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Generics: Details

Table of contents

Overview

This document goes into the details of the design of Carbon's generics, by which we mean generalizing some language construct with compile-time parameters. These parameters can be types, facets, or other values.

Imagine we want to write a function with a type (or facet) parameter. 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 facet 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.

That interface implementation has the definitions of the functions declared in the interface. For example, the types i32 and String would have different implementations of the ToString method of the ConvertibleToString interface.

In addition to function members, interfaces can include other members that associate a compile-time value for any implementing type, called associated constants. For example, this can allow a container interface to include the type of iterators that are returned from and passed to various container methods.

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 "compile-time parameter" syntax :!. By default, this defines a checked-generics parameter below. In this case, 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.

Alternatively, the template keyword can be included in the signature to make the type a template parameter. In this case, 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.

When the implementation of ConvertibleToString for Song is declared with extend, 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 type extends the implementation or not, 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.

We originally considered following Swift and using a witness table implementation strategy for checked generics, but ultimately decided to only use that for the dynamic-dispatch case. This is because of the limitations of that strategy prevent some features that we considered important, as described in the witness-table appendix.

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 the `Self` keyword means
  // "the type implementing this interface".
  fn Add[self: Self](b: Self) -> Self;
  fn Scale[self: 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. A type implements an interface by providing definitions for all the associated entities declared in the interface,

An interface defines a facet type, that is a type whose values are facets. Every type implementing the interface has a corresponding facet value. So if the type Point implements interface Vector, the facet value Point as Vector has type Vector.

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, called the implementing 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 implementing type for that interface.

Inline impl

An impl may be defined inline inside the type definition:

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

extend impl

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

class Point_Extend {
  var x: f64;
  var y: f64;
  extend impl as Vector {
    fn Add[self: Self](b: Self) -> Self {
      return {.x = self.x + b.x, .y = self.y + b.y};
    }
    fn Scale[self: Self](v: f64) -> Self {
      return {.x = self.x * v, .y = self.y * v};
    }
  }
}

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

Without extend, those methods may only be accessed with qualified member names and compound member access:

// Point_Inline did not use `extend` when
// implementing `Vector`:
var a: Point_Inline = {.x = 1.0, .y = 2.0};
// `a` does *not* have `Add` and `Scale` methods:
// ❌ Error: a.Add(a.Scale(2.0));

This is consistent with the general Carbon rule that if the names of another entity affect a class' API, then that is mentioned with an extend declaration in the class definition.

Comparison with other languages: Rust only defines implementations lexically outside of the class definition. Carbon's approach results in the property that every type's API is described by declarations inside its class definition and doesn't change afterwards.

References: Carbon's interface implementation syntax was first defined in proposal #553. In particular, see the alternatives considered. This syntax was changed to use extend in proposal #2760: Consistent class and interface syntax.

Out-of-line impl

An impl may also be defined after the type definition, by naming the type between impl and as:

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

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

Since extend impl may only be used inside the class definition, out-of-line definitions do not contribute to the class's API unless there is a corresponding forward declaration in the class definition using extend.

Conversely, being declared or 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?

Comparison with other languages: Both Rust and Swift support out-of-line implementation. Swift's syntax does this as an "extension" of the original type. In Rust, all implementations are out-of-line 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.

Defining an impl in another library than the type

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

You can't use extend outside the class definition, so an impl declaration in a different library will never affect the class's API. This means that the API of a class such as Point_OutOfLine 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 and entities referenced in by an extend declaration in that definition. The only thing that may be in another library is an impl of an interface.

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.

Forward impl declaration

An impl declaration may be forward declared and then defined later. If this is done using extend to add to the type's API, only the declaration in the class definition will use the extend keyword, as in this example:

class Point_ExtendForward {
  var x: f64;
  var y: f64;
  // Forward declaration in class definition using `extend`.
  // Signals that you should look in the definition of
  // `Vector` since those methods are included in this type.
  extend impl as Vector;
}

// Definition outside class definition does not.
impl Point_ExtendForward as Vector {
  fn Add[self: Self](b: Self) -> Self {
    return {.x = self.x + b.x, .y = self.y + b.y};
  }
  fn Scale[self: Self](v: f64) -> Self {
    return {.x = self.x * v, .y = self.y * v};
  }
}

More about forward declaring implementations in its dedicated section.

Implementing multiple interfaces

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

class Point_2Extend {
  var x: f64;
  var y: f64;
  extend impl as Vector {
    fn Add[self: Self](b: Self) -> Self { ... }
    fn Scale[self: Self](v: f64) -> Self { ... }
  }
  extend impl as Drawable {
    fn Draw[self: Self]() { ... }
  }
}

Since both were declared using extend, all the functions Add, Scale, and Draw end up a part of the API for Point_2Extend.

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.

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

Avoiding name collisions

To avoid name collisions, you can't extend implementations of two interfaces that have a name in common:

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

To implement two interfaces that have a name in common, omit extend for one or both.

You might also omit extend when implementing an interface for a type to avoid cluttering the API of that type or to avoid a name collision with another member of that type. A syntax for reusing method implementations allows us to include names from an implementation selectively:

class Point_ReuseMethodInImpl {
  var x: f64;
  var y: f64;
  // `Add()` is a method of `Point_ReuseMethodInImpl`.
  fn Add[self: Self](b: Self) -> Self {
    return {.x = self.x + b.x, .y = self.y + b.y};
  }
  // No `extend`, so other members of `Vector` are not
  // part of `Point_ReuseMethodInImpl`'s API.
  impl as Vector {
    // Syntax TBD:
    alias Add = Point_ReuseMethodInImpl.Add;
    fn Scale[self: Self](v: f64) -> Self {
      return {.x = self.x * v, .y = self.y * v};
    }
  }
}

// OR:

class Point_IncludeMethodFromImpl {
  var x: f64;
  var y: f64;
  // No `extend`, so members of `Vector` are not
  // part of `Point_IncludeMethodFromImpl`'s API.
  impl as Vector {
    fn Add[self: Self](b: Self) -> Self {
      return {.x = self.x + b.x, .y = self.y + b.y};
    }
    fn Scale[self: Self](v: f64) -> Self {
      return {.x = self.x * v, .y = self.y * v};
    }
  }
  // Include `Add` explicitly as a member.
  alias Add = Vector.Add;
}

// OR:

// This is the same as `Point_ReuseMethodInImpl`,
// except the `impl` is out-of-line.
class Point_ReuseByOutOfLine {
  var x: f64;
  var y: f64;
  fn Add[self: Self](b: Self) -> Self {
    return {.x = self.x + b.x, .y = self.y + b.y};
  }
}

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

Qualified member names and compound member access

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

impl Point_NoExtend as Vector { ... }

Given a value of type Point_NoExtend 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 with an extend impl declaration. The qualified member access expression writes the member's qualified name in the parentheses of the compound member access syntax:

var p1: Point_NoExtend = {.x = 1.0, .y = 2.0};
var p2: Point_NoExtend = {.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 Point_NoExtend. So if there was another interface Drawable with method Draw defined in the Plot package also implemented for Point_NoExtend, as in:

package Plot;
import Points;

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

impl Points.Point_NoExtend as Drawable { ... }

You could access Draw with a qualified name:

import Plot;
import Points;

var p: Points.Point_NoExtend = {.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 declared 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.

Checked-generic functions

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_Extend = AddAndScaleGeneric(a, w, 2.5);

Here T is a facet whose type is Vector. The :! syntax means that T is a compile-time binding. Here specifically it declares a symbolic binding since it did not use the template keyword to mark it as a template binding.

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

Since this symbolic binding pattern is in a function declaration, it marks a checked generic parameter. That means its value must be known to the caller at compile-time, but we will only use the information present in the signature of the function to type check the body of AddAndScaleGeneric's definition.

Note that types may also be given compile-time parameters, see the "parameterized types" section.

Symbolic facet bindings

In our example, T is a facet which may be used in type position in the rest of the function. Furthermore, since it omits the keyword template prefix, this is a symbolic binding. so we need to be able to typecheck the body of the function without knowing the specific value T from the caller.

This typechecking is done by looking at the constraint on T. In the example, the constraint on T says that every value of T implements the Vector interface and so has a Vector.Add and a Vector.Scale method.

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 extend the implementation of its constraint. The only oddity is that the archetype may have different names for members than specific types T that don't extend the implementation of interfaces from the constraint. 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_Extend is to set T to Point_Extend after all the names have been qualified.

// AddAndScaleGeneric with T = Point_Extend
fn AddAndScaleForPoint_Extend(
    a: Point_Extend, b: Point_Extend, s: Double)
    -> Point_Extend {
  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 does not extend the implementation of the interface, like Point_NoExtend:

// AddAndScaleGeneric with T = Point_NoExtend
fn AddAndScaleForPoint_NoExtend(
    a: Point_NoExtend, b: Point_NoExtend, s: Double)
    -> Point_NoExtend {
  // ✅ 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_Extend values returns a Point_Extend and called with Point_NoExtend values returns a Point_NoExtend. So looking up a member on the resulting value will look in Point_Extend or Point_NoExtend 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_Extend and AddAndScaleForPoint_NoExtend without affecting the return types. This may require a conversion of the return value to the type that the caller expects, from the erased type used inside a checked-generic function.

A checked-generic caller of a checked-generic function performs the same substitution process to determine the return type, but the result may be a symbolic value. In this example of calling a checked generic from another checked 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 acts as if it extends Vector 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) {
  impl as Vector { ... }
  fn Get[self: 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 but does not extend `Vector`,
  //    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`, 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 without extend the return value in this case does not directly have a Scale method.

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 facet types, facet types are a more general concept, for which interfaces are a building block.

Facet types

A facet 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 facet type. For example, Vector as a facet 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 may be implicitly converted to a given facet type. The result of this conversion is a facet. For example, Point_Inline from the "Inline impl" section implements Vector, so Point_Inline may be implicitly converted to Vector as considered as a type. The result is Point_Inline as Vector, which has the members of Vector instead of the members of Point_Inline. If the facet Point_Inline as Vector is used in a type position, it is implicitly converted back to type type, see "values usable as types" in the design overview. This recovers the original type for the facet, so (Point_Inline as Vector) as type is Point_Inline again.

However, when a facet type like Vector is used as the binding type of a symbolic binding, as in T:! Vector, the symbolic facet binding T is disassociated with whatever facet value T is eventually bound to. Instead, T is treated as an archetype, with the members and member access determined by the names of the facet type.

This general structure of facet 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 facet types, 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 have to 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 require Self impls declarations and names using alias declarations. Note that this allows us to declare the aspects of a facet type directly.

constraint VectorLegoFish {
  // Interface implementation requirements
  require Self impls Vector;
  require Self impls LegoFish;
  // Names
  alias Scale = Vector.Scale;
  alias VAdd = Vector.Add;
  alias LFAdd = LegoFish.Add;
}

A require Self impls requirement may alternatively be on a named constraint, instead of an interface, to add all the requirements of another named constraint without adding any of the names:

constraint DrawVectorLegoFish {
  // The same as requiring both `Vector` and `LegoFish`.
  require Self impls VectorLegoFish;
  // A regular interface requirement. No syntactic difference.
  require Self impls Drawable;
}

In general, Carbon makes no syntactic distinction between the uses of named constraints and interfaces, so one may be replaced with the other without affecting users. To accomplish this, Carbon allows a named constraint to be used whenever an interface may be. This includes all of these uses of interfaces:

  • A type may impl a named constraint to say that it implements all of the requirements of the named constraint, as described below.
  • A named constraint may be used as a namespace name in a qualified name. For example, VectorLegoFish.VAdd refers to the same name as Vector.Add.
  • A named constraint may be used as a facet type for a facet binding.

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, if type were not a keyword, we could define the Carbon builtin type as:

constraint type { }

That is, type is the facet 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");

In general, the declarations in constraint definition match a subset of the declarations in an interface. These named constraints can be used with checked generics, as opposed to templates, and 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 constant, and associated function requirements may only be declared inside a template constraint. Note that a checked-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 template constraint and in an interface definition. If an interface I has (non-alias, non-require) 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 a template constraint, S:

template constraint S {
  X;
  Y;
  Z;
}

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

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

Subtyping between facet types

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

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

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

constraint PrintAndRender {
  require Self impls Printable;
  require Self impls Renderable;
}
constraint JustPrint {
  require Self impls 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 facet types

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

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

// `Printable & Renderable` is syntactic sugar for this facet type:
constraint {
  require Self impls Printable;
  require Self impls 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 {
  // ...
  extend impl as Printable {
    fn Print[self: Self]() { ... }
  }
  extend impl as Renderable {
    fn Center[self: Self]() -> (i32, i32) { ... }
    fn Draw[self: Self]() { ... }
  }
}

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

It is an error to use any names that conflict between the two interfaces.

interface Renderable {
  fn Center[self: Self]() -> (i32, i32);
  fn Draw[self: Self]();
}
interface EndOfGame {
  fn Draw[self: Self]();
  fn Winner[self: Self](player: i32);
}
fn F[T:! Renderable & EndOfGame](x: T) {
  // ❌ Error: Ambiguous, use either `(Renderable.Draw)`
  //           or `(EndOfGame.Draw)`.
  x.Draw();
}

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 {
  require Self impls Renderable;
  require Self impls 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();
}

Note that & is associative and commutative, and so it is well defined on sets of interfaces, or other facet types, independent of order.

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

To add to the requirements of a facet type without affecting the names, and so avoid the possibility of name conflicts, names, use a where .Self impls clause.

// `Printable where .Self impls Renderable` is equivalent to:
constraint {
  require Self impls Printable;
  require Self impls Renderable;
  alias Print = Printable.Print;
}

You might use this to add requirements on interfaces used for operator overloading, where merely implementing the interface is enough to be able to use the operator to access the functionality.

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

Alternatives considered: See Carbon: Access to interface methods.

Rejected alternative: Instead of using & as the combining operator, we considered using +, like Rust. The main difference from Rust's + is how you qualify names when there is a conflict. See issue #531 for the discussion.

Interface requiring other interfaces

Some interfaces 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, Eq, and Swappable. This is already a capability for facet types in general. For consistency we use the same semantics and require Self impls syntax as we do for named constraints:

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

interface Iterable {
  fn Advance[addr self: Self*]() -> bool;
  require Self impls Equatable;
}

fn 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 {
  extend impl as Iterable { fn Advance[self: Self]() { ... } }
  extend impl as Equatable { fn Equals[self: 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[self: Self]() -> u64;
  require Self impls Equatable;
  alias Equals = Equatable.Equals;
}

fn 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 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 {
  extend impl as Hashable {
    fn Hash[self: Self]() -> u64 { ... }
    fn Equals[self: 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 interface syntax:

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

interface Hashable {
  extend Equatable;
  fn Hash[self: Self]() -> u64;
}
// is equivalent to the definition of Hashable from before:
// interface Hashable {
//   require Self impls Equatable;
//   alias Equals = Equatable.Equals;
//   fn Hash[self: 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 extend 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 {
  extend Equatable;
  extend ExpressibleByArrayLiteral;
}

Alternative considered: The extend declarations are in the body of the interface definition instead of the header so we can use associated constants 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 AssociatedFacet:! type;
  // `extend` is in the body of an `interface`
  // definition. This allows extending an expression
  // that uses an associated facet.
  extend ConvertibleTo(AssociatedFacet);
}

extend and impl with named constraints

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

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

constraint Combined {
  extend Media;
  extend Job;
}

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

// Equivalent
constraint Combined {
  require Self impls Media;
  alias Play = Media.Play;
  require Self impls 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 {
  extend impl as Combined {
    fn Play[self: Self]() { ... }
    fn Run[self: Self]() { ... }
  }
}

This is equivalent to implementing the required interfaces directly:

class Song {
  extend impl as Media {
    fn Play[self: Self]() { ... }
  }
  extend impl as Job {
    fn Run[self: 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 {
  extend Combined;

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

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

interface MovieCodec {
  require Self impls Media;
  alias Play = Media.Play;
  require Self impls Job;
  alias Run = Job.Run;

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

Diamond dependency issue

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

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

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

interface EdgeListGraph {
  extend Graph;
  fn Edges[addr self: 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 {
  extend impl as IncidenceGraph { ... }
  extend 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 {
  extend impl as IncidenceGraph {
    fn Source[self: Self](e: EdgeDescriptor) -> VertexDescriptor { ... }
    fn Target[self: Self](e: EdgeDescriptor) -> VertexDescriptor { ... }
    fn OutEdges[addr self: Self*](u: VertexDescriptor)
        -> (EdgeIterator, EdgeIterator) { ... }
  }
  extend impl as EdgeListGraph {
    fn Edges[addr self: Self*]() -> (EdgeIterator, EdgeIterator) { ... }
  }
}

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

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

  • Explicitly implementing Graph.

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

  • Implementing Graph out-of-line.

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

If interface E extends another interface I, that gives the information to the compiler that the any type implementing E also implements I. This can be used to detect unreachable code.

For example, the impl prioritization rule is used to pick between impl declarations based on an explicit priority ordering given by the developer. If the broader interface I is prioritized over the more specific interface E, the compiler can conclude that the more specific declaration will never be selected and report an error. Similar situations could be detected in function overloading.

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[self: Self]();
}
interface Ordered {
  fn Less[self: Self](rhs: Self) -> bool;
}
class Song {
  extend impl as Printable { fn Print[self: Self]() { ... } }
}
class SongByTitle {
  adapt Song;
  extend impl as Ordered {
    fn Less[self: Self](rhs: Self) -> bool { ... }
  }
}
class FormattedSong {
  adapt Song;
  extend impl as Printable { fn Print[self: Self]() { ... } }
}
class FormattedSongByTitle {
  adapt Song;
  extend impl as Printable = FormattedSong;
  extend impl as Ordered = 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 specific implementations of virtual functions are part of the type representation, and so no virtual functions may be overridden in an adapter either.
  • 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:

class SongByTitle {
  adapt Song;
  extend impl as Ordered {
    fn Less[self: Self](rhs: Self) -> bool {
      return (self as Song).Title() < (rhs as Song).Title();
    }
  }
}

or using a qualified member access expression:

class SongByTitle {
  adapt Song;
  extend impl as Ordered {
    fn Less[self: Self](rhs: Self) -> bool {
      return self.(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 facet parameter, like a hash map:

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

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

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

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

Since the KeyT and ValueT are symbolic parameters, the Find function is a checked generic, and it can only use the capabilities of KeyT and ValueT specified as requirements. 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:

class PlayableSong {
  adapt Song;
  extend impl as Hashable = Song;
  extend impl as Media { ... }
}
class SongHashedByTitle {
  adapt Song;
  extend 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 extend keyword before adapt:

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

class SongByArtist {
  extend adapt Song;

  // Add an implementation of a new interface
  extend impl as Ordered { ... }

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

The resulting type SongByArtist would:

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

The rule is that when looking up if SongByArtist implements an interface I and no implementation is found, the compiler repeats the search to see if Song implements I. If that is found, it is reused if possible. The reuse will be successful if all types that reference Self in the signatures of interface's functions can be cast to the corresponding type with SongByArtist substituted in for Song.

Unlike the similar class B { extend base: A; } notation, class B { extend adapt A; } is permitted even if A is a final class. Also, there is no implicit conversion from B to A, matching adapt without extend but unlike class extension.

To avoid or resolve name conflicts between interfaces, an impl may be declared without extend. The names in that interface may then be pulled in individually or renamed using alias declarations.

class SongRenderToPrintDriver {
  extend adapt Song;

  // Add a new `Print()` member function.
  fn Print[self: Self]() { ... }

  // Avoid name conflict with new `Print`
  // function by implementing the `Printable`
  // interface without `extend`.
  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 checked-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 extend facility of adapters to preserve the SongLib.Song API.

import CompareLib;
import SongLib;

class Song {
  extend adapt SongLib.Song;
  extend impl as CompareLib.Comparable { ... }
}
// Or, to keep the names from CompareLib.Comparable out of Song's API:
class Song {
  extend adapt SongLib.Song;
}
impl Song as CompareLib.Comparable { ... }
// Or, equivalently:
class Song {
  extend adapt SongLib.Song;
  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[self: Self](rhs: Self) -> bool;
}

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

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

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

class ComparableFromDifferenceFn
    (T:! type, Difference:! fnty(T, T)->i32) {
  adapt T;
  extend impl as Comparable {
    fn Less[self: Self](rhs: Self) -> bool {
      return Difference(self as T, rhs as T) < 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 self parameter to the adapter type when it wants to make use of the private impl.

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

// Private

class ByReal {
  extend adapt Complex64;

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

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

Use case: Accessing interface names

Consider a case where a function will call several functions from an interface that the type does not extend the implementation of.

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

An adapter can make that more convenient by making a compatible type that does extend the implementation of the interface. This avoids having to qualify each call to methods in the interface.

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

Note: Another way to achieve this is to use a local symbolic facet constant.

fn Render(w: Window) {
  let DrawInWindow:! Draw = Window;
  // Implicit conversion to `w as DrawInWindow`.
  let d: DrawInWindow = w;
  d.SetPen(...);
  d.SetFill(...);
  d.DrawRectangle(...);
  ...
}

Future work: 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. One possibility would be to add the keyword private before adapt, so you might write extend private adapt Date;.

Associated constants

In addition to associated methods, we allow other kinds of associated entities. For consistency, we use the same syntax to describe a compile-time 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 self: Self*](i: i32) -> f64;
  fn Set[addr self: Self*](i: i32, value: f64);
  // Associated constants may be used in signatures:
  fn SetAll[addr self: 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 {
  extend impl as NSpacePoint where .N = 2 {
    fn Get[addr self: Self*](i: i32) -> f64 { ... }
    fn Set[addr self: Self*](i: i32, value: f64) { ... }
    fn SetAll[addr self: Self*](value: Array(f64, 2)) { ... }
  }
}

class Point3D {
  extend impl as NSpacePoint where .N = 3 {
    fn Get[addr self: Self*](i: i32) -> f64 { ... }
    fn Set[addr self: Self*](i: i32, value: f64) { ... }
    fn SetAll[addr self: 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) {
  var i: i32 = 0
  while (i < PointT.N) {
    if (i > 0) { Print(", "); }
    Print(p.Get(i));
    ++i;
  }
}

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

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

Aside: 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;

  extend 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 facets

Associated facets are associated constants that happen to have a facet type. 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 facet constant under a specified name. For example:

interface StackAssociatedFacet {
  let ElementType:! type;
  fn Push[addr self: Self*](value: ElementType);
  fn Pop[addr self: Self*]() -> ElementType;
  fn IsEmpty[addr self: Self*]() -> bool;
}

Here we have an interface called StackAssociatedFacet 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 StackAssociatedFacet must also define. For example, maybe a DynamicArray parameterized type implements StackAssociatedFacet:

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

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

The keyword Self can be used after the as in an impl declaration as a shorthand for the type being implemented, including in the where clause specifying the values of associated facets, as in:

impl VeryLongTypeName as Add
    // `Self` here means `VeryLongTypeName`
    where .Result = Self {
  ...
}

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

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

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

Inside the checked-generic function PeekAtTopOfStack, the ElementType associated facet member of StackType is an archetype, like other symbolic facet bindings. This means StackType.ElementType has the API dictated by the declaration of ElementType in the interface StackAssociatedFacet.

Outside the checked-generic, associated facets have the concrete facet values determined by impl lookup, rather than the erased version of that facet used inside a checked-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 facets can also be implemented using a member type.

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

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

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

Comparison with other languages: Both Rust and Swift support these, but call them "associated types."

Parameterized interfaces

Associated constants 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, also known as generic interfaces. To write a parameterized version of the stack interface, instead of using associated constants, write a parameter list after the name of the interface:

interface StackParameterized(ElementType:! type) {
  fn Push[addr self: Self*](value: ElementType);
  fn Pop[addr self: Self*]() -> ElementType;
  fn IsEmpty[addr self: 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);
  extend impl as StackParameterized(Fruit) {
    fn Push[addr self: Self*](value: Fruit) {
      self->fruit.Push(value);
    }
    fn Pop[addr self: Self*]() -> Fruit {
      return self->fruit.Pop();
    }
    fn IsEmpty[addr self: Self*]() -> bool {
      return self->fruit.IsEmpty();
    }
  }
  extend impl as StackParameterized(Veggie) {
    fn Push[addr self: Self*](value: Veggie) {
      self->veggie.Push(value);
    }
    fn Pop[addr self: Self*]() -> Veggie {
      return self->veggie.Pop();
    }
    fn IsEmpty[addr self: Self*]() -> bool {
      return self->veggie.IsEmpty();
    }
  }
}

Unlike associated constants 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 facets" 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*. Either T should be replaced by a concrete type, like Fruit:

fn PeekAtTopOfFruitStack
    [StackType:! StackParameterized(Fruit)]
    (s: StackType*) -> T { ... }

var produce: Produce = ...;
var top_fruit: Fruit =
    PeekAtTopOfFruitStack(&produce);

Or the value for T would be passed explicitly, using where constraints described in this section:

fn PeekAtTopOfStackParameterizedImpl
    (T:! type, StackType:! StackParameterized(T), s: StackType*) -> T {
  ...
}
fn PeekAtTopOfStackParameterized[StackType:! type]
    (s: StackType*, T:! type where StackType impls StackParameterized(T)) -> T {
  return PeekAtTopOfStackParameterizedImpl(T, StackType, s);
}

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

Note: Alternative ways of declaraing PeekAtTopOfStackParameterized are described and discussed in #578: Value patterns as function parameters.

Parameterized interfaces are useful for operator overloads. For example, the EqWith(T) and OrderedWith(T) interfaces have a parameter that allows type to be comparable with multiple other types, as in:

interface EqWith(T:! type) {
  fn Equal[self: 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.
  extend impl as EqWith(f64) { ... }
  // Same as: impl as EqWith(Complex) { ... }
  extend impl as EqWith(Self) { ... }
}

All interface parameters must be marked as "symbolic", using the :! binding pattern 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 symbolic or template values to be passed in.

Future work: We might also allow template bindings for interface parameters, once we have a use case.

Note: Interface parameters aren't required to be facets, 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 self[index]
  fn Get[self: Self]() -> T;
}

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

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 self: Self*](needle: FromType) -> Optional(ToType);
}
class Bijection(FromType:! type, ToType:! type) {
  extend impl as Map(FromType, ToType) { ... }
  extend impl as Map(ToType, FromType) { ... }
}
// ❌ Error: Bijection has two different impl definitions 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) {
  extend impl as Map(FromType, ToType) { ... }
}
class ReverseLookup(FromType:! type, ToType:! type) {
  adapt Bijection(FromType, ToType);
  extend impl as Map(ToType, FromType) { ... }
}

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

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

Parameterized named constraints

Carbon also allows the named constraint construct to support parameters. Those parameters work the same way as for interfaces.

Where constraints

So far, we have restricted a symbolic facet binding 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 associated constants. This is done using the where operator that adds constraints to a facet type.

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

// Constraints on generic 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[self: Self, V:! D where ...](v: V);
}

// Constraints on an interface parameter:
interface A(T:! B where ...) {
  // Constraints on an associated facet:
  let U:! C where ...;
  // Constraints on an associated method:
  fn G[self: 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 "kinds of where constraints" section, but generally look like boolean expressions that should evaluate to true.

The result of applying a where operator to a facet type is another facet type. Note that this expands the kinds of requirements that facet 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 a member of another. The where operator is not associative, so a type expression using multiple must use round parens (...) to specify grouping.

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.

References: where constraints were added in proposal #818: Constraints for generics (generics details 3).

Kinds of where constraints

There are three kinds of where constraints, each of which uses a different binary operator:

  • Rewrite constraints: where...=...
  • Same-type constraints: where...==...
  • Implements constraints: where...impls...

And there are two positions that where can be written:

  • At the end of an impl as declaration, before the body of the impl. 
    impl Class as Interface where .A = i32 { ... }
  • Inside a type expression. 
    fn F[T: Interface where .A impls OtherInterface](t: T) { ... }

A rewrite constraint is written where .A = B, where A is the name of an associated constant which is rewritten to B. Any use of .A thereafter is the same as using B, including direct access to the API of B.

The "dot followed by the name of a member" construct, like .A, is called a designator. The name of the designator is looked up in the constraint, and refers to the value of that member for whatever type is to satisfy this constraint.

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 same-type constraint is written where X == Y, where X and Y both name facets. The constraint is that X as type must be the same as Y as type. It would normally only be used in the type expression position.

A same-type constraint does not rewrite the type on the left-hand side to the right-hand side, and they are still treated as distinct types. A value of type X would need to be cast to Y in order to use the API of Y. So for constraint clauses that name a single facet type on the right-hand side, using a rewrite constraint is preferred. Note that switching between the two forms does not change which types satisfies the constraint, and so is a compatible change for callers.

An implements constraint is written where T impls C, where T is a facet and C is a facet type. The constraint is that T satisfies the requirements of C. It would normally only be used in the type expression position.

References: The definition of rewrite and same-type constraints were in proposal #2173. Implements constraints switched to using the impls keyword in proposal #2483.

Alternatives considered:

Recursive constraints

We sometimes need to constrain a type to equal one of its associated facets. 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 facet MagnitudeType to encode the return type:

interface HasAbs {
  extend Numeric;
  let MagnitudeType:! Numeric;
  fn Abs[self: 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() function 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 facet member of every interface. We can then address it using .Self in a where clause, like any other associated facet 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 facet currently being defined.

interface Container;
constraint SliceConstraint(E:! type, S:! Container);

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

  // `.Self` means `SliceType`.
  let SliceType:! Container where .Self impls SliceConstraint(ElementType, .Self);

  // `Self` means the type implementing `Container`.
  fn GetSlice[addr self: Self*]
      (start: IteratorType, end: IteratorType) -> SliceType;
}

constraint SliceConstraint(E:! type, S:! Container) {
  extend Container where .ElementType = E and
                         .SliceType = S;
}

Note that naming a recursive constraint using the constraint introducer approach, we can name the implementing type using Self instead of .Self, since they refer to the same type. Note though they are different facets with different facet types:

constraint RealAbs {
  extend HasAbs where .MagnitudeType = Self;
  // Satisfied by the same types:
  extend HasAbs where .MagnitudeType = .Self;

  // While `Self as type` is the same as `.Self as type`,
  // they are different as facets: `Self` has type
  // `RealAbs` and `.Self` has type `HasAbs`.
}

constraint ContainerIsSlice {
  extend Container where .SliceType = Self;
  // Satisfied by the same types:
  extend Container where .SliceType = .Self;

  // `Self` has type `ContainerIsSlice` and
  // `.Self` has type `Container`.
}

The .Self construct follows these rules:

  • X :! introduces .Self:! type, where references to .Self are resolved to X. This allows you to use .Self as an interface parameter as in X:! I(.Self).
  • A where introduces .Self:! A and a .Foo designator for each member Foo of A.
  • It's an error to reference .Self if it refers to more than one different thing or isn't a facet.
  • You get the innermost, most-specific type for .Self if it is introduced twice in a scope. By the previous rule, it is only legal if they all refer to the same facet binding.
  • .Self may not be on the left side of the = in a rewrite constraint.

So in X:! A where ..., .Self is introduced twice, after the :! and the where. This is allowed since both times it means X. After the :!, .Self has the type type, which gets refined to A after the where. In contrast, it is an error if .Self could mean two different things, as in:

// ❌ Illegal: `.Self` could mean `T` or `T.A`.
fn F[T:! InterfaceA where .A impls
           (InterfaceB where .B = .Self)](x: T);

These two meanings can be disambiguated by defining a constraint:

constraint InterfaceBWithSelf {
  extend InterfaceB where .B = Self;
}
constraint InterfaceBWith(U:! InterfaceA) {
  extend InterfaceB where .B = U;
}
// `T.A impls InterfaceB where .B = T.A`
fn F[T:! InterfaceA where .A impls InterfaceBWithSelf](x: T);
// `T.A impls InterfaceB where .B = T`
fn F[T:! InterfaceA where .A impls InterfaceBWith(.Self)](x: T);

Rewrite constraints

In a rewrite constraint, the left-hand operand of = must be a . followed by the name of an associated constant. .Self is not permitted.

interface RewriteSelf {
  // ❌ Error: `.Self` is not the name of an associated constant.
  let Me:! type where .Self = Self;
}
interface HasAssoc {
  let Assoc:! type;
}
interface RewriteSingleLevel {
  // ✅ Uses of `A.Assoc` will be rewritten to `i32`.
  let A:! HasAssoc where .Assoc = i32;
}
interface RewriteMultiLevel {
  // ❌ Error: Only one level of associated constant is permitted.
  let B:! RewriteSingleLevel where .A.Assoc = i32;
}

This notation is permitted anywhere a constraint can be written, and results in a new constraint with a different interface: the named member effectively no longer names an associated constant of the constrained type, and is instead treated as a rewrite rule that expands to the right-hand side of the constraint, with any mentioned parameters substituted into that type.

interface Container {
  let Element:! type;
  let Slice:! Container where .Element = Element;
  fn Add[addr self: Self*](x: Element);
}
// `T.Slice.Element` rewritten to `T.Element`
//     because type of `T.Slice` says `.Element = Element`.
// `T.Element` rewritten to `i32`
//     because type of `T` says `.Element = i32`.
fn Add[T:! Container where .Element = i32](p: T*, y: T.Slice.Element) {
  // ✅ Argument `y` has the same type `i32` as parameter `x` of
  // `T.(Container.Add)`, which is also rewritten to `i32`.
  p->Add(y);
}

Rewrites aren't performed on the left-hand side of such an =, so where .A = .B and .A = C is not rewritten to where .A = .B and .B = C. Instead, such a where clause is invalid when the constraint is resolved unless each rule for .A specifies the same rewrite.

Note that T:! C where .R = i32 can result in a type T.R whose behavior is different from the behavior of T.R given T:! C. For example, member lookup into T.R can find different results and operations can therefore have different behavior. However, this does not violate coherence because the facet types C and C where .R = i32 don't differ by merely having more type information; rather, they are different facet types that have an isomorphic set of values, somewhat like i32 and u32. An = constraint is not merely learning a new fact about a type, it is requesting different behavior.

This approach has some good properties that same-type constraints have problems with:

The precise rules governing rewrite constraints are described in an appendix.

Same-type constraints

A same-type constraint describes that two type expressions are known to evaluate to the same value. Unlike a rewrite constraint, however, the two type expressions are treated as distinct types when type-checking a symbolic expression that refers to them.

Same-type constraints are brought into scope, looked up, and resolved exactly as if there were a SameAs(U:! type) interface and a T == U impl corresponded to T is SameAs(U), except that == is commutative.

Further, same-type equalities apply to type components, so that X(A, B, C) is SameType(X(D, E, F)) if we know that A == D, B == E, and C == F. Stated differently, if F is any pure type function, T impls SameAs(U) implies F(T) impls SameAs(F(U)). For example, if we know that T == i32 then we also have Vector(T) is single-step equal to Vector(i32).

This relationship is not transitive, though, so it's not possible to ask for a list of types that are the same as a given type, nor to ask whether there exists a type that is the same as a given type and has some property. But it is possible to ask whether two types are (non-transitively) known to be the same.

In order for same-type constraints to be useful, they must allow the two types to be treated as actually being the same in some context. This can be accomplished by the use of == constraints in an impl, such as in the built-in implementation of ImplicitAs:

final impl forall [T:! type, U:! type where .Self == T] T as ImplicitAs(U) {
  fn Convert[self: Self](other: U) -> U { ... }
}

Alternative considered: It superficially seems like it would be convenient if such implementations were made available implicitly –- for example, by writing impl forall [T:! type] T as ImplicitAs(T) -– but in more complex examples that turns out to be problematic. Consider:

interface CommonTypeWith(U:! type) {
  let Result:! type;
}
final impl forall [T:! type] T as CommonTypeWith(T) where .Result = T {}

fn F[T:! Potato, U:! Hashable where .Self == T](x: T, y: U) -> auto {
  // What is T.CommonTypeWith(U).Result? Is it T or U?
 return (if cond then x else y).Hash();
}

With this alternative, impl validation for T as CommonTypeWith(U) fails: we cannot pick a common type when given two distinct type expressions, even if we know they evaluate to the same type, because we would not know which API the result should have.

Implementation of same-type ImplicitAs

It is possible to implement the above impl of ImplicitAs directly in Carbon, without a compiler builtin, by taking advantage of the built-in conversion between C where .A = X and C where .A == X:

interface EqualConverter {
  let T:! type;
  fn Convert(t: T) -> Self;
}
fn EqualConvert[T:! type](t: T, U:! EqualConverter where .T = T) -> U {
  return U.Convert(t);
}
impl forall [U:! type] U as EqualConverter where .T = U {
  fn Convert(u: U) -> U { return u; }
}

impl forall [T:! type, U:! type where .Self == T] T as ImplicitAs(U) {
  fn Convert[self: Self]() -> U { return EqualConvert(self, U); }
}

The transition from (T as ImplicitAs(U)).Convert, where we know that U == T, to EqualConverter.Convert, where we know that .T = U, allows a same-type constraint to be used to perform a rewrite.

Manual type equality

A same-type constraint establishes type expressions are equal, and allows implicit conversions between them. However, determining whether two type expressions are transitively equal is in general undecidable, as has been shown in Swift.

Carbon does not combine these equalities between type expressions. 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 facets that are constrained to all be equal, with interfaces P, Q, and R:

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

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

  fn GetA[self: Self]() -> A;
  fn TakesC[self: 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());
}

The compiler may have several different where clauses to consider, particularly when an interface has associated facets that recursively satisfy the same interface, or mutual recursion between multiple interfaces. For example, given these Edge and Node interfaces (similar to those defined in the section on interfaces with cyclic references, but using == same-type constraints):

interface Edge;
interface Node;

private constraint EdgeFor(NodeT:! Node);
private constraint NodeFor(EdgeT:! Edge);

interface Edge {
  let N:! NodeFor(Self);
  fn GetN[self: Self]() -> N;
}
interface Node {
  let E:! EdgeFor(Self);
  fn GetE[self: Self]() -> E;
  fn AddE[addr self: Self*](e: E);
  fn NearN[self: Self](n: Self) -> bool;
}

constraint EdgeFor(NodeT:! Node) {
  extend Edge where .N == NodeT;
}
constraint NodeFor(EdgeT:! Edge) {
  extend Node where .E == EdgeT;
}

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

fn H[N:! Node](n: N) {
  // ✅ Legal: argument has type `N.E`, matches parameter
  n.AddE(n.GetE());

  // ✅ Legal:
  // - argument has type `N.E.N`
  // - `N.E` has type `EdgeFor(Self)` where `Self`
  //   is `N`, which means `Edge where .N == N`
  // - so we have the constraint `N.E.N == N`
  // - which means the argument type `N.E.N`
  //   is equal to the parameter type `N` using a
  //   single `==` constraint.
  n.NearN(n.GetE().GetN());

  // ✅ Legal:
  // - type `N.E.N.E.N` may be cast to `N.E.N`
  //   using a single `where ==` clause, either
  //   `(N.E.N).E.N == (N).E.N` or
  //   `N.E.(N.E.N) == N.E.(N)`
  // - argument of type `N.E.N` may be passed to
  //   function expecting `N`, using a single
  //   `where ==` clause, as in the previous call.
  n.NearN(n.GetE().GetN().GetE().GetN() as N.E.N);
}

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

Same-type constraints are non-transitive, just like ImplicitAs. The developer can use an observe declaration to bring a new same-type constraint into scope:

observe A == B == C;

notionally does much the same thing as

impl A as SameAs(C) { ... }

where the impl makes use of A impls SameAs(B) and B impls SameAs(C).

In general, 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 Edge {
  let N:! type;
}
interface Node {
  let E:! type;
}
interface Graph {
  let E:! Edge;
  let N:! Node where .E == E and E.N == .Self;
  observe E == N.E == E.N.E == N.E.N.E;
  // ...
}

fn H[G: Graph](g: G) {
  observe G.N == G.E.N == G.N.E.N == G.E.N.E.N;
  // ...
}

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,

fn J[G: Graph](g: G) {
  observe G.E.N == G.N.E.N == G.N == G.E.N.E.N;
  // ...
}

the expression G.E.N.E.N is one equality away from G.N.E.N and so it is allowed. This is true even though G.N.E.N isn't the type expression immediately prior to G.E.N.E.N.

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 facets A and C that allows function F to type check.

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

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

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

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

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

  // ✅ Allowed: `T.A` values implicitly convert to
  // `T.C` using `observe` in interface definition.
  t.TakesC(a);

  // ✅ Allowed: `T.C` extends and implements `R`.
  (a as T.C).InR();
}

Only the current type is searched for interface implementations, so the call to InR() would be illegal without the cast. However, an observe...==...impls declaration can be used to identify interfaces that must be implemented through some equal type. This does not extend the API of the type, that is solely determined by the definition of the type. Continuing the previous example:

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` and
  // includes its API, as if it extends `P`.
  a.InP();

  // ❌ Illegal: only the current type is
  // searched for interface implementations.
  a.(Q.InQ());

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

  // ✅ Allowed: `T.A` == `T.B` that implements `Q`.
  observe T.A == T.B impls Q;
  a.(Q.InQ());

  // ❌ Illegal: `T.A` still does not extend `Q`.
  a.InQ();

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

Since adding an observe...impls declaration only adds non-extending implementations of interfaces to symbolic facets, they may be added without breaking existing code.

Implements constraints

An implements constraint is written where T impls C, and expresses that the facet T must implement the requirements of facet type C. This is more flexible than using & to add a constraint since it can be applied to associated facet members as well.

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 Ordered interface, using an impls constraint:

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

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

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

The specific case of a clause of the form where .AssociatedFacet impls AConstraint, where the constraint is applied to a direct associated facet member of the facet type being constrained (similar to the restriction on rewrite constraints), gets special treatment. In this case, the type of the associated facet is combined with the constraint. In the above example, Container defines ElementType as having type type, but ContainerType.ElementType has type type & Ordered (which is equivalent to Ordered). This is because ContainerType has type Container where .ElementType impls Ordered, 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.

Future work: We may want to use a different operator in this case, such as &=, in place of impls, to reflect the change in the type. This is analogous to rewrite constraints using = instead of == to visibly reflect the different impact on the type.

An implements constraint can be applied to .Self, as in I where .Self impls C. This has the same requirements as I & C, but that where clause does not affect the API. This means that a symbolic facet binding with that facet type, so T in T:! I where .Self impls C, is represented by an archetype that implements both I and C, but only extends I.

Implied constraints

Imagine we have a checked-generic function that accepts an arbitrary HashMap parameterized type:

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

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

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

class HashMap(
    KeyT:! Hashable & Eq & Movable,
    ...) { ... }

In this case, KeyT gets Hashable and so on as implied constraints. Effectively that means that these functions are automatically rewritten to add a where .Self impls constraint on KeyT:

fn LookUp[
    KeyT:! type
        where .Self impls Hashable & Eq & Movable]
    (hm: HashMap(KeyT, i32)*, k: KeyT) -> i32;

fn PrintValueOrDefault[
    KeyT:! Printable
        where .Self impls Hashable & Eq & Movable,
    ValueT:! Printable & HasDefault]
    (map: HashMap(KeyT, ValueT), key: KeyT);

In this case, Carbon will accept the definition and infer the needed constraints on the symbolic facet 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 symbolic facet 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[self: 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 facet. 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).

Combining constraints

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

fn EqualContainers
    [CT1:! Container,
     CT2:! Container where .ElementType impls 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.

Satisfying both facet types

If the two facet bindings being constrained to be equal, using either a rewrite constraint or a same-type constraint, have been declared with different facet types, then the actual type value they are set to will have to satisfy the requirements of both facet types. For example, if SortedContainer.ElementType is declared to have a Ordered requirement, then in these declarations:

// With `=` rewrite constraint:
fn Contains_Rewrite
    [SC:! SortedContainer,
     CT:! Container where .ElementType = SC.ElementType]
    (haystack: SC, needles: CT) -> bool;

// With `==` same-type constraint:
fn Contains_SameType
    [SC:! SortedContainer,
     CT:! Container where .ElementType == SC.ElementType]
    (haystack: SC, needles: CT) -> bool;

the where constraints in both cases mean CT.ElementType must satisfy Ordered as well. However, the behavior inside the body of these two inside the body of the two functions is different.

In Contains_Rewrite, CT.ElementType is rewritten to SC.ElementType and uses the facet type of SC.ElementType.

In Contains_SameType, the where clause does not affect the API of CT.ElementType, and it would not even be considered to implement Ordered unless there is some declaration like observe CT.ElementType == SC.ElementType impls Ordered. Even then, the items from the needles container won't directly have a Compare method member.

The rule is that a same-type where constraint between two type variables does not modify the set of member names of either type. This is in contrast to rewrite constraints like where .ElementType = String with a =, then .ElementType is actually set to String including the complete String API.

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

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

Constraints must use a designator

We don't allow a where constraint unless it applies a restriction to the current type. This means referring to some designator, like .MemberName, or .Self. Examples:

  • Container where .ElementType = i32
  • type where Vector(.Self) impls Sortable
  • Addable where i32 impls AddableWith(.Result)

Constraints that only refer to other types should be moved to the type that is declared last. So:

// ❌ Error: `where A == B` does not use `.Self` or a designator
fn F[A:! type, B:! type, C:! type where A == B](a: A, b: B, c: C);

must be replaced by:

// ✅ Allowed
fn F[A:! type, B:! type where A == .Self, C:! type](a: A, b: B, c: C);

This includes where clauses used in an impl declaration:

// ❌ Error: `where T impls B` does not use `.Self` or a designator
impl forall [T:! type] T as A where T impls B {}
// ✅ Allowed
impl forall [T:! type where .Self impls B] T as A {}
// ✅ Allowed
impl forall [T:! B] T as A {}

This clarifies the meaning of the where clause and reduces the number of redundant ways to express a restriction, following the one-way principle.

Alternative considered: This rule was added in proposal #2376, which considered whether this rule should be added.

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:

// ❌ Illegal: `E` references `V` declared later.
interface Graph {
  let E: Edge where .V = V;
  let V: Vert where .E = E;
}

// ✅ Allowed: Only references to earlier names.
interface Graph {
  let E: Edge;
  let V: Vert where .E = E and .Self == E.V;
}

Constraint examples and use cases

  • Set associated constant to a constant: For example in NSpacePoint where .N = 2, the associated constant N of NSpacePoint must be 2. This syntax is also used to specify the values of associated constants when implementing an interface for a type, as in impl MyPoint as NSpacePoint where .N = 2 {...}.

  • Set an associated facet to a specific value: Associated facets are treated like any other associated constant. So Stack where .ElementType = i32 is a facet type that restricts to types that implement the Stack interface with integer elements, as in:

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

    Note that this is a case that can use an == same-type constraint instead of an = rewrite constraint.

  • One associated constant must equal another: For example with this definition of the interface PointCloud:

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

    an implementation of PointCloud for a type T will have T.PointT.N == T.Dim.

  • Equal facet bindings:

    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;
  ...
}

    In a function signature, this may be done by referencing an earlier parameter:

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

    In that example, FT.InputType is constrained to equal CT.InputType. Given an interface with two associated facets

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

    we can constrain them to be equal using PairInterface where .Left = .Right.

    Note that this is a case that can use an == same-type constraint instead of an = rewrite constraint.

  • Associated facet implements interface: Given these definitions (omitting ElementType for brevity):

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

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

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

Parameterized type implements interface

There are times when a function will pass a symbolic facet parameter of the function as an argument to a parameterized type, and the function needs the result to implement a specific interface.

// A parameterized type
class DynArray(T:! type) { ... }

interface Printable { fn Print[self: Self](); }

// The parameterized type `DynArray` implements interface
// `Printable` only for some arguments.
impl DynArray(String) as Printable { ... }

// Constraint: `T` such that `DynArray(T)` implements `Printable`
fn PrintThree
    [T:! type where DynArray(.Self) impls Printable]
    (a: T, b: T, c: T) {
  // Create a `DynArray(T)` of size 3.
  var v: auto = DynArray(T).Make(a, b, c);
  // Known to be implemented due to the constraint on `T`.
  v.(Printable.Print)();
}

// ✅ Allowed: `DynArray(String)` implements `Printable`.
let s: String = "Ai ";
PrintThree(s, s, s);
// ❌ Forbidden: `DynArray(i32)` doesn't implement `Printable`.
let i: i32 = 3;
PrintThree(i, i, i);

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 symbolic facet parameter. The syntax for this case follows the previous case, except now the .Self parameter is on the interface to the right of the impls. For example, we might need a type parameter T to support explicit conversion from an i32:

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

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

Must be legal type argument constraints

Now consider the case that the symbolic facet parameter is going to be used as an argument to a parameterized type in a function body, but 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. To say a parameterized type is allowed to be passed a specific argument, just write that it impls type, which all types do. This is a trivial case of a parameterized type implements interface where constraint.

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) impls 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 other implied constraints.

Named constraint constants

A facet type with a where constraint, such as C where <condition>, can be named two different ways:

  • Using let template as in:

    let template NameOfConstraint:! auto = C where <condition>;

    or, since the type of a facet type is type:

    let template NameOfConstraint:! type = C where <condition>;

  • Using a named constraint with the constraint keyword introducer:

    constraint NameOfConstraint {
  extend C where <condition>;
}

Whichever approach is used, the result is NameOfConstraint is a compile-time constant that is equivalent to C where <condition>.

Other constraints as facet types

There are some constraints that Carbon naturally represents as named facet types. These can either be used directly to constrain a facet binding, or in a where ... impls ... implements constraint to constrain an associated facet.

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

These facet types extend the requirements that facet types are allowed to include beyond interfaces implemented and where clauses.

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 facet type whose values are facets that are (transitively) derived from T. That is, U:! Extends(T) means U has an extend base: T; declaration, or there is a chain of extend base declarations connecting T to U.

base class BaseType { ... }

fn F[T:! Extends(BaseType)](p: T*);
fn UpCast[U:! type]
    (p: U*, V:! type where U impls Extends(.Self)) -> V*;
fn DownCast[X:! type](p: X*, Y:! Extends(X)) -> Y*;

class DerivedType {
  extend base: BaseType;
}
var d: DerivedType = {};
// `T` is set to `DerivedType`
// `DerivedType impls Extends(BaseType)`
F(&d);

// `U` is set to `DerivedType`
let p: BaseType* = UpCast(&d, BaseType);

// `X` is set to `BaseType`
// `Y` is set to facet `DerivedType as Extends(BaseType)`.
Assert(DownCast(p, DerivedType) == &d);

Open question: Alternatively, we could define a new extends operator for use in where clauses:

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 facet type CompatibleWith(U) as follows:

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

CompatibleWith determines an equivalence relationship between types. Specifically, given two types T1 and T2, they are equivalent if T1 impls CompatibleWith(T2), which is true if and only if T2 impls CompatibleWith(T1).

Note: Just like interface parameters, we require the user to supply U, it 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 facet type CompatibleWith(U, C) are facets satisfying CompatibleWith(U) that have the same implementation of C 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 impls CompatibleWith(U, Hashable). The one-parameter interpretation of CompatibleWith(U) is recovered by letting the default for the second parameter (C) 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.

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

Used as:

class Song { ... }
class SongByArtist { adapt Song; impl as Ordered { ... } }
class SongByTitle { adapt Song; impl as Ordered { ... } }
let s1: Song = ...;
let s2: Song = ...;
assert(CombinedLess(s1, s2, SongByArtist, SongByTitle) == True);

Open question: We might generalize this to a list of implementations using variadics:

fn CombinedCompare[T:! type]
    (a: T, b: T, ... each CompareT:! CompatibleWith(T) & Ordered)
    -> CompareResult {
  ... block {
    let result: CompareResult =
        (a as each CompareT).Compare(b as each CompareT);
    if (result != CompareResult.Equal) {
      return result;
    }
  }
  return CompareResult.Equal;
}

assert(CombinedCompare(s1, s2, SongByArtist, SongByTitle)
       == CompareResult.Less);

However, variadic support is still future work.

Example: Creating an impl out of other implementations

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

class ThenCompare(
      T:! type,
      ... each CompareT:! CompatibleWith(T) & Ordered) {
  adapt T;
  extend impl as Ordered {
    fn Compare[self: Self](rhs: Self) -> CompareResult {
      ... block {
        let result: CompareResult =
            (self as each CompareT).Compare(rhs as each CompareT);
        if (result != CompareResult.Equal) {
          return result;
        }
      }
      return CompareResult.Equal;
    }
  }
}

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

Sized types and facet 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 symbolically. 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 facet 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 symbolically

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.

Example:

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

// Classes are "sized" by default.
class Name {
  extend 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 symbolically.
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: Should the Sized facet type expose an associated constant with the size? So you could say T.ByteSize in the above example to get a symbolic integer 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.

Destructor constraints

There are four facet 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 facet 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 facet types Concrete, Deletable, and TrivialDestructor all extend Destructible. Combinations of them may be formed using the & operator. For example, a checked-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 facet types directly. Instead they use destructor declarations in their class definition and the compiler uses them to determine which of these facet types are implemented.

Compile-time let

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

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

This introduces a symbolic constant T with type C and value U. This implicitly includes an observe T == U; declaration, when T and U are facets, which allows values to implicitly convert from the concrete type U to the erased type T, as in:

let x: i32 = 7;
let T:! Add = i32;
// ✅ Allowed to convert `i32` values to `T`.
let y: T = x;

TODO: The implied observe declaration is from question-for-leads issue #996 and should be approved in a proposal.

This makes the SymbolicLet function roughly equivalent to:

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

The where .Self == U modifier captures the observe declaration introduced by the let (at the cost of changing the type of T).

A symbolic let can be used to switch to the API of C when U does not extend C, as an alternative to using an adapter, or to simplify inlining of a generic function while preserving semantics.

To get a template binding instead of symbolic binding, add the template keyword before the binding pattern, as in:

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

which introduces a template constant T with type C and value U. This is roughly equivalent to:

fn TemplateLet(...) {
  ...
  fn Closure(template T:! C) {
    X;
    Y;
    Z;
  }
  Closure(U);
}

In this case, the where .Self == U modifier is superfluous.

References:

Parameterized impl declarations

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:

  • Defining an impl that applies to multiple arguments to a parameterized type.
  • Conditional conformance where a parameterized type implements some interface if the parameter to the type satisfies some criteria, like implementing the same interface.
  • Blanket impl declarations where an interface is implemented for all types that implement another interface, or some other criteria beyond being a specific type.
  • Wildcard impl declarations where a family of interfaces are implemented for single type.

The syntax for an out-of-line parameterized impl declaration is:

impl forall [] as [ where ] ;

This may also be called a generic impl declaration.

Impl for a parameterized type

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

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

This is equivalent to naming the implementing type between impl and as, though this form is not allowed after extend:

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

An out-of-line impl declaration must declare all parameters in a forall clause:

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, with or without extend:

class HashMap(KeyT:! Hashable, ValueT:! type) {
  extend impl as Has(KeyT) { ... }
  impl as Contains(HashSet(KeyT)) { ... }
}

or out-of-line the same forall parameter can be passed to both:

class HashMap(KeyT:! Hashable, ValueT:! type) { ... }
impl forall [KeyT:! Hashable, ValueT:! type]
    HashMap(KeyT, ValueT) as Has(KeyT) { ... }
impl forall [KeyT:! Hashable, ValueT:! type]
    HashMap(KeyT, ValueT) as Contains(HashSet(KeyT)) { ... }

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.

This may be done by specifying a more specific implementing type to the left of the as in the declaration:

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

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

Note that no forall clause or type may be specified when declaring an impl with the extend keyword:

class Array(T:! type, template N:! i64) {
  // ❌ Illegal: nothing allowed before `as` after `extend impl`:
  extend impl forall [P:! Printable] Array(P, N) as Printable { ... }
}

Note: This was changed in proposal #2760.

Instead, the class can declare aliases to members of the interface. Those aliases will only be usable when the type implements the interface.

class Array(T:! type, template N:! i64) {
  alias Print = Printable.Print;
}
impl forall [P:! Printable] Array(P, N) as Printable { ... }

impl String as Printable { ... }
var can_print: Array(String, 2) = ("Hello ", "world");
// ✅ Allowed: `can_print.Print` resolves to
// `can_print.(Printable.Print)`, which exists as long as
// `Array(String, 2) impls Printable`, which exists since
// `String impls Printable`.
can_print.Print();

var no_print: Array(Unprintable, 2) = ...;
// ❌ Illegal: `no_print.Print` resolves to
// `no_print.(Printable.Print)`, but there is no
// implementation of `Printable` for `Array(Unprintable, 2)`
// as long as `Unprintable` doesn't implement `Printable`.
no_print.Print();

It is legal to declare or define a conditional impl lexically inside the class scope without extend, as in:

class Array(T:! type, template N:! i64) {
  // ✅ Allowed: non-extending impl defined in class scope may
  // use `forall` and may specify a type.
  impl forall [P:! Printable] Array(P, N) as Printable { ... }
}

Inside the scope of this impl definition, both P and T refer to the same type, but P has the facet 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.

Open question: 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) { ... }
impl forall [T:! type] Pair(T, T) as Foo(T) { ... }

As before, you may also define the impl inline, but it may not be combined with the extend keyword:

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

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

class X(T:! type) {
  // ✅ Allowed: `X(T).F` consistently means `X(T).(Foo.F)`
  // even though that may have different definitions for
  // different values of `T`.
  alias F = Foo.F;
}
impl X(i32) as Foo {
  fn F[self: Self]() { DoOneThing(); }
}
impl X(i64) as Foo {
  fn F[self: Self]() { DoADifferentThing(); }
}

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

Blanket impl declarations

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

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

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

  • T implements CommonType(T) for all T

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

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

Blanket impl declarations may never be declared using extend and must always be defined lexically out-of-line.

Difference between a blanket impl and a named constraint

A blanket impl declaration 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 impl declarations

A wildcard impl declaration is an impl declaration that defines how a family of interfaces are implemented 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 {
  impl forall [T:! ImplicitAs(i32)] as AddTo(T) { ... }
}
// Or out-of-line:
impl forall [T:! ImplicitAs(i32)] BigInt as AddTo(T) { ... }

Wildcard impl declarations may never be declared using extend, to avoid having the names in the interface defined for the type multiple times.

Combinations

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

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 definition to use that achieve these three goals:

For this to work, we need a rule that picks a single impl definition 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 impl declarations that are 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 extend 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, impl declarations 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.

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 definition, 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 partially 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 generics. More detail can be found in this appendix with the rationale and alternatives considered.

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 contain impl definitions 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 impl declarations, which type structure is considered "most specific" to use as the implementation of that type for that interface.

Given two different type structures of impl declarations 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 contain impl definitions with a given type structure, all impl definitions 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 declaration 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 { ... }
}

To increase expressivity, Carbon allows prioritization blocks to contain a mix of type structures, which is resolved using this rule:

The compiler first picks the impl declaration with the type structure most favored for the query, and then picks the highest priority (earliest) matching impl declaration in the same prioritization block.

Alternatives considered: We considered two other options:

  • "Intersection rule:" Prioritization blocks implicitly define all non-empty intersections of contained impl declarations, which are then selected by their type structure.
  • "Same type structure rule:" All the impl declarations in a prioritization block are required to have the same type structure, at a cost in expressivity. This option was not chosen since it wouldn't support the different type structures created by the like operator.

To see the difference from the first option, 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. Ultimately we decided that it was too surprising to prioritize based on the implicit intersection of impl declarations, rather than something explicitly written in the code.

We chose between these alternatives in the open discussion on 2023-07-18. TODO: This decision needs to be approved in a proposal.

Acyclic rule

A cycle is when a query, such as "does type T implement interface I?", considers an impl declaration that might match, and whether that impl declaration 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 impl declarations 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).

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 impl declarations 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 impls 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 impl declarations are selected.

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

There is no reason 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 as 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 as D(i16)).Cond == A. This implies that (i16 as 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 as 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 as D(i16)).Cond == B, (i16 as D(i8)).Cond would have to be A. This happens when i16 implements D(i8) using the third blanket impl. However, (i8 as 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 impl declarations gives you an immediate error if there exists queries using them 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 have a set of impl declarations 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 impls B if Optional(A) impls B, if Optional(Optional(A)) impls B, and so on. This could be the result of a single impl:

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

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

Determining whether a particular set of impl declarations terminates is equivalent to the halting problem (content warning: contains many instances of an obscene word as part of a programming language name 1, 2), and so is undecidable in general. Carbon adopts an approximation that guarantees termination, but may mistakenly report an error when the query would terminate if left to run long enough. The hope is that this criteria is accurate on code that occurs in practice.

Rule: the types in the impl query must never get strictly more complicated when considering the same impl declaration again. The way we measure the complexity of a set of types is by counting how many of each base type appears. A base type is the name of a type without its parameters. For example, the base types in this query Pair(Optional(i32), bool) impls AddWith(Optional(i32)) are:

  • Pair
  • Optional twice
  • i32 twice
  • bool
  • AddWith

A query is strictly more complicated if at least one count increases, and no count decreases. So Optional(Optional(i32)) is strictly more complicated than Optional(i32) but not strictly more complicated than Optional(bool).

This rule, when combined with the acyclic rule that a query can't repeat exactly, guarantees termination.

Consider the example from before,

impl forall [A:! type where Optional(.Self) impls B] A as B;

This impl declaration matches the query i32 impls B as long as Optional(i32) impls B. That is a strictly more complicated query, though, since it contains all the base types of the starting query (i32 and B), plus one more (Optional). As a result, an error can be given after one step, rather than after hitting a large recursion limit. And that error can state explicitly what went wrong: we went from a query with no Optional to one with one, without anything else decreasing.

Note this only triggers a failure when the same impl declaration is considered with the strictly more complicated query. For example, if the declaration is not considered since there is a more specialized impl declaration that is preferred by the type-structure overlap rule, as in:

impl forall [A:! type where Optional(.Self) impls B] A as B;
impl Optional(bool) as B;
// OK, because we never consider the first `impl`
// declaration when looking for `Optional(bool) impls I`.
let U:! B = bool;
// Error: cycle with `i32 impls B` depending on
// `Optional(i32) impls B`, using the same `impl`
// declaration, as before.
let V:! B = i32;

Note: Issue #2880 is a tracking bug for known issues with this "strictly more complex" rule for impl termination. We are using that issue to track any code that arises in practice that would terminate but is rejected by this rule.

Comparison with other languages: 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, because of the concern that increasing the number of steps needed to resolve an impl query could cause far away code to hit the recursion limit.

Carbon's approach is robust in the face of refactoring:

  • It does not depend on the specifics of how an impl declaration is parameterized, only on the query.
  • It does not depend on the length of the chain of queries.
  • It does not depend on a measure of type-expression complexity, like depth.

Carbon's approach also results in identifying the minimal steps in the loop, which makes error messages as short and understandable as possible.

Alternatives considered:

-   [Recursion limit](/proposals/p2687.md#problem)
-   [Measure complexity using type tree depth](/proposals/p2687.md#measure-complexity-using-type-tree-depth)
-   [Consider each type parameter in an `impl` declaration separately](/proposals/p2687.md#consider-each-type-parameter-in-an-impl-declaration-separately)
-   [Consider types in the interface being implemented as distinct](/proposals/p2687.md#consider-types-in-the-interface-being-implemented-as-distinct)
-   [Require some count to decrease](/proposals/p2687.md#require-some-count-to-decrease)
-   [Require non-type values to stay the same](/proposals/p2687.md#require-non-type-values-to-stay-the-same)

References: This algorithm is from proposal #2687: Termination algorithm for impl selection, replacing the recursion limit originally proposed in #920: Generic parameterized impls (details 5) before we came up with this algorithm.

Non-facet arguments

For non-facet arguments we have to expand beyond base types to consider other kinds of keys. These other keys are in a separate namespace from base types.

  • Values with an integral type use the name of the type as the key and the absolute value as a count. This means integer arguments are considered more complicated if they increase in absolute value. For example, if the values 2 and -3 are used as arguments to parameters with type i32, then the i32 key will have count 5.
  • Every option of a choice type is its own key, counting how many times a value using that option occurs. Any parameters to the option are recorded as separate keys. For example, the Optional(i32) value of .Some(7) is recorded as keys .Some (with a count of 1) and i32 (with a count of 7).
  • Yet another namespace of keys is used to track counts of variadic arguments, under the base type. This is to defend against having a variadic type V that takes any number of i32 arguments, with an infinite set of distinct instantiations: V(0), V(0, 0), V(0, 0, 0), ...
    • A tuple key in this namespace is used to track the total number of components of tuple values. The values of those elements will be tracked using their own keys.

Non-facet argument values not covered by these cases are deleted from the query entirely for purposes of the termination algorithm. This requires that two queries that only differ by non-facet arguments are considered identical and therefore are rejected by the acyclic rule. Otherwise, we could construct an infinite family of non-facet argument values that could be used to avoid termination.

final impl declarations

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 call to a generic function, such as using an operator:

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

// Types implementing `Deref`
class Ptr(T:! type) {
  ...
  impl as Deref where .Result = T {
    fn Op[self: Self]() -> Result { ... }
  }
}
class Optional(T:! type) {
  ...
  impl as Deref where .Result = T {
    fn Op[self: 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.Op 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 impl as Deref where .Result = T {
    fn Op[self: Self]() -> Result { ... }
  }
}
class Optional(T:! type) {
  ...
  // Note: added `final`
  final impl as Deref where .Result = T {
    fn Op[self: Self]() -> Result { ... }
  }
}

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

This prevents any higher-priority impl that overlaps a final impl from being defined unless it agrees with the final impl on the overlap. Overlap is computed between two non-template impl declaration by unifying the corresponding parts. For example, the intersection of these two declarations

final impl forall [T:! type]
    T as CommonTypeWith(T)
    where .Result = T {}

impl forall [V:! type, U:! CommonTypeWith(V)]
    Vec(U) as CommonTypeWith(Vec(V))
    where .Result = Vec(U.Result) {}

is found by unifying T with Vec(U) and CommonTypeWith(T) with CommonTypeWith(Vec(V)). In this case, the intersection is when T == Vec(U) and U == V. For templated impl declarations, overlap and agreement is delayed until the template is instantiated with concrete types.

Since we do not require the compiler to compare the definitions of functions, agreement is only possible for interfaces without any function members.

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 constants 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`
}

Alternatives considered:

Libraries that can contain a final impl

To prevent the possibility of two unrelated libraries defining conflicting impl declarations, 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 impl declarations.
  • 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 impl declarations 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 impl declarations 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 design 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 impl declarations default to allowing specialization, with restrictions on which may be declared final.
  • Since a Rust impl is not specializable by default, generic functions can assume that if a matching blanket impl declaration is found, the associated constants from that impl will be used. In Carbon, if a checked-generic function requires an associated constant 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 impl definitions. 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.

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 require or extend 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 in its signature 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.

If C is the name of an incomplete interface or named constraint, then it can be used in the following contexts:

  • ✅ T:! C
  • ✅ C & D
    • There may be conflicts between C and D making this invalid that will only be discovered once they are both complete.
  • ✅ interface ... { require ... impls C; } or constraint ... { require ... impls C; }
    • Nothing implied by implementing C will be visible until C is complete.
  • ✅ T:! C ... T impls C
  • ✅ T:! A & C ... T impls C
    • This includes constructs requiring T impls C such as T as C or U:! C = T.
  • ✅ impl ... as C;
    • Checking that all associated constants of C are correctly assigned values will be delayed until C is complete.

An incomplete C cannot be used in the following contexts:

  • ❌ T:! C ... T.X
  • ❌ T:! C where ...
  • ❌ class ... { extend impl as C; }
    • The names of C are added to the class, and so those names need to be known.
  • ❌ T:! C ... T impls A where A is an interface or named constraint different from C
    • Need to see the definition of C to see if it implies A.
  • ❌ impl ... as C { ... }

Future work: It is currently undecided whether an interface needs to be complete to be extended, as in:

interface I { extend C; }

There are three different approaches being considered:

  • If we detect name collisions between the members of the interface I and C when the interface I is defined, then we need C to be complete.
  • If we instead only generate errors on ambiguous use of members with the same name, as we do with A & B, then we don't need to require C to be complete.
  • Another option, being discussed in #2745, is that names in interface I shadow the names in any interface being extended, then C would not be required to be complete.

Declaring implementations

The declaration of an interface implementation consists of:

Note: The extend keyword, when present, is not part of the impl declaration. It precedes the impl declaration in class scope.

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 parameterized impl definitions 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 can't forward declare an implementation of an incomplete interface. This allows the assignment of associated constants in the impl declaration to be verified with the declaration. An impl forward declaration may be for any declared type, whether it is incomplete or defined.
  • Every extending 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 declaration 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. This matches the information accumulation principle.

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 expressions is performed.

Interface implementation declarations match if the type and interface expressions match along with the forall clause, if any:

  • 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 { ... }, Self is rewritten to MyClass. In class Vector(T:! Movable) { ... }, Self is rewritten to forall [T:! Movable] Vector(T).
  • 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 { extend MyInterface; }, is not considered to match.

For implementations to agree:

  • The presence of the modifier keyword final 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.
// 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;
}

// Out-of-line forward declarations
impl MyClass as Interface1 where .T1 = i32;
impl MyClass as Interface2 where .T2 = bool;
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 {
  // Inline definition of previously declared impl.
  // Note: no need to repeat assignments to associated
  // constants.
  impl as Interface1 where _ { }

  // Inline extending definition of previously declared
  // impl.
  // Note: `extend` only appears on the declaration in
  // class scope
  // Note: allowed even though `MyClass` is incomplete.
  // Note: allowed but not required to repeat `where`
  // clause.
  extend impl as Interface3 where .T3 = f32 { }

  // Extending redeclaration of previously declared
  // impl. Every extending implementation must be
  // declared in the class definition.
  extend impl as Interface4 where _;

  // Inline forward declaration of implementation.
  impl MyClass as Interface5 where .T5 = u64;
  // or: impl as Interface5 where .T5 = u64;

  // Forward declaration of extending implementation.
  extend impl as Interface6 where .T6 = u8;
  // *Not*:
  //   extend impl MyClass as Interface6 where .T6 = u8;
  // No optional type after `extend impl`, it must be
  // followed immediately by `as`
}

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

// Definitions of previously declared implementations.
impl MyClass as Interface2 where _ { }
impl MyClass as Interface5 where _ { }

// Definition of previously declared extending
// implementations.
impl MyClass as Interface4 where _ { }
impl MyClass as Interface6 where _ { }

Example of declaring interfaces with cyclic references

In this example, Node has an EdgeT associated facet that is constrained to implement Edge, and Edge has a NodeT associated facet that is constrained to implement Node. Furthermore, the NodeT of an EdgeT 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 NodeT:! NodeFor(Self);
  fn Head[self: Self]() -> NodeT;
}
interface Node {
  let EdgeT:! EdgeFor(Self);
  fn Edges[self: Self]() -> DynArray(EdgeT);
}

// 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) {
  extend Edge where .NodeT = N;
}
constraint NodeFor(E:! Edge) {
  extend Node where .EdgeT = E;
}

Future work: This approach has limitations. For example the compiler only knows EdgeT is convertible to type in the body of the interface Node definition, which may not be enough to satisfy the requirements to be an argument to DynArray. If this proves to be a problem, we may decided to expand what can be done with incomplete interfaces and types to allow the above to be written without the additional private constraints:

interface Node;

interface Edge {
  let NodeT:! Node where .EdgeT = Self;
  fn Head[self: Self]() -> NodeT;
}

interface Node {
  let EdgeT:! Movable & Edge where .NodeT = Self;
  fn Edges[self: Self]() -> DynArray(EdgeT);
}

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.
  require T impls CommonType(Self);
}

Note however that CommonType is still incomplete inside its definition, so no constraints on members of CommonType are allowed, and that this require T impls declaration must involve Self.

interface CommonType(T:! type) {
  let Result:! type;
  // ❌ Illegal: `CommonType` is incomplete
  require T impls 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.
  require T impls CommonTypeResult(Self, Result);
}

constraint CommonTypeResult(T:! type, R:! type) {
  extend 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[self: Self](b: Self) -> Self;
  fn Scale[self: Self](v: f64) -> Self;
  // Default definition of `Invert` calls `Scale`.
  default fn Invert[self: Self]() -> Self {
    return self.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[self: Self](b: Self) -> Self;
  fn Scale[self: Self](v: f64) -> Self;
  default fn Invert[self: Self]() -> Self;
}
// `Vector` is considered complete at this point,
// even though `Vector.Invert` is still incomplete.
fn Vector.Invert[self: Self]() -> Self {
  return self.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 facets, and interface parameters, using the = <default value> syntax.

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

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

Note that Self is a legal default value for an associated facet or facet 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 {
  extend 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 constants 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[self: Self](right: Self) -> bool;
  // ❌ Illegal: May not provide definition
  //             for required interface.
  require Self impls PartialOrder {
    fn PartialLess[self: Self](right: Self) -> bool {
      return self.TotalLess(right);
    }
  }
}

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

interface TotalOrder {
  fn TotalLess[self: Self](right: Self) -> bool;
  // No `require` declaration, since implementers of
  // `TotalOrder` don't need to also implement
  // `PartialOrder`, since an implementation is provided.
}

// Any type that implements `TotalOrder` also has at
// least this implementation of `PartialOrder`:
impl forall [T:! TotalOrder] T as PartialOrder {
  fn PartialLess[self: Self](right: Self) -> bool {
    return self.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 impl definitions.

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

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

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

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

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

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 {
  require Self impls 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 require and impls to say some type other than Self must implement an interface. For example,

interface IntLike {
  require i32 impls As(Self);
  // ...
}

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

interface CommonTypeWith(T:! type) {
  require T impls CommonTypeWith(Self);
  // ...
}

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

A require...impls constraint in an interface, or constraint, definition must still use Self in some way. It can be an argument to either the type or interface. For example:

  • ✅ Allowed: require Self impls Equatable
  • ✅ Allowed: require Vector(Self) impls Equatable
  • ✅ Allowed: require i32 impls CommonTypeWith(Self)
  • ✅ Allowed: require Self impls CommonTypeWith(Self)
  • ❌ Error: require i32 impls Equatable
  • ❌ Error: require T impls Equatable where T is some parameter to the interface

This restriction allows the Carbon compiler to know where to look for facts about a type. If require i32 impls Equatable could appear in any interface definition, that implies having to search all of them when considering what interfaces i32 implements. This would create a coherence problem, since then the set of facts true for a type would depend on which interfaces have been imported.

When implementing an interface with an require...impls 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.
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 impls Equatable`.
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.
impl forall [T:! type where Foo(T) impls 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 {}
impl Foo(Bar) as Equatable {}
// Gives `Foo(Bar) impls 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) {
  require Self impls 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 facet 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, and 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...impls 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 { require Self impls A; }
interface C { require Self impls B; }
interface D { require Self impls 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 impls D` and `D` directly requires `C` to be
  // implemented.
  observe T impls C;

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

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

Note that observe statements do not affect which impl is selected 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 definition to select.

Observing blanket impl declarations

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

  // There is a blanket implementation of `C` for
  // types implementing `B`.
  observe T impls 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 impl declarations and suggest observe declarations that would make the code compile if any solution is found.

Observing equal to a type implementing an interface

The observe...== form can be combined with the observe...impls form to show that a type implements an interface because it is equal to another type that is known to implement that interface.

interface I {
  fn F();
}

fn G(T:! I, U:! type where .Self == T) {
  // ❌ Illegal: No implementation of `I` for `U`.
  U.(I.F)();

  // ✅ Allowed: Implementation of `I` for `U`
  //             through `T`.
  observe U == T impls I;
  U.(I.F)();

  // ❌ Illegal: `U` does not extend `I`.
  U.F();
}

Multiple == clauses are allowed in an observe declaration, so you may write observe A == B == C impls I;.

Operator overloading

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

// Unary `-`.
interface Negate {
  default let Result:! type = Self;
  fn Op[self: Self]() -> Result;
}

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

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, which was implemented in proposal #1178.

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[self: 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 the interface for a binary operator like *:

// Binary `*`.
interface MulWith(U:! type) {
  default let Result:! type = Self;
  fn Op[self: 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.(MulWith(f64).Result)
    = left.(MulWith(f64).Op)(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 OrderedWith(U:! type) {
  fn Compare[self: Self](u: U) -> Ordering;
  // ...
}

class ReverseComparison(T:! type, U:! OrderedWith(T)) {
  adapt T;
  extend impl as OrderedWith(U) {
    fn Compare[self: Self](u: U) -> Ordering {
      match (u.Compare(self)) {
        case .Less         => return .Greater;
        case .Equivalent   => return .Equivalent;
        case .Greater      => return .Less;
        case .Incomparable => return .Incomparable;
      }
    }
  }
}

impl SongByTitle as OrderedWith(SongTitle) { ... }
impl SongTitle as OrderedWith(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[self: Self]() -> i64;
}

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

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

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

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

like operator for implicit conversions

Because the type of the operands is directly used to select the operator interface implementation, 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[self: Self](s: f64) -> Self;
}
// "Implementation One"
impl Meters as MulWith(f64)
    where .Result = Meters {
  fn Op[self: Self](other: f64) -> Result {
    return self.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
//             `MulWith(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"
impl forall [T:! ImplicitAs(f64)]
    Meters as MulWith(T) where .Result = Meters {
  fn Op[self: Self](other: T) -> Result {
    // Carbon will implicitly convert `other` from type
    // `T` to `f64` to perform this call.
    return self.((Meters as MulWith(f64)).Op)(other);
  }
}
// ✅ Allowed: uses `Meters as MulWith(T)` impl
//             with `T == f32` since `f32 impls 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 facet 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.
impl Meters as MulWith(like f64)
    where .Result = Meters {
  fn Op[self: Self](other: f64) -> Result {
    return self.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".

Note: We have decided to change the following in a discussion on 2023-07-13. The new approach is to have one parameterized implementation replacing all of the like expressions on the left of the as, and another replacing all of the like expressions on the right of the as. However, in a discussion on 2023-07-20, we decided that this change would not affect how we handle nested like expressions: like Vector(like i32) is still like Vector(i32) plus Vector(like i32). These changes have not yet gone through the proposal process, and we may decide to reject nested like until we have a demonstrated need.

In general, each like adds one additional parameterized implementation. There is always the impl defined 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 automatic impl definition with it replaced by a new parameter. These additional automatic implementations will delegate to the main impl definition, 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

impl like Meters as MulWith(like f64)
    where .Result = Meters {
  fn Op[self: Self](other: f64) -> Result {
    return self.Scale(other);
  }
}

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

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

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

impl like Meters as MulWith(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.
impl Meters as MulWith(f64) where .Result = Meters;

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

// Second `like` replaced with a wildcard. Same as the
// declaration part of "implementation two", without the
// body of the definition.
impl forall [T:! ImplicitAs(f64)]
    Meters as MulWith(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 defined. That is, it is injected in the API file if the impl definition is in an API file, and in the sole impl file with the impl definition otherwise.

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:

impl like Vector(like String) as Printable;

Which will generate implementations with declarations:

impl Vector(String) as Printable;
impl forall [T:! ImplicitAs(Vector(String))] T as Printable;
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 have those impl definitions 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 `self`
//             parameter of `Printable.Print`.
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
impl like Meters as Printable;

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

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

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

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

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

Parameterized types

Generic types may be defined by giving them compile-time 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 a facet describing the type of its elements:

class HashMap(
    KeyT:! Hashable & Eq & Movable,
    ValueT:! Movable) {
  // `Self` is `HashMap(KeyT, ValueT)`.

  // Class parameters may be used in function signatures.
  fn Insert[addr self: Self*](k: KeyT, v: ValueT);

  // Class parameters may be used in field types.
  private var buckets: DynArray((KeyT, ValueT));

  // Class parameters may be used in interfaces implemented.
  extend impl as Container where .ElementType = (KeyT, ValueT);
  impl as OrderedWith(HashMap(KeyT, ValueT));
}

Note that, unlike functions, every parameter to a type must be a compile-time binding, either symbolic using :! or template using template...:!, not runtime, with a plain :.

Two types are the same if they have the same name and the same arguments, after applying aliases and rewrite constraints. 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[KeyT:! Movable, ValueT:! Movable]
    (haystack: HashMap(KeyT, ValueT), needle: KeyT)
    -> bool { ... }
fn MyMapContains(s: String) {
  var map: HashMap(String, i32) = (("foo", 3), ("bar", 5));
  // ✅ Deduces `KeyT` = `String as Movable` from the types of both arguments.
  // Deduces `ValueT` = `i32 as Movable` 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. In the above example, the KeyT parameter to ContainsKey gets Hashable & Eq implied constraints from the declaration of the corresponding parameter to HashMap.

Future work: We may want to support optional deduced parameters in square brackets [...] before the explicit parameters in round parens (...).

References: This feature is from proposal #1146: Generic details 12: parameterized types.

Generic methods

A generic type may have methods with additional compile-time parameters. For example, this Set(T) type may be compared to anything implementing the Container interface as long as the element types match:

class Set(T:! Ordered) {
  fn Less[U:! Container with .ElementType = T, self: Self](u: U) -> bool;
  // ...
}

The Less method is parameterized both by the T parameter to the Set type and its own U parameter deduced from the type of its first argument.

Conditional methods

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

class DynArray(T:! type) {
  // `DynArray(T)` has a `Sort()` method if `T impls Ordered`.
  fn Sort[C:! Ordered, addr self: DynArray(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.

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 impl forall [T:! type] T* as OptionalStorage
    where .Storage = Array(Byte, sizeof(T*)) {
  ...
}
// Specialization for type `bool`.
final 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 checked-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;
}

Alternative considered: Direct support for specialization of types was considered in proposal #1146.

Future work

Dynamic types

Checked-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-compile-time) 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 checked 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.

Impl with state

A feature we might consider where an impl itself can have state.

Generic associated facets and higher-ranked facets

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 facets

Generic associated facets are about when this is a requirement of an interface. These are also called "associated type constructors."

Rust has stabilized this feature.

Higher-ranked types

Higher-ranked types are used to represent this requirement in a function signature. They can be emulated using generic associated facets.

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 take a variable number of arguments, with the definition checked independent of calls. Open proposal #2240 is adding this feature.

Value constraints for template parameters

We have planned support for predicates that constrain the value of non-facet template parameters. For example, we might support a predicate that constrains an integer to live inside a specified range. See question-for-leads issue #2153: Checked generics calling templates and future work in proposal #2200: Template generics.

References