carbon-lang/docs/design/generics/details.md

Generics: Details

Table of contents

• Overview
• Interfaces
• Implementing interfaces
  • Facet type
  • Implementing multiple interfaces
  • External impl
  • Qualified member names
  • Access
• Generics
  • Implementation model
• Interfaces recap
• Type-of-types and facet types
• Named constraints
  • Subtyping between type-of-types
• Combining interfaces by anding type-of-types
• Interface requiring other interfaces
  • Interface extension
    • extends and impl with named constraints
    • Diamond dependency issue
  • Use case: overload resolution
• Type compatibility
• Adapting types
  • Adapter compatibility
  • Extending adapter
  • Use case: Using independent libraries together
  • Use case: Defining an impl for use by other types
  • Use case: Private impl
  • Adapter with stricter invariants
• Associated constants
  • Associated class functions
• Associated types
  • Implementation model
• Parameterized interfaces
  • Impl lookup
  • Parameterized named constraints
• Where constraints
  • Constraint use cases
    • Set an associated constant to a specific value
    • Same type constraints
      • Set an associated type to a specific value
      • Equal generic types
        • Satisfying both type-of-types
    • Type bound for associated type
      • Type bounds on associated types in declarations
      • Type bounds on associated types in interfaces
    • Combining constraints
    • Recursive constraints
    • Parameterized type implements interface
    • Another type implements parameterized interface
  • Implied constraints
    • Must be legal type argument constraints
  • Open question: referencing names in the interface being defined
  • Manual type equality
    • observe declarations
• Other constraints as type-of-types
  • Is a derived class
  • Type compatible with another type
    • Same implementation restriction
    • Example: Multiple implementations of the same interface
    • Example: Creating an impl out of other impls
  • Type facet of another type
  • Sized types and type-of-types
    • Implementation model
  • TypeId
• Future work
  • Conditional conformance
  • Parameterized impls
    • Lookup resolution and specialization
  • Dynamic types
    • Runtime type parameters
    • Runtime type fields
  • Abstract return types
  • Interface defaults
  • Evolution
  • Testing
  • Operator overloading
  • Impls with state
  • Generic associated types and higher-ranked types
    • Generic associated types
    • Higher-ranked types
  • Field requirements
  • Generic type specialization
  • Bridge for C++ customization points
  • Variadic arguments
  • Range constraints on generic integers
• References

Overview

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

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

Since we can figure out T from the type of val, we don't need the caller to pass in T explicitly, so it can be a deduced parameter (also see deduced parameters in the Generics overview doc). Basically, the user passes in a value for val, and the type of val determines T. T still gets passed into the function though, and it plays an important role -- it defines the implementation of the interface. We can think of the interface as defining a struct type whose members are function pointers, and an implementation of an interface as a value of that struct with actual function pointer values. So an implementation is a table of function pointers (one per function defined in the interface) that gets passed into a function as the type argument. For more on this, see the implementation model section below.

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

• associated types
• type parameters
• interface requirements

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

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

The last piece of the puzzle is how the caller of the function can produce a value with the right type. Let's say the user has a value of type Song, and of course songs have all sorts of functionality. If we want a Song to be printed using the PrintToStdout function, it needs to implement the ConvertibleToString interface. Note that we don't say that Song is of type ConvertibleToString but instead that it has a "facet type". This means there is another type, called Song as ConvertibleToString, with the following properties:

• Song as ConvertibleToString has the same data representation as Song.
• Song as ConvertibleToString is an implementation of the interface ConvertibleToString. The functions of Song as ConvertibleToString are just implementations of the names and signatures defined in the ConvertibleToString interface, like ToString, and not the functions defined on Song values.
• Carbon will implicitly convert values from type Song to type Song as ConvertibleToString when calling a function that can only accept types of type ConvertibleToString.
• In the normal case where the implementation of ConvertibleToString for Song is not defined as external, every member of Song as ConvertibleToString is also a member of Song. This includes members of ConvertibleToString that are not explicitly named in the impl definition but have defaults.
• You may access the ToString function for a Song value w by writing a qualified function call, like w.(ConvertibleToString.ToString)(). The same effect may be achieved by casting, as in (w as (Song as ConvertibleToString)).ToString(). This qualified syntax is available whether or not the implementation is defined as external.
• If other interfaces are implemented for Song, they are also implemented for Song as ConvertibleToString. The only thing that changes when casting a Song w to Song as ConvertibleToString are the names that are accessible without using the qualification syntax. A Song as ConvertibleToString value can likewise be cast to a Song; a Song acts just like another facet type for these purposes.

We define these facet types (alternatively, interface implementations) either with the type, with the interface, or somewhere else where Carbon can be guaranteed to see when needed. For more on this, see the implementing interfaces section below.

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

Interfaces

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

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

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

An interface defines a type-of-type, that is a type whose values are types. The values of an interface are specifically facet types, by which we mean types that are declared as specifically implementing exactly this interface, and which provide definitions for all the functions (and other members) declared in the interface.

Implementing interfaces

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

Impls may be defined inline inside the type definition:

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

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

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

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

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

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

Facet type

The impl definition defines a facet type: Point as Vector. While the API of Point includes the two fields x and y along with the Add and Scale methods, the API of Point as Vector only has the Add and Scale methods of the Vector interface. The facet type Point as Vector is compatible with Point, meaning their data representations are the same, so we allow you to convert between the two freely:

var a: Point = {.x = 1.0, .y = 2.0};
// `a` has `Add` and `Scale` methods:
a.Add(a.Scale(2.0));

// Cast from Point implicitly
var b: Point as Vector = a;
// `b` has `Add` and `Scale` methods:
b.Add(b.Scale(2.0));

// Will also implicitly convert when calling functions:
fn F(c: Point as Vector, d: Point) {
  d.Add(c.Scale(2.0));
}
F(a, b);

// Explicit casts
var z: Point as Vector = (a as (Point as Vector)).Scale(3.0);
z.Add(b);
var w: Point = z as Point;

These conversions change which names are exposed in the type's API, but as much as possible we don't want the meaning of any given name to change. Instead we want these casts to simply change the subset of names that are visible.

Note: In general the above is written assuming that casts are written "a as T" where a is a value and T is the type to cast to. When we write Point as Vector, the value Point is a type, and Vector is a type of a type, or a "type-of-type".

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, so for example Point as Vector is well defined.

We don't expect users to ordinarily name facet types explicitly in source code. Instead, values are implicitly converted to a facet type as part of calling a generic function, as described in the Generics section.

Implementing multiple interfaces

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

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

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

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

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

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

External impl

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

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

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

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

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

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

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

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

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

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

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

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

// OR:

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

// OR:

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

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

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

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

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

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

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

Qualified member names

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

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

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

package Plot;
import Points;

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

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

You could access Draw with a qualified name:

import Plot;
import Points;

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

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

Access

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

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

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

Generics

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

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

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

When we call AddAndScaleGeneric, we need to determine the value of T to use when passed values with type Point. Since T has type Vector, the compiler simply sets T to Point as Vector. This cast erases all of the API of Point and substitutes the api of Vector, without changing anything about the data representation. It acts like we called this non-generic function, found by setting T to Point as Vector:

fn AddAndScaleForPointAsVector(
      a: Point as Vector, b: Point as Vector, s: Double)
      -> Point as Vector {
  return a.Add(b).Scale(s);
}
// May still be called with Point arguments, due to implicit conversions.
// Similarly the return value can be implicitly converted to a Point.
var v2: Point = AddAndScaleForPointAsVector(a, w, 2.5);

Since Point implements Vector inline, Point also has definitions for Add and Scale:

fn AddAndScaleForPoint(a: Point, b: Point, s: Double) -> Point {
  return a.Add(b).Scale(s);
}

AddAndScaleForPoint(a, w, 2.5);

However, for another type implementing Vector but externally, such as Point2, or out-of-line using an external impl statement like Point3, the situation is different:

fn AddAndScaleForPoint2(a: Point2, b: Point2, s: Double) -> Point2 {
  // ❌ ERROR: `Point2` doesn't have `Add` or `Scale` methods.
  return a.Add(b).Scale(s);
}
fn AddAndScaleForPoint3(a: Point3, b: Point3, s: Double) -> Point3 {
  // ❌ ERROR: `Point3` doesn't have `Add` or `Scale` methods.
  return a.Add(b).Scale(s);
}

Even though Point2 and Point3 don't have Add and Scale methods, they still implement Vector and so can still call AddAndScaleGeneric:

var a2: Point2 = {.x = 1.0, .y = 2.0};
var w2: Point2 = {.x = 3.0, .y = 4.0};
var v3: Point2 = AddAndScaleGeneric(a, w, 2.5);

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

Implementation model

The underlying model here is interfaces are type-of-types, in particular, the type of facet types:

• Interfaces are types of witness tables
• Facet types (defined by Impls) are witness table values
• The compiler rewrites functions with an implicit type argument (fn Foo[InterfaceName:! T](...)) to have an actual argument with type determined by the interface, and supplied at the callsite using a value determined by the impl.

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

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

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

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

Finally we can define a generic function and call it, like AddAndScaleGeneric from the "Generics" section by making the witness table an explicit argument to the function:

fn AddAndScaleGeneric
    (t:! Vector, a: t.Self, b: t.Self, s: Double) -> t.Self {
  return t.Scale(t.Add(a, b), s);
}
// Point implements Vector.
var v: Point = AddAndScaleGeneric(VectorForPoint, a, w, 2.5);

The rule is that generic arguments (declared using :!) are passed at compile time, so the actual value of the t argument here can be used to generate the code for AddAndScaleGeneric. So AddAndScaleGeneric is using a static-dispatch witness table.

Note that this implementation strategy only works for impls that the caller knows the callee needs.

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:

• to define an impl for a type,
• as a namespace name in a qualified name, and
• as a type-of-type for a generic type parameter.

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

Type-of-types and facet types

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

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

The requirements determine which types may be converted to a given type-of-type. The result of converting a type T to a type-of-type I (written T as I) is called a facet type, you might say a facet type F is the I facet of T if F is T as I. The API of F is determined by the set of names in the type-of-type.

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

Named constraints

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

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

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

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

constraint Type { }

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

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

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

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

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

To declare a named constraint that includes other declarations for use with template parameters, use the template keyword before constraint. Method, associated type, and associated function requirements may only be declared inside a template constraint. Note that a generic constraint matches all facets of a type if it matches any, but a template constraint can depend on the specific names of members used in a particular facet.

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

interface I {
  X;
  Y;
  Z;
}

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

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

But the corresponding constraint or template constraint, S:

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

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

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

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

Subtyping between type-of-types

There is a subtyping relationship between type-of-types that allows you to call one generic function from another as long as you are calling a function with a subset of your requirements.

Given a generic type T with type-of-type I1, it may be implicitly converted to a type-of-type I2, resulting in T as I2, as long as the requirements of I1 are a superset of the requirements of I2. Further, given a value x of type T, it can be implicitly converted to T as I2. For example:

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

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

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

Combining interfaces by anding type-of-types

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Alternatives considered: See Carbon: Access to interface methods.

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

Interface requiring other interfaces

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

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

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

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

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

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

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

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

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

Interface extension

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

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

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

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

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

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

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

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

Examples:

• The C++ Boost.Graph library graph concepts has many refining relationships between concepts. Carbon generics use case: graph library shows how those concepts might be translated into Carbon interfaces.
• The C++ concepts for containers, iterators, and concurrency include many requirement relationships.
• Swift protocols, such as Collection.

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

interface SetAlgebra {
  extends Equatable;
  extends ExpressibleByArrayLiteral;
}

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

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

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

extends and impl with named constraints

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

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

constraint Combined {
  extends Media;
  extends Job;
}

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

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

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

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

This is equivalent to implementing the required interfaces directly:

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

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

Conversely, an interface can extend a constraint:

interface MovieCodec {
  extends Combined;

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

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

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

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

Diamond dependency issue

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

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

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

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

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

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

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

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

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

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

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

• Explicitly implementing Graph.

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

• Implementing Graph externally.

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

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

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

Use case: overload resolution

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

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

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

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

Type compatibility

None of the conversions between facet types change the implementation of any interfaces for a type. So the result of a conversion does not depend on the sequence of conversions you perform, just the original type and the final type-of-type. That is, these types will all be equal:

• T as I
• (T as A) as I
• (((T as A) as B) as C) as I

Now consider a type with a generic type parameter, like a hash map type:

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

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

var hm: HashMap(String, i32) = ...;
var result: Optional(i32) = hm.Find("Needle");

Since the Find function is generic, it can only use the capabilities that HashMap requires of KeyT and ValueT. This implies that the implementation of HashMap(String, i32).Find and HashMap(String as Hashable, i32).Find are the same. In fact, we could substitute any facet of String, and Find would still use String as Hashable in its implementation. So these types:

• HashMap(String, i32)
• HashMap(String as Hashable, i32 as Type)
• HashMap(String as Printable, i32)
• HashMap((String as Printable & Hashable) as Hashable, i32)

are also facets of each other, and Carbon can freely allow casts and implicit conversions between them.

This means we don't generally need to worry about getting the wrong facet type as the argument for a generic type. This means we don't get type mismatches when calling functions as in this example, where the type parameters have different constraints than the type requires:

fn PrintValue
    [KeyT:! Printable & Hashable, ValueT:! Printable]
    (map: HashMap(KeyT, ValueT), key: KeyT) { ... }

var m: HashMap(String, i32) = ...;
PrintValue(m, "key");

However, those types are still different. A caller of Find observes that its signature reflects the actual type parameters passed to HashMap, not their projection onto the Hashable or Type facets. In particular, the return type of hm.Find is Optional(i32), not Optional(i32 as Type). (Incidentally, Optional(i32) and Optional(i32 as Type) are also facets of each other.)

Adapting types

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

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

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

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

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

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

or using qualified names:

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

Open question: As an alternative to:

impl as Printable = FormattedSong as Printable;

we could allow users to write:

impl as Printable = FormattedSong;

This would remove ceremony that the compiler doesn't need. The concern is whether it makes sense or is a category error. In this example, is FormattedSong, a type, a suitable value to provide when asking for a Printable implementation? An argument for this terser syntax is that the implicit conversion is legal in other contexts:

// ✅ Legal implicit conversion
var v:! Printable = FormattedSong;

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

The framework from the type compatibility section allows us to evaluate when we can convert between two different arguments to a parameterized type. Consider three compatible types, all of which implement Hashable:

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

Observe that Song as Hashable is different from SongHashedByTitle as Hashable, since they have different definitions of the Hashable interface even though they are compatible types. However Song as Hashable and PlayableSong as Hashable are almost the same. In addition to using the same data representation, they both implement one interface, Hashable, and use the same implementation for that interface. The one difference between them is that Song as Hashable may be implicitly converted to Song, which implements interface Printable, and PlayableSong as Hashable may be implicitly converted to PlayableSong, which implements interface Media. This means that it is safe to convert between HashMap(Song, i32) and HashMap(PlayableSong, i32) (though maybe only with an explicit cast), since the implementation of all the methods will use the same implementation of the Hashable interface. But HashMap(SongHashedByTitle, i32) is incompatible. This is a relief, because we know that in practice the invariants of a HashMap implementation rely on the hashing function staying the same.

Extending adapter

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

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

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

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

The resulting type SongByArtist would:

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

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

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

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

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

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

Use case: Using independent libraries together

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

import CompareLib;
import SongLib;

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

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

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

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

Use case: Defining an impl for use by other types

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

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

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

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

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

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

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

Use case: Private impl

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

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

// Private

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

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

Adapter with stricter invariants

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

Associated constants

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

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

Implementations of NSpacePoint for different types might have different values for N:

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

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

And these values may be accessed as members of the type:

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

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

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

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

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

Associated class functions

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

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

class MySerializableType {
  var i: i32;

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

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

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

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

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

Associated types

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

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

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

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

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

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

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

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

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

Associated types can also be implemented using a member type.

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

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

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

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

Implementation model

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

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

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

is represented by:

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

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

Parameterized interfaces

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Impl lookup

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

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

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

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

Parameterized named constraints

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

Where constraints

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

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

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

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

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

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

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

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

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

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

Constraint use cases

Set an associated constant to a specific value

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

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

Similarly in an interface definition:

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

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

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

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

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

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

Same type constraints

Set an associated type to a specific value

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

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

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

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

Equal generic types

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

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

Given an interface with two associated types

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

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

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

or in an interface definition:

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

This kind of constraint can be named:

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

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

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

Satisfying both type-of-types

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

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

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

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

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

Type bound for associated type

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

Type bounds on associated types in declarations

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

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

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

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

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

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

Type bounds on associated types in interfaces

Given these definitions (omitting ElementType for brevity):

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

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

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

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

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

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

Combining constraints

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

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

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

Recursive constraints

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

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

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

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

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

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

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

interface Container {
  let ElementType:! Type;

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

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

These recursive constraints can be named:

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

Note that using the constraint approach we can name these constraints using Self instead of .Self, since they are facets of the same type: Self is the facet corresponding to the containing interface and .Self is the facet corresponding to the interface being extended.

Parameterized type implements interface

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

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

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

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

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

Another type implements parameterized interface

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

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

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

Implied constraints

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Must be legal type argument constraints

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

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

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

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

Open question: referencing names in the interface being defined

Should the constraint in a where clause be required to only reference earlier names from this scope, as in this example?

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

The downside is that if you could reference later names, there is a more pleasingly symmetric formulation of those same constraints:

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

TODO: Revisit this question once issue #472: Open question: Calling functions defined later in the same file and proposal #875: Principle: information accumulation are resolved.

Manual type equality

Imagine we have some function with generic parameters:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  // ❌ Not allowed: a.InQ();

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

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

  // ❌ Not allowed: TakesPQR(a);

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

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

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

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

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

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

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

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

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

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

The benefits of the manual approach include:

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

The main downsides are:

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

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

observe declarations

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Other constraints as type-of-types

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

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

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

Is a derived class

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

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

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

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

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

Type compatible with another type

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

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

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

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

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

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

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

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

Same implementation restriction

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

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

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

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

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

Example: Multiple implementations of the same interface

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

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

Used as:

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

We might generalize this to a list of implementations:

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

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

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

Example: Creating an impl out of other impls

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

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

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

Type facet of another type

Similar to CompatibleWith(T), FacetOf(T) introduces an equivalence relationship between types. T1 is FacetOf(T2) if both T1 and T2 are facets of the same type.

Sized types and type-of-types

What is the size of a type?

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

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

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

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

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

Example:

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

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

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

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

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

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

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

Implementation model

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

TypeId

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

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

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

Note: To achieve this goal, the user will not even be allowed to destroy a value of type T in this case.

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

Future work

Conditional conformance

The problem we are trying to solve here is expressing that we have an impl of some interface for some type, but only if some additional type restrictions are met.

Parameterized impls

Also known as "blanket impls", these are when you have an impl definition that is parameterized so it applies to more than a single type and interface combination.

Lookup resolution and specialization

For this to work, we need a rule that picks a single impl in the case where there are multiple impl definitions that match a particular type and interface combination.

Dynamic types

Generics provide enough structure to support runtime dispatch for values with types that vary at runtime, without giving up type safety. Both Rust and Swift have demonstrated the value of this feature.

Runtime type parameters

This feature is about allowing a function's type parameter to be passed in as a dynamic (non-generic) parameter. All values of that type would still be required to have the same type.

Runtime type fields

Instead of passing in a single type parameter to a function, we could store a type per value. This changes the data layout of the value, and so is a somewhat more invasive change. It also means that when a function operates on multiple values they could have different real types.

Abstract return types

This lets you return an anonymous type implementing an interface from a function. In Rust this is the impl Trait return type.

In Swift, there are discussions about implementing this feature under the name "reverse generics" or "opaque result types": 1, 2, 3, 4, Swift is considering spelling this <V: Collection> V or some Collection.

Interface defaults

Rust supports specifying defaults for interface parameters, methods, associated constants. We should support this too. It is 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 user's desire.

Evolution

There are a collection of use cases for making different changes to interfaces that are already in use. These should be addressed either by describing how they can be accomplished with existing generics features, or by adding features.

In addition, evolution from (C++ or Carbon) templates to generics needs to be supported and made safe.

Testing

The idea is that you would write tests alongside an interface that validate the expected behavior of any type implementing that interface.

Operator overloading

We will need a story for defining how an operation is overloaded for a type by implementing an interface for that type.

Impls with state

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

Generic associated types and higher-ranked types

This would be some way to express the requirement that there is a way to go from a type to an implementation of an interface parameterized by that type.

Generic associated types

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

Higher-ranked types

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

Field requirements

We might want to allow interfaces to express the requirement that any implementing type has a particular field. This would be to match the expressivity of inheritance, which can express "all subtypes start with this list of fields."

Generic type specialization

See generic specialization for a description of what this might involve.

Bridge for C++ customization points

See details in the goals document.

Variadic arguments

Some facility for allowing a function to generically take a variable number of arguments.

Range constraints on generic integers

We currently only support where clauses on type-of-types. We may want to also support constraints on generic integers. The constraint with the most expected value is the ability to do comparisons like <, or >=. For example, you might constrain the N member of NSpacePoint using an expression like PointT:! NSpacePoint where 2 <= .N and .N <= 3.

The concern here is supporting this at compile time with more benefit than complexity. For example, we probably don't want to support integer-range based types at runtime, and there are also concerns about reasoning about comparisons between multiple generic integer parameters. For example, if J < K and K <= L, can we call a function that requires J < L? There is also a secondary syntactic concern about how to write this kind of constraint on a parameter, as opposed to an associated type, as in N:! u32 where ___ >= 2.

References

• #553: Generics details part 1
• #731: Generics details 2: adapters, associated types, parameterized interfaces
• #818: Constraints for generics (generics details 3)
• #931: Generic impls access (details 4)