(...) {
  ...
  fn Closure(T:! C where .Self == U) {
    X;
    Y;
    Z;
  }
  Closure(U);
}

The where .Self == U modifier allows values to implicitly convert between type T, the erased type, and type U, the concrete type. Note that implicit conversion is only performed across a single where equality. This can be used to switch to the API of C when it is external, as an alternative to using an adapter, or to simplify inlining of a generic function while preserving semantics.

Parameterized impls

There are cases where an impl definition should apply to more than a single type and interface combination. The solution is to parameterize the impl definition, so it applies to a family of types, interfaces, or both. This includes:

  • Declare an impl for a parameterized type, which may be external or declared out-of-line.
  • "Conditional conformance" where a parameterized type implements some interface if the parameter to the type satisfies some criteria, like implementing the same interface.
  • "Blanket" impls where an interface is implemented for all types that implement another interface, or some other criteria beyond being a specific type.
  • "Wildcard" impls where a family of interfaces are implemented for single type.

Impl for a parameterized type

Interfaces may be implemented for a parameterized type. This can be done lexically in the class' scope:

class Vector(T:! Type) {
  impl as Iterable where .ElementType = T {
    ...
  }
}

This is equivalent to naming the type between impl and as:

class Vector(T:! Type) {
  impl Vector(T) as Iterable where .ElementType = T {
    ...
  }
}

An impl may be declared external by adding an external keyword before impl. External impls may also be declared out-of-line, but all parameters must be declared in a forall clause:

external impl forall [T:! Type] Vector(T) as Iterable
    where .ElementType = T {
  ...
}

The parameter for the type can be used as an argument to the interface being implemented:

class HashMap(Key:! Hashable, Value:! Type) {
  impl as Has(Key) { ... }
  impl as Contains(HashSet(Key)) { ... }
}

or externally out-of-line:

class HashMap(Key:! Hashable, Value:! Type) { ... }
external impl forall [Key:! Hashable, Value:! Type]
    HashMap(Key, Value) as Has(Key) { ... }
external impl forall [Key:! Hashable, Value:! Type]
    HashMap(Key, Value) as Contains(HashSet(Key)) { ... }

Conditional conformance

Conditional conformance is expressing that we have an impl of some interface for some type, but only if some additional type restrictions are met. Examples where this would be useful include being able to say that a container type, like Vector, implements some interface when its element type satisfies the same interface:

  • A container is printable if its elements are.
  • A container could be compared to another container with the same element type using a lexicographic comparison if the element type is comparable.
  • A container is copyable if its elements are.

To do this with an external impl, specify a more-specific Self type to the left of the as in the declaration:

interface Printable {
  fn Print[me: Self]();
}
class Vector(T:! Type) { ... }

// By saying "T:! Printable" instead of "T:! Type" here,
// we constrain T to be Printable for this impl.
external impl forall [T:! Printable] Vector(T) as Printable {
  fn Print[me: Self]() {
    for (let a: T in me) {
      // Can call `Print` on `a` since the constraint
      // on `T` ensures it implements `Printable`.
      a.Print();
    }
  }
}

To define these impls inline in a class definition, include a forall clause with a more-specific type between the impl and as keywords.

class Array(T:! Type, template N:! Int) {
  impl forall [P:! Printable] Array(P, N) as Printable { ... }
}

It is legal to add the keyword external before the impl keyword to switch to an external impl defined lexically within the class scope. Inside the scope, both P and T refer to the same type, but P has the type-of-type of Printable and so has a Print member. The relationship between T and P is as if there was a where P == T clause.

TODO: Need to resolve whether the T name can be reused, or if we require that you need to use new names, like P, when creating new type variables.

Example: Consider a type with two parameters, like Pair(T, U). In this example, the interface Foo(T) is only implemented when the two types are equal.

interface Foo(T:! Type) { ... }
class Pair(T:! Type, U:! Type) { ... }
external impl forall [T:! Type] Pair(T, T) as Foo(T) { ... }

You may also define the impl inline, in which case it can be internal:

class Pair(T:! Type, U:! Type) {
  impl Pair(T, T) as Foo(T) { ... }
}

Clarification: Method lookup will look at all internal implementations, whether or not the conditions on those implementations hold for the Self type. If the conditions don't hold, then the call will be rejected because Self has the wrong type, just like any other argument/parameter type mismatch. This means types may not implement two different interfaces internally if they share a member name, even if their conditions are mutually exclusive:

class X(T:! Type) {
  impl X(i32) as Foo {
    fn F[me: Self]();
  }
  impl X(i64) as Bar {
    // ❌ Illegal: name conflict between `Foo.F` and `Bar.F`
    fn F[me: Self](n: i64);
  }
}

However, the same interface may be implemented multiple times as long as there is no overlap in the conditions:

class X(T:! Type) {
  impl X(i32) as Foo {
    fn F[me: Self]();
  }
  impl X(i64) as Foo {
    // ✅ Allowed: `X(T).F` consistently means `X(T).(Foo.F)`
    fn F[me: Self]();
  }
}

This allows a type to express that it implements an interface for a list of types, possibly with different implementations.

In general, X(T).F can only mean one thing, regardless of T.

Comparison with other languages: Swift supports conditional conformance, but bans cases where there could be ambiguity from overlap. Rust also supports conditional conformance.

Conditional methods

A method could be defined conditionally for a type by using a more specific type in place of Self in the method declaration. For example, this is how to define a vector type that only has a Sort method if its elements implement the Comparable interface:

class Vector(T:! Type) {
  // `Vector(T)` has a `Sort()` method if `T` is `Comparable`.
  fn Sort[C:! Comparable, addr me: Vector(C)*]();
}

Comparison with other languages: In Rust this feature is part of conditional conformance. Swift supports conditional methods using conditional extensions or contextual where clauses.

Blanket impls

A blanket impl is an impl that could apply to more than one root type, so the impl will use a type variable for the Self type. Here are some examples where blanket impls arise:

  • Any type implementing Ordered should get an implementation of PartiallyOrdered.

    external impl forall [T:! Ordered] T as PartiallyOrdered { ... }

  • T implements CommonType(T) for all T

    external impl forall [T:! Type] T as CommonType(T)
    where .Result = T { }

    This means that every type is the common type with itself.

Blanket impls must always be external and defined lexically out-of-line.

Difference between blanket impls and named constraints

A blanket interface can be used to say "any type implementing interface I also implements interface B." Compare this with defining a constraint C that requires I. In that case, C will also be implemented any time I is. There are differences though:

  • There can be other implementations of interface B without a corresponding implementation of I, unless B has a requirement on I. However, the types implementing C will be the same as the types implementing I.
  • More specialized implementations of B can override the blanket implementation.

Wildcard impls

A wildcard impl is an impl that defines a family of interfaces for a single Self type. For example, the BigInt type might implement AddTo(T) for all T that implement ImplicitAs(i32). The implementation would first convert T to i32 and then add the i32 to the BigInt value.

class BigInt {
  external impl forall [T:! ImplicitAs(i32)] as AddTo(T) { ... }
}
// Or out-of-line:
external impl forall [T:! ImplicitAs(i32)] BigInt as AddTo(T) { ... }

Wildcard impls must always be external, to avoid having the names in the interface defined for the type multiple times.

Combinations

The different kinds of parameters to impls may be combined. For example, if T implements As(U), then this implements As(Optional(U)) for Optional(T):

external impl forall [U:! Type, T:! As(U)]
  Optional(T) as As(Optional(U)) { ... }

This has a wildcard parameter U, and a condition on parameter T.

Lookup resolution and specialization

As much as possible, we want rules for where an impl is allowed to be defined and for selecting which impl to use that achieve these three goals:

For this to work, we need a rule that picks a single impl in the case where there are multiple impl definitions that match a particular type and interface combination. This is called specialization when the rule is that most specific implementation is chosen, for some definition of specific.

Type structure of an impl declaration

Given an impl declaration, find the type structure by deleting deduced parameters and replacing type parameters by a ?. The type structure of this declaration:

impl forall [T:! ..., U:! ...] Foo(T, i32) as Bar(String, U) { ... }

is:

impl Foo(?, i32) as Bar(String, ?)

To get a uniform representation across different impl definitions, before type parameters are replaced the declarations are normalized as follows:

  • For impls declared lexically inline in a class definition, the type is added between the impl and as keywords if the type is left out.
  • Pointer types T* are replaced with Ptr(T).
  • The external keyword is removed, if present.
  • The forall clause introducing type parameters is removed, if present.
  • Any where clauses that are setting associated constants or types are removed.

The type structure will always contain a single interface name, which is the name of the interface being implemented, and some number of type names. Type names can be in the Self type to the left of the as keyword, or as parameters to other types or the interface. These names must always be defined either in the current library or be publicly defined in some library this library depends on.

Orphan rule

To achieve coherence, we need to ensure that any given impl can only be defined in a library that must be imported for it to apply. Specifically, given a specific type and specific interface, impls that can match can only be in libraries that must have been imported to name that type or interface. This is achieved with the orphan rule.

Orphan rule: Some name from the type structure of an impl declaration must be defined in the same library as the impl, that is some name must be local.

Only the implementing interface and types (self type and type parameters) in the type structure are relevant here; an interface mentioned in a constraint is not sufficient since it need not be imported.

Since Carbon in addition requires there be no cyclic library dependencies, we conclude that there is at most one library that can define impls with a particular type structure.

Overlap rule

Given a specific concrete type, say Foo(bool, i32), and an interface, say Bar(String, f32), the overlap rule picks, among all the matching impls, which type structure is considered "most specific" to use as the implementation of that type for that interface.

Given two different type structures of impls matching a query, for example:

impl Foo(?, i32) as Bar(String, ?)
impl Foo(?, ?) as Bar(String, f32)

We pick the type structure with a non-? at the first difference as most specific. Here we see a difference between Foo(?, i32) and Foo(?, ?), so we select the one with Foo(?, i32), ignoring the fact that it has another ? later in its type structure

This rule corresponds to a depth-first traversal of the type tree to identify the first difference, and then picking the most specific choice at that difference.

Prioritization rule

Since at most one library can define impls with a given type structure, all impls with a given type structure must be in the same library. Furthermore by the impl declaration access rules, they will be defined in the API file for the library if they could match any query from outside the library. If there is more than one impl with that type structure, they must be defined or declared together in a prioritization block. Once a type structure is selected for a query, the first impl in the prioritization block that matches is selected.

Open question: How are prioritization blocks written? A block starts with a keyword like match_first or impl_priority and then a sequence of impl declarations inside matching curly braces { ... }.

match_first {
  // If T is Foo prioritized ahead of T is Bar
  impl forall [T:! Foo] T as Bar { ... }
  impl forall [T:! Baz] T as Bar { ... }
}

Open question: How do we pick between two different prioritization blocks when they contain a mixture of type structures? There are three options:

  • Prioritization blocks implicitly define all non-empty intersections of contained impls, which are then selected by their type structure.
  • The compiler first picks the impl with the type pattern most favored for the query, and then picks the definition of the highest priority matching impl in the same prioritization block.
  • All the impls in a prioritization block are required to have the same type structure, at a cost in expressivity.

To see the difference between the first two options, consider two libraries with type structures as follows:

  • Library B has impl (A, ?, ?, D) as I and impl (?, B, ?, D) as I in the same prioritization block.
  • Library C has impl (A, ?, C, ?) as I.

For the query (A, B, C, D) as I, using the intersection rule, library B is considered to have the intersection impl with type structure impl (A, B, ?, D) as I which is the most specific. If we instead just considered the rules mentioned explicitly, then impl (A, ?, C, ?) as I from library C is the most specific. The advantage of the implicit intersection rule is that if library B is changed to add an impl with type structure impl (A, B, ?, D) as I, it won't shift which library is serving that query.

Acyclic rule

A cycle is when a query, such as "does type T implement interface I?", considers an impl that might match, and whether that impl matches is ultimately dependent on whether that query is true. These are cycles in the graph of (type, interface) pairs where there is an edge from pair A to pair B if whether type A implements interface A determines whether type B implements interface B.

The test for whether something forms a cycle needs to be precise enough, and not erase too much information when considering this graph, that these impls are not considered to form cycles with themselves:

impl forall [T:! Printable] Optional(T) as Printable;
impl forall [T:! Type, U:! ComparableTo(T)] U as ComparableTo(Optional(T));

Example: If T implements ComparableWith(U), then U should implement ComparableWith(T).

external impl forall [U:! Type, T:! ComparableWith(U)]
    U as ComparableWith(T);

This is a cycle where which types implement ComparableWith determines which types implement the same interface.

Example: Cycles can create situations where there are multiple ways of selecting impls that are inconsistent with each other. Consider an interface with two blanket impl declarations:

class Y {}
class N {}
interface True {}
impl Y as True {}
interface Z(T:! Type) { let Cond:! Type; }
match_first {
  impl forall [T:! Type, U:! Z(T) where .Cond is True] T as Z(U)
      where .Cond = N { }
  impl forall [T:! Type, U:! Type] T as Z(U)
      where .Cond = Y { }
}

What is i8.(Z(i16).Cond)? It depends on which of the two blanket impls are selected.

  • An implementation of Z(i16) for i8 could come from the first blanket impl with T == i8 and U == i16 if i16 is Z(i8) and i16.(Z(i8).Cond) == Y. This condition is satisfied if i16 implements Z(i8) using the second blanket impl. In this case, i8.(Z(i16).Cond) == N.
  • Equally well Z(i8) could be implemented for i16 using the first blanket impl and Z(i16) for i8 using the second. In this case, i8.(Z(i16).Cond) == Y.

There is no reason to to prefer one of these outcomes over the other.

Example: Further, cycles can create contradictions in the type system:

class A {}
class B {}
class C {}
interface D(T:! Type) { let Cond:! Type; }
match_first {
  impl forall [T:! Type, U:! D(T) where .Cond = B] T as D(U)
      where .Cond = C { }
  impl forall [T:! Type, U:! D(T) where .Cond = A] T as D(U)
      where .Cond = B { }
  impl forall [T:! Type, U:! Type] T as D(U)
      where .Cond = A { }
}

What is i8.(D(i16).Cond)? The answer is determined by which blanket impl is selected to implement D(i16) for i8:

  • If the third blanket impl is selected, then i8.(D(i16).Cond) == A. This implies that i16.(D(i8).Cond) == B using the second blanket impl. If that is true, though, then our first impl choice was incorrect, since the first blanket impl applies and is higher priority. So i8.(D(i16).Cond) == C. But that means that i16 as D(i8) can't use the second blanket impl.
  • For the second blanket impl to be selected, so i8.(D(i16).Cond) == B, i16.(D(i8).Cond) would have to be A. This happens when i16 implements D(i8) using the third blanket impl. However, i8.(D(i16).Cond) == B means that there is a higher priority implementation of D(i8).Cond for i16.

In either case, we arrive at a contradiction.

The workaround for this problem is to either split an interface in the cycle in two, with a blanket implementation of one from the other, or move some of the criteria into a named constraint.

Concern: Cycles could be spread out across libraries with no dependencies between them. This means there can be problems created by a library that are only detected by its users.

Open question: Should Carbon reject cycles in the absence of a query? The two options here are:

  • Combining impls gives you an immediate error if there exists queries using those impls that have cycles.
  • Only when a query reveals a cyclic dependency is an error reported.

Open question: In the second case, should we ignore cycles if they don't affect the result of the query? For example, the cycle might be among implementations that are lower priority.

Termination rule

It is possible to define a set of impls where there isn't a cycle, but the graph is infinite. Without some rule to prevent exhaustive exploration of the graph, determining whether a type implements an interface could run forever.

Example: It could be that A implements B, so A is B if Optional(A) is B, if Optional(Optional(A)) is B, and so on. This could be the result of a single impl:

impl forall [A:! Type where Optional(.Self) is B] A as B { ... }

This problem can also result from a chain of impls, as in A is B if A* is C, if Optional(A) is B, and so on.

Rust solves this problem by imposing a recursion limit, much like C++ compilers use to terminate template recursion. This goes against Carbon's goal of predictability in generics, but at this time there are no known alternatives. Unfortunately, the approach Carbon uses to avoid undecidability for type equality, providing an explicit proof in the source, can't be used here. The code triggering the query asking whether some type implements an interface will typically be generic code with know specific knowledge about the types involved, and won't be in a position to provide a manual proof that the implementation should exist.

Open question: Is there some restriction on impl declarations that would allow our desired use cases, but allow the compiler to detect non-terminating cases? Perhaps there is some sort of complexity measure Carbon can require doesn't increase when recursing?

final impls

There are cases where knowing that a parameterized impl won't be specialized is particularly valuable. This could let the compiler know the return type of a generic function call, such as using an operator:

// Interface defining the behavior of the prefix-* operator
interface Deref {
  let Result:! Type;
  fn DoDeref[me: Self]() -> Result;
}

// Types implementing `Deref`
class Ptr(T:! Type) {
  ...
  external impl as Deref where .Result = T {
    fn DoDeref[me: Self]() -> Result { ... }
  }
}
class Optional(T:! Type) {
  ...
  external impl as Deref where .Result = T {
    fn DoDeref[me: Self]() -> Result { ... }
  }
}

fn F[T:! Type](x: T) {
  // uses Ptr(T) and Optional(T) in implementation
}

The concern is the possibility of specializing Optional(T) as Deref or Ptr(T) as Deref for a more specific T means that the compiler can't assume anything about the return type of Deref.DoDeref calls. This means F would in practice have to add a constraint, which is both verbose and exposes what should be implementation details:

fn F[T:! Type where Optional(T).(Deref.Result) == .Self
                and Ptr(T).(Deref.Result) == .Self](x: T) {
  // uses Ptr(T) and Optional(T) in implementation
}

To mark an impl as not able to be specialized, prefix it with the keyword final:

class Ptr(T:! Type) {
  ...
  // Note: added `final`
  final external impl as Deref where .Result = T {
    fn DoDeref[me: Self]() -> Result { ... }
  }
}
class Optional(T:! Type) {
  ...
  // Note: added `final`
  final external impl as Deref where .Result = T {
    fn DoDeref[me: Self]() -> Result { ... }
  }
}

// ❌ Illegal: external impl Ptr(i32) as Deref { ... }
// ❌ Illegal: external impl Optional(i32) as Deref { ... }

This prevents any higher-priority impl that overlaps a final impl from being defined. Further, if the Carbon compiler sees a matching final impl, it can assume it won't be specialized so it can use the assignments of the associated types in that impl definition.

fn F[T:! Type](x: T) {
  var p: Ptr(T) = ...;
  // *p has type `T`
  var o: Optional(T) = ...;
  // *o has type `T`
}

Libraries that can contain final impls

To prevent the possibility of two unrelated libraries defining conflicting impls, Carbon restricts which libraries may declare an impl as final to only:

  • the library declaring the impl's interface and
  • the library declaring the root of the Self type.

This means:

  • A blanket impl with type structure impl ? as MyInterface(...) may only be defined in the same library as MyInterface.
  • An impl with type structure impl MyType(...) as MyInterface(...) may be defined in the library with MyType or MyInterface.

These restrictions ensure that the Carbon compiler can locally check that no higher-priority impl is defined superseding a final impl.

  • An impl with type structure impl MyType(...) as MyInterface(...) defined in the library with MyType must import the library defining MyInterface, and so will be able to see any final blanket impls.
  • A blanket impl with type structure impl ? as MyInterface(...ParameterType(...)...) may be defined in the library with ParameterType, but that library must import the library defining MyInterface, and so will be able to see any final blanket impls that might overlap. A final impl with type structure impl MyType(...) as MyInterface(...) would be given priority over any overlapping blanket impl defined in the ParameterType library.
  • An impl with type structure impl MyType(...ParameterType(...)...) as MyInterface(...) may be defined in the library with ParameterType, but that library must import the libraries defining MyType and MyInterface, and so will be able to see any final impls that might overlap.

Comparison to Rust

Rust has been designing a specialization feature, but it has not been completed. Luckily, Rust team members have done a lot of blogging during their design process, so Carbon can benefit from the work they have done. However, getting specialization to work for Rust is complicated by the need to maintain compatibility with existing Rust code. This motivates a number of Rust rules where Carbon can be simpler. As a result there are both similarities and differences between the Carbon and Rust plans:

  • A Rust impl defaults to not being able to be specialized, with a default keyword used to opt-in to allowing specialization, reflecting the existing code base developed without specialization. Carbon impls default to allowing specialization, with restrictions on which may be declared final.
  • Since Rust impls are not specializable by default, generic functions can assume that if a matching blanket impl is found, the associated types from that impl will be used. In Carbon, if a generic function requires an associated type to have a particular value, the function commonly will need to state that using an explicit constraint.
  • Carbon will not have the "fundamental" attribute used by Rust on types or traits, as described in Rust RFC 1023: "Rebalancing Coherence".
  • Carbon will not use "covering" rules, as described in Rust RFC 2451: "Re-Rebalancing Coherence" and Little Orphan Impls: The covered rule.
  • Like Rust, Carbon does use ordering, favoring the Self type and then the parameters to the interface in left-to-right order, see Rust RFC 1023: "Rebalancing Coherence" and Little Orphan Impls: The ordered rule, but the specifics are different.
  • Carbon is not planning to support any inheritance of implementation between impls. This is more important to Rust since Rust does not support class inheritance for implementation reuse. Rust has considered multiple approaches here, see Aaron Turon: "Specialize to Reuse" and Supporting blanket impls in specialization.
  • Supporting blanket impls in specialization proposes a specialization rule for Rust that considers type structure before other constraints, as in Carbon, though the details differ.
  • Rust has more orphan restrictions to avoid there being cases where it is ambiguous which impl should be selected. Carbon instead has picked a total ordering on type structures, picking one as higher priority even without one being more specific in the sense of only applying to a subset of types.

Forward declarations and cyclic references

Interfaces, named constraints, and their implementations may be forward declared and then later defined. This is needed to allow cyclic references, for example when declaring the edges and nodes of a graph. It is also a tool that may be used to make code more readable.

The interface, named constraint, and implementation sections describe the syntax for their definition, which consists of a declaration followed by a body contained in curly braces { ... }. A forward declaration is a declaration followed by a semicolon ;. A forward declaration is a promise that the entity being declared will be defined later. Between the first declaration of an entity, which may be in a forward declaration or the first part of a definition, and the end of the definition the interface or implementation is called incomplete. There are additional restrictions on how the name of an incomplete entity may be used.

Declaring interfaces and named constraints

The declaration for an interface or named constraint consists of:

  • an optional access-control keyword like private,
  • the keyword introducer interface, constraint, or template constraint,
  • the name of the interface or constraint, and
  • the parameter list, if any.

The name of an interface or constraint can not be used until its first declaration is complete. In particular, it is illegal to use the name of the interface in its parameter list. There is a workaround for the use cases when this would come up.

An expression forming a constraint, such as C & D, is incomplete if any of the interfaces or constraints used in the expression are incomplete. A constraint expression using a where clause, like C where ..., is invalid if C is incomplete, since there is no way to look up member names of C that appear after where.

An interface or named constraint may be forward declared subject to these rules:

  • The definition must be in the same file as the declaration.
  • Only the first declaration may have an access-control keyword.
  • An incomplete interface or named constraint may be used as constraints in declarations of types, functions, interfaces, or named constraints. This includes an impl as or extends declaration inside an interface or named constraint, but excludes specifying the values for associated constants because that would involve name lookup into the incomplete constraint.
  • An attempt to define the body of a generic function using an incomplete interface or named constraint is illegal.
  • An attempt to call a generic function using an incomplete interface or named constraint in its signature is illegal.
  • Any name lookup into an incomplete interface or named constraint is an error. For example, it is illegal to attempt to access a member of an interface using MyInterface.MemberName or constrain a member using a where clause.

Declaring implementations

The declaration of an interface implementation consists of:

An implementation of an interface for a type may be forward declared subject to these rules:

  • The definition must be in the same library as the declaration. They must either be in the same file, or the declaration can be in the API file and the definition in an impl file. Future work: Carbon may require the definition of parameterized impls to be in the API file, to support separate compilation.
  • If there is both a forward declaration and a definition, only the first declaration must specify the assignment of associated constants with a where clause. Later declarations may omit the where clause by writing where _ instead.
  • You may forward declare an implementation of a defined interface but not an incomplete interface. This allows the assignment of associated constants in the impl declaration to be verified. An impl forward declaration may be for any declared type, whether it is incomplete or defined. Note that this does not apply to impl as declarations in an interface or named constraint definition, as those are considered interface requirements not forward declarations.
  • Every internal implementation must be declared (or defined) inside the scope of the class definition. It may also be declared before the class definition or defined afterwards. Note that the class itself is incomplete in the scope of the class definition, but member function bodies defined inline are processed as if they appeared immediately after the end of the outermost enclosing class.
  • For coherence, we require that any impl that matches an impl lookup query in the same file, must be declared before the query. This can be done with a definition or a forward declaration.

Matching and agreeing

Carbon needs to determine if two declarations match in order to say which definition a forward declaration corresponds to and to verify that nothing is defined twice. Declarations that match must also agree, meaning they are consistent with each other.

Interface and named constraint declarations match if their names are the same after name and alias resolution. To agree:

  • The introducer keyword or keywords much be the same.
  • The types and order of parameters in the parameter list, if any, must match. The parameter names may be omitted, but if they are included in both declarations, they must match.
  • Types agree if they correspond to the same expression tree, after name and alias resolution and canonicalization of parentheses. Note that no other evaluation of type expressions is performed.

Interface implementation declarations match if the type and interface expressions match:

  • If the type part is omitted, it is rewritten to Self in the context of the declaration.
  • Self is rewritten to its meaning in the scope it is used. In a class scope, this should match the type name and optional parameter expression after class. So in class MyClass extends MyBase { ... }, Self is rewritten to MyClass. In class Vector(T:! Movable) { ... }, Self is rewritten to Vector(T:! Movable).
  • Types match if they have the same name after name and alias resolution and the same parameters, or are the same type parameter.
  • Interfaces match if they have the same name after name and alias resolution and the same parameters. Note that a named constraint that is equivalent to an interface, as in constraint Equivalent { extends MyInterface; }, is not considered to match.

For implementations to agree:

  • The presence of modifier keywords such as external before impl must match between a forward declaration and definition.
  • If either declaration includes a where clause, they must both include one. If neither uses where _, they must match in that they produce the associated constants with the same values considered separately.

Declaration examples

// Forward declaration of interfaces
interface Interface1;
interface Interface2;
interface Interface3;
interface Interface4;
interface Interface5;
interface Interface6;

// Forward declaration of class type
class MyClass;

// ❌ Illegal: Can't declare implementation of incomplete
//             interface.
// external impl MyClass as Interface1;

// Definition of interfaces that were previously declared
interface Interface1 {
  let T1:! Type;
}
interface Interface2 {
  let T2:! Type;
}
interface Interface3 {
  let T3:! Type;
}
interface Interface4 {
  let T4:! Type;
}

// Forward declaration of external implementations
external impl MyClass as Interface1 where .T1 = i32;
external impl MyClass as Interface2 where .T2 = bool;

// Forward declaration of an internal implementation
impl MyClass as Interface3 where .T3 = f32;
impl MyClass as Interface4 where .T4 = String;

interface Interface5 {
  let T5:! Type;
}
interface Interface6 {
  let T6:! Type;
}

// Definition of the previously declared class type
class MyClass {
  // Definition of previously declared external impl.
  // Note: no need to repeat assignments to associated
  // constants.
  external impl as Interface1 where _ { }

  // Definition of previously declared internal impl.
  // Note: allowed even though `MyClass` is incomplete.
  // Note: allowed but not required to repeat `where`
  // clause.
  impl as Interface3 where .T3 = f32 { }

  // Redeclaration of previously declared internal impl.
  // Every internal implementation must be declared in
  // the class definition.
  impl as Interface4 where _;

  // Forward declaration of external implementation.
  external impl MyClass as Interface5 where .T5 = u64;

  // Forward declaration of internal implementation.
  impl MyClass as Interface6 where .T6 = u8;
}

// It would be legal to move the following definitions
// from the API file to the implementation file for
// this library.

// Definition of previously declared external impls.
external impl MyClass as Interface2 where _ { }
external impl MyClass as Interface5 where _ { }

// Definition of previously declared internal impls.
impl MyClass as Interface4 where _ { }
impl MyClass as Interface6 where _ { }

Example of declaring interfaces with cyclic references

In this example, Node has an EdgeType associated type that is constrained to implement Edge, and Edge has a NodeType associated type that is constrained to implement Node. Furthermore, the NodeType of an EdgeType is the original type, and the other way around. This is accomplished by naming and then forward declaring the constraints that can't be stated directly:

// Forward declare interfaces used in
// parameter lists of constraints.
interface Edge;
interface Node;

// Forward declare named constraints used in
// interface definitions.
private constraint EdgeFor(N:! Node);
private constraint NodeFor(E:! Edge);

// Define interfaces using named constraints.
interface Edge {
  let NodeType:! NodeFor(Self);
  fn Head[me: Self]() -> NodeType;
}
interface Node {
  let EdgeType:! EdgeFor(Self);
  fn Edges[me: Self]() -> Vector(EdgeType);
}

// Now that the interfaces are defined, can
// refer to members of the interface, so it is
// now legal to define the named constraints.
constraint EdgeFor(N:! Node) {
  extends Edge where .NodeType == N;
}
constraint NodeFor(E:! Edge) {
  extends Node where .EdgeType == E;
}

Interfaces with parameters constrained by the same interface

To work around the restriction about not being able to name an interface in its parameter list, instead include that requirement in the body of the interface.

// Want to require that `T` satisfies `CommonType(Self)`,
// but that can't be done in the parameter list.
interface CommonType(T:! Type) {
  let Result:! Type;
  // Instead add the requirement inside the definition.
  impl T as CommonType(Self);
}

Note however that CommonType is still incomplete inside its definition, so no constraints on members of CommonType are allowed.

interface CommonType(T:! Type) {
  let Result:! Type;
  // ❌ Illegal: `CommonType` is incomplete
  impl T as CommonType(Self) where .Result == Result;
}

Instead, a forward-declared named constraint can be used in place of the constraint that can only be defined later. This is the same strategy used to work around cyclic references.

private constraint CommonTypeResult(T:! Type, R:! Type);

interface CommonType(T:! Type) {
  let Result:! Type;
  // ✅ Allowed: `CommonTypeResult` is incomplete, but
  //             no members are accessed.
  impl T as CommonTypeResult(Self, Result);
}

constraint CommonTypeResult(T:! Type, R:! Type) {
  extends CommonType(T) where .Result == R;
}

Interface members with definitions

Interfaces may provide definitions for members, such as a function body for an associated function or method or a value for an associated constant. If these definitions may be overridden in implementations, they are called "defaults" and prefixed with the default keyword. Otherwise they are called "final members" and prefixed with the final keyword.

Interface defaults

An interface may provide a default implementation of methods in terms of other methods in the interface.

interface Vector {
  fn Add[me: Self](b: Self) -> Self;
  fn Scale[me: Self](v: f64) -> Self;
  // Default definition of `Invert` calls `Scale`.
  default fn Invert[me: Self]() -> Self {
    return me.Scale(-1.0);
  }
}

A default function or method may also be defined out of line, later in the same file as the interface definition:

interface Vector {
  fn Add[me: Self](b: Self) -> Self;
  fn Scale[me: Self](v: f64) -> Self;
  default fn Invert[me: Self]() -> Self;
}
// `Vector` is considered complete at this point,
// even though `Vector.Invert` is still incomplete.
fn Vector.Invert[me: Self]() -> Self {
  return me.Scale(-1.0);
}

An impl of that interface for a type may omit a definition of Invert to use the default, or provide a definition to override the default.

Interface defaults are helpful for evolution, as well as reducing boilerplate. Defaults address the gap between the minimum necessary for a type to provide the desired functionality of an interface and the breadth of API that developers desire. As an example, in Rust the iterator trait only has one required method but dozens of "provided methods" with defaults.

Defaults may also be provided for associated constants, such as associated types, and interface parameters, using the = <default value> syntax.

interface Add(Right:! Type = Self) {
  default let Result:! Type = Self;
  fn DoAdd[me: Self](right: Right) -> Result;
}

impl String as Add() {
  // Right == Result == Self == String
  fn DoAdd[me: Self](right: Self) -> Self;
}

Note that Self is a legal default value for an associated type or type parameter. In this case the value of those names is not determined until Self is, so Add() is equivalent to the constraint:

// Equivalent to Add()
constraint AddDefault {
  extends Add(Self);
}

Note also that the parenthesis are required after Add, even when all parameters are left as their default values.

More generally, default expressions may reference other associated types or Self as parameters to type constructors. For example:

interface Iterator {
  let Element:! Type;
  default let Pointer:! Type = Element*;
}

Carbon does not support providing a default implementation of a required interface.

interface TotalOrder {
  fn TotalLess[me: Self](right: Self) -> bool;
  // ❌ Illegal: May not provide definition
  //             for required interface.
  impl as PartialOrder {
    fn PartialLess[me: Self](right: Self) -> bool {
      return me.TotalLess(right);
    }
  }
}

The workaround for this restriction is to use a blanket impl instead:

interface TotalOrder {
  fn TotalLess[me: Self](right: Self) -> bool;
  impl as PartialOrder;
}

external impl forall [T:! TotalOrder] T as PartialOrder {
  fn PartialLess[me: Self](right: Self) -> bool {
    return me.TotalLess(right);
  }
}

Note that by the orphan rule, this blanket impl must be defined in the same library as PartialOrder.

Comparison with other languages: Rust supports specifying defaults for methods, interface parameters, and associated constants. Rust has found them valuable.

final members

As an alternative to providing a definition of an interface member as a default, members marked with the final keyword will not allow that definition to be overridden in impls.

interface TotalOrder {
  fn TotalLess[me: Self](right: Self) -> bool;
  final fn TotalGreater[me: Self](right: Self) -> bool {
    return right.TotalLess(me);
  }
}

class String {
  impl as TotalOrder {
    fn TotalLess[me: Self](right: Self) -> bool { ... }
    // ❌ Illegal: May not provide definition of final
    //             method `TotalGreater`.
    fn TotalGreater[me: Self](right: Self) -> bool { ... }
  }
}

interface Add(T:! Type = Self) {
  // `AddWith` *always* equals `T`
  final let AddWith:! Type = T;
  // Has a *default* of `Self`
  let Result:! Type = Self;
  fn DoAdd[me: Self](right: AddWith) -> Result;
}

Final members may also be defined out-of-line:

interface TotalOrder {
  fn TotalLess[me: Self](right: Self) -> bool;
  final fn TotalGreater[me: Self](right: Self) -> bool;
}
// `TotalOrder` is considered complete at this point, even
// though `TotalOrder.TotalGreater` is not yet defined.
fn TotalOrder.TotalGreater[me: Self](right: Self) -> bool {
 return right.TotalLess(me);
}

There are a few reasons for this feature:

  • When overriding would be inappropriate.
  • Matching the functionality of non-virtual methods in base classes, so interfaces can be a replacement for inheritance.
  • Potentially reduce dynamic dispatch when using the interface in a DynPtr.

Note that this applies to associated entities, not interface parameters.

Interface requiring other interfaces revisited

Recall that an interface can require another interface be implemented for the type, as in:

interface Iterable {
  impl as Equatable;
  // ...
}

This states that the type implementing the interface Iterable, which in this context is called Self, must also implement the interface Equatable. As is done with conditional conformance, we allow another type to be specified between impl and as to say some type other than Self must implement an interface. For example,

interface IntLike {
  impl i32 as As(Self);
  // ...
}

says that if Self implements IntLike, then i32 must implement As(Self). Similarly,

interface CommonTypeWith(T:! Type) {
  impl T as CommonTypeWith(Self);
  // ...
}

says that if Self implements CommonTypeWith(T), then T must implement CommonTypeWith(Self).

The previous description of impl as in an interface definition matches the behavior of using a default of Self when the type between impl and as is omitted. So the previous definition of interface Iterable is equivalent to:

interface Iterable {
  // ...
  impl Self as Equatable;
  // Equivalent to: impl as Equatable;
}

When implementing an interface with an impl as requirement, that requirement must be satisfied by an implementation in an imported library, an implementation somewhere in the same file, or a constraint in the impl declaration. Implementing the requiring interface is a promise that the requirement will be implemented. This is like a forward declaration of an impl except that the definition can be broader instead of being required to match exactly.

// `Iterable` requires `Equatable`, so there must be some
// impl of `Equatable` for `Vector(i32)` in this file.
external impl Vector(i32) as Iterable { ... }

fn RequiresEquatable[T:! Equatable](x: T) { ... }
fn ProcessVector(v: Vector(i32)) {
  // ✅ Allowed since `Vector(i32)` is known to
  // implement `Equatable`.
  RequiresEquatable(v);
}

// Satisfies the requirement that `Vector(i32)` must
// implement `Equatable` since `i32` is `Equatable`.
external impl forall [T:! Equatable] Vector(T) as Equatable { ... }

In some cases, the interface's requirement can be trivially satisfied by the implementation itself, as in:

impl forall [T:! Type] T as CommonTypeWith(T) { ... }

Here is an example where the requirement of interface Iterable that the type implements interface Equatable is satisfied by a constraint in the impl declaration:

class Foo(T:! Type) {}
// This is allowed because we know that an `impl Foo(T) as Equatable`
// will exist for all types `T` for which this impl is used, even
// though there's neither an imported impl nor an impl in this file.
external impl forall [T:! Type where Foo(T) is Equatable]
    Foo(T) as Iterable {}

This might be used to provide an implementation of Equatable for types that already satisfy the requirement of implementing Iterable:

class Bar {}
external impl Foo(Bar) as Equatable {}
// Gives `Foo(Bar) is Iterable` using the blanket impl of
// `Iterable` for `Foo(T)`.

Requirements with where constraints

An interface implementation requirement with a where clause is harder to satisfy. Consider an interface B that has a requirement that interface A is also implemented.

interface A(T:! Type) {
  let Result:! Type;
}
interface B(T:! Type) {
  impl as A(T) where .Result == i32;
}

An implementation of B for a set of types can only be valid if there is a visible implementation of A with the same T parameter for those types with the .Result associated type set to i32. That is not sufficient, though, unless the implementation of A can't be specialized, either because it is marked final or is not parameterized. Implementations in other libraries can't make A be implemented for fewer types, but can cause .Result to have a different assignment.

Observing a type implements an interface

An observe declaration can be used to show that two types are equal so code can pass type checking without explicitly writing casts, without requiring the compiler to do a unbounded search that may not terminate. An observe declaration can also be used to show that a type implements an interface, in cases where the compiler will not work this out for itself.

Observing interface requirements

One situation where this occurs is when there is a chain of interfaces requiring other interfaces. During the impl validation done during type checking, Carbon will only consider the interfaces that are direct requirements of the interfaces the type is known to implement. An observe...is declaration can be used to add an interface that is a direct requirement to the set of interfaces whose direct requirements will be considered for that type. This allows a developer to provide a proof that there is a sequence of requirements that demonstrate that a type implements an interface, as in this example:

interface A { }
interface B { impl as A; }
interface C { impl as B; }
interface D { impl as C; }

fn RequiresA[T:! A](x: T);
fn RequiresC[T:! C](x: T);
fn RequiresD[T:! D](x: T) {
  // ✅ Allowed: `D` directly requires `C` to be implemented.
  RequiresC(x);

  // ❌ Illegal: No direct connection between `D` and `A`.
  // RequiresA(x);

  // `T` is `D` and `D` directly requires `C` to be
  // implemented.
  observe T is C;

  // `T` is `C` and `C` directly requires `B` to be
  // implemented.
  observe T is B;

  // ✅ Allowed: `T` is `B` and `B` directly requires
  //             `A` to be implemented.
  RequiresA(x);
}

Note that observe statements do not affect the selection of impls during code generation. For coherence, the impl used for a (type, interface) pair must always be the same, independent of context. The termination rule governs when compilation may fail when the compiler can't determine the impl to select.

Observing blanket impls

An observe...is declaration can also be used to observe that a type implements an interface because there is a blanket impl in terms of requirements a type is already known to satisfy. Without an observe declaration, Carbon will only use blanket impls that are directly satisfied.

interface A { }
interface B { }
interface C { }
interface D { }

impl forall [T:! A] T as B { }
impl forall [T:! B] T as C { }
impl forall [T:! C] T as D { }

fn RequiresD(T:! D)(x: T);
fn RequiresB(T:! B)(x: T);

fn RequiresA(T:! A)(x: T) {
  // ✅ Allowed: There is a blanket implementation
  //             of `B` for types implementing `A`.
  RequiresB(x);

  // ❌ Illegal: No implementation of `D` for type
  //             `T` implementing `A`
  // RequiresD(x);

  // There is a blanket implementation of `B` for
  // types implementing `A`.
  observe T is B;

  // There is a blanket implementation of `C` for
  // types implementing `B`.
  observe T is C;

  // ✅ Allowed: There is a blanket implementation
  //             of `D` for types implementing `C`.
  RequiresD(x);
}

In the case of an error, a quality Carbon implementation will do a deeper search for chains of requirements and blanket impls and suggest observe declarations that would make the code compile if any solution is found.

Operator overloading

Operations are overloaded for a type by implementing an interface specific to that interface for that type. For example, types implement the Negatable interface to overload the unary - operator:

// Unary `-`.
interface Negatable {
  let Result:! Type = Self;
  fn Negate[me: Self]() -> Result;
}

Expressions using operators are rewritten into calls to these interface methods. For example, -x would be rewritten to x.(Negatable.Negate)().

The interfaces and rewrites used for a given operator may be found in the expressions design. Question-for-leads issue #1058 defines the naming scheme for these interfaces.

Binary operators

Binary operators will have an interface that is parameterized based on the second operand. For example, to say a type may be converted to another type using an as expression, implement the As interface:

interface As(Dest:! Type) {
  fn Convert[me: Self]() -> Dest;
}

The expression x as U is rewritten to x.(As(U).Convert)(). Note that the parameterization of the interface means it can be implemented multiple times to support multiple operand types.

Unlike as, for most binary operators the interface's argument will be the type of the right-hand operand instead of its value. Consider an interface for a binary operator like *:

// Binary `*`.
interface MultipliableWith(U:! Type) {
  let Result:! Type = Self;
  fn Multiply[me: Self](other: U) -> Result;
}

A use of binary * in source code will be rewritten to use this interface:

var left: Meters = ...;
var right: f64 = ...;
var result: auto = left * right;
// Equivalent to:
var equivalent: left.(MultipliableWith(f64).Result)
    = left.(MultipliableWith(f64).Multiply)(right);

Note that if the types of the two operands are different, then swapping the order of the operands will result in a different implementation being selected. It is up to the developer to make those consistent when that is appropriate. The standard library will provide adapters for defining the second implementation from the first, as in:

interface ComparableWith(RHS:! Type) {
  fn Compare[me: Self](right: RHS) -> CompareResult;
}

adapter ReverseComparison
    (T:! Type, U:! ComparableWith(RHS)) for T {
  impl as ComparableWith(U) {
    fn Compare[me: Self](right: RHS) -> CompareResult {
      return ReverseCompareResult(right.Compare(me));
    }
  }
}

external impl SongByTitle as ComparableWith(SongTitle);
external impl SongTitle as ComparableWith(SongByTitle)
    = ReverseComparison(SongTitle, SongByTitle);

In some cases the reverse operation may not be defined. For example, a library might support subtracting a vector from a point, but not the other way around.

Further note that even if the reverse implementation exists, the impl prioritization rule might not pick it. For example, if we have two types that support comparison with anything implementing an interface that the other implements:

interface IntLike {
  fn AsInt[me: Self]() -> i64;
}

class EvenInt { ... }
external impl EvenInt as IntLike;
external impl EvenInt as ComparableWith(EvenInt);
// Allow `EvenInt` to be compared with anything that
// implements `IntLike`, in either order.
external impl forall [T:! IntLike] EvenInt as ComparableWith(T);
external impl forall [T:! IntLike] T as ComparableWith(EvenInt);

class PositiveInt { ... }
external impl PositiveInt as IntLike;
external impl PositiveInt as ComparableWith(PositiveInt);
// Allow `PositiveInt` to be compared with anything that
// implements `IntLike`, in either order.
external impl forall [T:! IntLike] PositiveInt as ComparableWith(T);
external impl forall [T:! IntLike] T as ComparableWith(PositiveInt);

Then it will favor selecting the implementation based on the type of the left-hand operand:

var even: EvenInt = ...;
var positive: PositiveInt = ...;
// Uses `EvenInt as ComparableWith(T)` impl
if (even < positive) { ... }
// Uses `PositiveInt as ComparableWith(T)` impl
if (positive > even) { ... }

like operator for implicit conversions

Because the type of the operands is directly used to select the implementation to use, there are no automatic implicit conversions, unlike with function or method calls. Given both a method and an interface implementation for multiplying by a value of type f64:

class Meters {
  fn Scale[me: Self](s: f64) -> Self;
}
// "Implementation One"
external impl Meters as MultipliableWith(f64)
    where .Result = Meters {
  fn Multiply[me: Self](other: f64) -> Result {
    return me.Scale(other);
  }
}

the method will work with any argument that can be implicitly converted to f64 but the operator overload will only work with values that have the specific type of f64:

var height: Meters = ...;
var scale: f32 = 1.25;
// ✅ Allowed: `scale` implicitly converted
//             from `f32` to `f64`.
var allowed: Meters = height.Scale(scale);
// ❌ Illegal: `Meters` doesn't implement
//             `MultipliableWith(f32)`.
var illegal: Meters = height * scale;

The workaround is to define a parameterized implementation that performs the conversion. The implementation is for types that implement the ImplicitAs interface.

// "Implementation Two"
external impl forall [T:! ImplicitAs(f64)]
    Meters as MultipliableWith(T) where .Result = Meters {
  fn Multiply[me: Self](other: T) -> Result {
    // Carbon will implicitly convert `other` from type
    // `T` to `f64` to perform this call.
    return me.(Meters.(MultipliableWith(f64).Multiply))(other);
  }
}
// ✅ Allowed: uses `Meters as MultipliableWith(T)` impl
//             with `T == f32` since `f32 is ImplicitAs(f64)`.
var now_allowed: Meters = height * scale;

Observe that the prioritization rule will still prefer the unparameterized impl when there is an exact match.

To reduce the boilerplate needed to support these implicit conversions when defining operator overloads, Carbon has the like operator. This operator can only be used in the type or type-of-type part of an impl declaration, as part of a forward declaration or definition, in a place of a type.

// Notice `f64` has been replaced by `like f64`
// compared to "implementation one" above.
external impl Meters as MultipliableWith(like f64)
    where .Result = Meters {
  fn Multiply[me: Self](other: f64) -> Result {
    return me.Scale(other);
  }
}

This impl definition actually defines two implementations. The first is the same as this definition with like f64 replaced by f64, giving something equivalent to "implementation one". The second implementation replaces the like f64 with a parameter that ranges over types that can be implicitly converted to f64, equivalent to "implementation two".

In general, each like adds one additional impl. There is always the impl with all of the like expressions replaced by their arguments with the definition supplied in the source code. In addition, for each like expression, there is an impl with it replaced by a new parameter. These additional impls will delegate to the main impl, which will trigger implicit conversions according to Carbon's ordinary implicit conversion rules. In this example, there are two uses of like, producing three implementations

external impl like Meters as MultipliableWith(like f64)
    where .Result = Meters {
  fn Multiply[me: Self](other: f64) -> Result {
    return me.Scale(other);
  }
}

is equivalent to "implementation one", "implementation two", and:

external impl forall [T:! ImplicitAs(Meters)]
    T as MultipliableWith(f64) where .Result = Meters {
  fn Multiply[me: Self](other: f64) -> Result {
    // Will implicitly convert `me` to `Meters` in order to
    // match the signature of this `Multiply` method.
    return me.(Meters.(MultipliableWith(f64).Multiply))(other);
  }
}

like may be used in forward declarations in a way analogous to impl definitions.

external impl like Meters as MultipliableWith(like f64)
    where .Result = Meters;
}

is equivalent to:

// All `like`s removed. Same as the declaration part of
// "implementation one", without the body of the definition.
external impl Meters as MultipliableWith(f64)
    where .Result = Meters;

// First `like` replaced with a wildcard.
external impl forall [T:! ImplicitAs(Meters)]
    T as MultipliableWith(f64) where .Result = Meters;

// Second `like` replaced with a wildcard. Same as the
// declaration part of "implementation two", without the
// body of the definition.
external impl forall [T:! ImplicitAs(f64)]
    Meters as MultipliableWith(T) where .Result = Meters;

In addition, the generated impl definition for a like is implicitly injected at the end of the (unique) source file in which the impl is first declared. That is, it is injected in the API file if the impl is declared in an API file, and in the sole impl file declaring the impl otherwise. This means an impl declaration using like in an API file also makes the parameterized definition

If one impl declaration uses like, other declarations must use like in the same way to match.

The like operator may be nested, as in:

external impl like Vector(like String) as Printable;

Which will generate implementations with declarations:

external impl Vector(String) as Printable;
external impl forall [T:! ImplicitAs(Vector(String))] T as Printable;
external impl forall [T:! ImplicitAs(String)] Vector(T) as Printable;

The generated implementations must be legal or the like is illegal. For example, it must be legal to define those impls in this library by the orphan rule. In addition, the generated impl definitions must only require implicit conversions that are guaranteed to exist. For example, there existing an implicit conversion from T to String does not imply that there is one from Vector(T) to Vector(String), so the following use of like is illegal:

// ❌ Illegal: Can't convert a value with type
//             `Vector(T:! ImplicitAs(String))`
//             to `Vector(String)` for `me`
//             parameter of `Printable.Print`.
external impl Vector(like String) as Printable;

Since the additional implementation definitions are generated eagerly, these errors will be reported in the file with the first declaration.

The argument to like must either not mention any type parameters, or those parameters must be able to be determined due to being repeated outside of the like expression.

// ✅ Allowed: no parameters
external impl like Meters as Printable;

// ❌ Illegal: No other way to determine `T`
external impl forall [T:! IntLike] like T as Printable;

// ❌ Illegal: `T` being used in a `where` clause
//             is insufficient.
external impl forall [T:! IntLike] like T
    as MultipliableWith(i64) where .Result = T;

// ❌ Illegal: `like` can't be used in a `where`
//             clause.
external impl Meters as MultipliableWith(f64)
    where .Result = like Meters;

// ✅ Allowed: `T` can be determined by another
//             part of the query.
external impl forall [T:! IntLike] like T
    as MultipliableWith(T) where .Result = T;
external impl forall [T:! IntLike] T
    as MultipliableWith(like T) where .Result = T;

// ✅ Allowed: Only one `like` used at a time, so this
//             is equivalent to the above two examples.
external impl forall [T:! IntLike] like T
    as MultipliableWith(like T) where .Result = T;

Parameterized types

Types may have generic parameters. Those parameters may be used to specify types in the declarations of its members, such as data fields, member functions, and even interfaces being implemented. For example, a container type might be parameterized by the type of its elements:

class HashMap(
    KeyType:! Hashable & EqualityComparable & Movable,
    ValueType:! Movable) {
  // `Self` is `HashMap(KeyType, ValueType)`.

  // Parameters may be used in function signatures.
  fn Insert[addr me: Self*](k: KeyType, v: ValueType);

  // Parameters may be used in field types.
  private var buckets: Vector((KeyType, ValueType));

  // Parameters may be used in interfaces implemented.
  impl as Container where .ElementType = (KeyType, ValueType);
  impl as ComparableWith(HashMap(KeyType, ValueType));
}

Note that, unlike functions, every parameter to a type must either be generic or template, using :! or template...:!, not dynamic, with a plain :.

Two types are the same if they have the same name and the same arguments. Carbon's manual type equality approach means that the compiler may not always be able to tell when two type expressions are equal without help from the user, in the form of observe declarations. This means Carbon will not in general be able to determine when types are unequal.

Unlike an interface's parameters, a type's parameters may be deduced, as in:

fn ContainsKey[KeyType:! Movable, ValueType:! Movable]
    (haystack: HashMap(KeyType, ValueType), needle: KeyType)
    -> bool { ... }
fn MyMapContains(s: String) {
  var map: HashMap(String, i32) = (("foo", 3), ("bar", 5));
  // ✅ Deduces `KeyType` = `String` from the types of both arguments.
  // Deduces `ValueType` = `i32` from the type of the first argument.
  return ContainsKey(map, s);
}

Note that restrictions on the type's parameters from the type's declaration can be implied constraints on the function's parameters.

Specialization

Specialization is used to improve performance in specific cases when a general strategy would be inefficient. For example, you might use binary search for containers that support random access and keep their contents in sorted order but linear search in other cases. Types, like functions, may not be specialized directly in Carbon. This effect can be achieved, however, through delegation.

For example, imagine we have a parameterized class Optional(T) that has a default storage strategy that works for all T, but for some types we have a more efficient approach. For pointers we can use a null value to represent "no pointer", and for booleans we can support True, False, and None in a single byte. Clients of the optional library may want to add additional specializations for their own types. We make an interface that represents "the storage of Optional(T) for type T," written here as OptionalStorage:

interface OptionalStorage {
  let Storage:! Type;
  fn MakeNone() -> Storage;
  fn Make(x: Self) -> Storage;
  fn IsNone(x: Storage) -> bool;
  fn Unwrap(x: Storage) -> Self;
}

The default implementation of this interface is provided by a blanket implementation:

// Default blanket implementation
impl forall [T:! Movable] T as OptionalStorage
    where .Storage = (bool, T) {
  ...
}

This implementation can then be specialized for more specific type patterns:

// Specialization for pointers, using nullptr == None
final external impl forall [T:! Type] T* as OptionalStorage
    where .Storage = Array(Byte, sizeof(T*)) {
  ...
}
// Specialization for type `bool`.
final external impl bool as OptionalStorage
    where .Storage = Byte {
  ...
}

Further, libraries can implement OptionalStorage for their own types, assuming the interface is not marked private. Then the implementation of Optional(T) can delegate to OptionalStorage for anything that can vary with T:

class Optional(T:! Movable) {
  fn None() -> Self {
    return {.storage = T.(OptionalStorage.MakeNone)()};
  }
  fn Some(x: T) -> Self {
    return {.storage = T.(OptionalStorage.Make)(x)};
  }
  ...
  private var storage: T.(OptionalStorage.Storage);
}

Note that the constraint on T is just Movable, not Movable & OptionalStorage, since the Movable requirement is sufficient to guarantee that some implementation of OptionalStorage exists for T. Carbon does not require callers of Optional, even generic callers, to specify that the argument type implements OptionalStorage:

// ✅ Allowed: `T` just needs to be `Movable` to form `Optional(T)`.
//             A `T:! OptionalStorage` constraint is not required.
fn First[T:! Movable & Eq](v: Vector(T)) -> Optional(T);

Adding OptionalStorage to the constraints on the parameter to Optional would obscure what types can be used as arguments. OptionalStorage is an implementation detail of Optional and need not appear in its public API.

In this example, a let is used to avoid repeating OptionalStorage in the definition of Optional, since it has no name conflicts with the members of Movable:

class Optional(T:! Movable) {
  private let U:! Movable & OptionalStorage = T;
  fn None() -> Self {
    return {.storage = U.MakeNone()};
  }
  fn Some(x: T) -> Self {
    return {.storage = u.Make(x)};
  }
  ...
  private var storage: U.Storage;
}

Future work

Dynamic types

Generics provide enough structure to support runtime dispatch for values with types that vary at runtime, without giving up type safety. Both Rust and Swift have demonstrated the value of this feature.

Runtime type parameters

This feature is about allowing a function's type parameter to be passed in as a dynamic (non-generic) parameter. All values of that type would still be required to have the same type.

Runtime type fields

Instead of passing in a single type parameter to a function, we could store a type per value. This changes the data layout of the value, and so is a somewhat more invasive change. It also means that when a function operates on multiple values they could have different real types.

Abstract return types

This lets you return an anonymous type implementing an interface from a function. In Rust this is the impl Trait return type.

In Swift, there are discussions about implementing this feature under the name "reverse generics" or "opaque result types": 1, 2, 3, 4, Swift is considering spelling this <V: Collection> V or some Collection.

Evolution

There are a collection of use cases for making different changes to interfaces that are already in use. These should be addressed either by describing how they can be accomplished with existing generics features, or by adding features.

In addition, evolution from (C++ or Carbon) templates to generics needs to be supported and made safe.

Testing

The idea is that you would write tests alongside an interface that validate the expected behavior of any type implementing that interface.

Impls with state

A feature we might consider where an impl itself can have state.

Generic associated types and higher-ranked types

This would be some way to express the requirement that there is a way to go from a type to an implementation of an interface parameterized by that type.

Generic associated types

Generic associated types are about when this is a requirement of an interface. These are also called "associated type constructors."

Higher-ranked types

Higher-ranked types are used to represent this requirement in a function signature. They can be emulated using generic associated types.

Field requirements

We might want to allow interfaces to express the requirement that any implementing type has a particular field. This would be to match the expressivity of inheritance, which can express "all subtypes start with this list of fields."

Bridge for C++ customization points

See details in the goals document.

Variadic arguments

Some facility for allowing a function to generically take a variable number of arguments.

Range constraints on generic integers

We currently only support where clauses on type-of-types. We may want to also support constraints on generic integers. The constraint with the most expected value is the ability to do comparisons like <, or >=. For example, you might constrain the N member of NSpacePoint using an expression like PointT:! NSpacePoint where 2 <= .N and .N <= 3.

The concern here is supporting this at compile time with more benefit than complexity. For example, we probably don't want to support integer-range based types at runtime, and there are also concerns about reasoning about comparisons between multiple generic integer parameters. For example, if J < K and K <= L, can we call a function that requires J < L? There is also a secondary syntactic concern about how to write this kind of constraint on a parameter, as opposed to an associated type, as in N:! u32 where ___ >= 2.

References