• Start Date: 2014-08-04
• RFC PR #: rust-lang/rfcs#195
• Rust Issue #: rust-lang/rust#17307

Summary

This RFC extends traits with associated items, which make generic programming more convenient, scalable, and powerful. In particular, traits will consist of a set of methods, together with:

• Associated functions (already present as “static” functions)
• Associated consts
• Associated types
• Associated lifetimes

These additions make it much easier to group together a set of related types, functions, and constants into a single package.

This RFC also provides a mechanism for multidispatch traits, where the impl is selected based on multiple types. The connection to associated items will become clear in the detailed text below.

Note: This RFC was originally accepted before RFC 246 introduced the distinction between const and static items. The text has been updated to clarify that associated consts will be added rather than statics, and to provide a summary of restrictions on the initial implementation of associated consts. Other than that modification, the proposal has not been changed to reflect newer Rust features or syntax.

Motivation

A typical example where associated items are helpful is data structures like graphs, which involve at least three types: nodes, edges, and the graph itself.

In today’s Rust, to capture graphs as a generic trait, you have to take the additional types associated with a graph as parameters:

trait Graph<N, E> {
    fn has_edge(&self, &N, &N) -> bool;
    ...
}

The fact that the node and edge types are parameters is confusing, since any concrete graph type is associated with a unique node and edge type. It is also inconvenient, because code working with generic graphs is likewise forced to parameterize, even when not all of the types are relevant:

fn distance<N, E, G: Graph<N, E>>(graph: &G, start: &N, end: &N) -> uint { ... }

With associated types, the graph trait can instead make clear that the node and edge types are determined by any impl:

trait Graph {
    type N;
    type E;
    fn has_edge(&self, &N, &N) -> bool;
}

and clients can abstract over them all at once, referring to them through the graph type:

fn distance<G: Graph>(graph: &G, start: &G::N, end: &G::N) -> uint { ... }

The following subsections expand on the above benefits of associated items, as well as some others.

Associated types: engineering benefits for generics

As the graph example above illustrates, associated types do not increase the expressiveness of traits per se, because you can always use extra type parameters to a trait instead. However, associated types provide several engineering benefits:

• Readability and scalability

  Associated types make it possible to abstract over a whole family of types at once, without having to separately name each of them. This improves the readability of generic code (like the distance function above). It also makes generics more “scalable”: traits can incorporate additional associated types without imposing an extra burden on clients that don’t care about those types.

  In today’s Rust, by contrast, adding additional generic parameters to a trait often feels like a very “heavyweight” move.

• Ease of refactoring/evolution

  Because users of a trait do not have to separately parameterize over its associated types, new associated types can be added without breaking all existing client code.

  In today’s Rust, by contrast, associated types can only be added by adding more type parameters to a trait, which breaks all code mentioning the trait.

Clearer trait matching

Type parameters to traits can either be “inputs” or “outputs”:

• Inputs. An “input” type parameter is used to determine which impl to use.

• Outputs. An “output” type parameter is uniquely determined by the impl, but plays no role in selecting the impl.

Input and output types play an important role for type inference and trait coherence rules, which is described in more detail later on.

In the vast majority of current libraries, the only input type is the Self type implementing the trait, and all other trait type parameters are outputs. For example, the trait Iterator<A> takes a type parameter A for the elements being iterated over, but this type is always determined by the concrete Self type (e.g. Items<u8>) implementing the trait: A is typically an output.

Additional input type parameters are useful for cases like binary operators, where you may want the impl to depend on the types of both arguments. For example, you might want a trait

trait Add<Rhs, Sum> {
    fn add(&self, rhs: &Rhs) -> Sum;
}

to view the Self and Rhs types as inputs, and the Sum type as an output (since it is uniquely determined by the argument types). This would allow impls to vary depending on the Rhs type, even though the Self type is the same:

impl Add<int, int> for int { ... }
impl Add<Complex, Complex> for int { ... }

Today’s Rust does not make a clear distinction between input and output type parameters to traits. If you attempted to provide the two impls above, you would receive an error like:

error: conflicting implementations for trait `Add`

This RFC clarifies trait matching by:

• Treating all trait type parameters as input types, and
• Providing associated types, which are output types.

In this design, the Add trait would be written and implemented as follows:

// Self and Rhs are *inputs*
trait Add<Rhs> {
    type Sum; // Sum is an *output*
    fn add(&self, &Rhs) -> Sum;
}

impl Add<int> for int {
    type Sum = int;
    fn add(&self, rhs: &int) -> int { ... }
}

impl Add<Complex> for int {
    type Sum = Complex;
    fn add(&self, rhs: &Complex) -> Complex { ... }
}

With this approach, a trait declaration like trait Add<Rhs> { ... } is really defining a family of traits, one for each choice of Rhs. One can then provide a distinct impl for every member of this family.

Expressiveness

Associated types, lifetimes, and functions can already be expressed in today’s Rust, though it is unwieldy to do so (as argued above).

But associated consts cannot be expressed using today’s traits.

For example, today’s Rust includes a variety of numeric traits, including Float, which must currently expose constants as static functions:

trait Float {
    fn nan() -> Self;
    fn infinity() -> Self;
    fn neg_infinity() -> Self;
    fn neg_zero() -> Self;
    fn pi() -> Self;
    fn two_pi() -> Self;
    ...
}

Because these functions cannot be used in constant expressions, the modules for float types also export a separate set of constants as consts, not using traits.

Associated constants would allow the consts to live directly on the traits:

trait Float {
    const NAN: Self;
    const INFINITY: Self;
    const NEG_INFINITY: Self;
    const NEG_ZERO: Self;
    const PI: Self;
    const TWO_PI: Self;
    ...
}

Why now?

The above motivations aside, it may not be obvious why adding associated types now (i.e., pre-1.0) is important. There are essentially two reasons.

First, the design presented here is not backwards compatible, because it re-interprets trait type parameters as inputs for the purposes of trait matching. The input/output distinction has several ramifications on coherence rules, type inference, and resolution, which are all described later on in the RFC.

Of course, it might be possible to give a somewhat less ideal design where associated types can be added later on without changing the interpretation of existing trait type parameters. For example, type parameters could be explicitly marked as inputs, and otherwise assumed to be outputs. That would be unfortunate, since associated types would also be outputs – leaving the language with two ways of specifying output types for traits.

But the second reason is for the library stabilization process:

• Since most existing uses of trait type parameters are intended as outputs, they should really be associated types instead. Making promises about these APIs as they currently stand risks locking the libraries into a design that will seem obsolete as soon as associated items are added. Again, this risk could probably be mitigated with a different, backwards-compatible associated item design, but at the cost of cruft in the language itself.

• The binary operator traits (e.g. Add) should be multidispatch. It does not seem possible to stabilize them now in a way that will support moving to multidispatch later.

• There are some thorny problems in the current libraries, such as the _equiv methods accumulating in HashMap, that can be solved using associated items. (See “Defaults” below for more on this specific example.) Additional examples include traits for error propagation and for conversion (to be covered in future RFCs). Adding these traits would improve the quality and consistency of our 1.0 library APIs.

Detailed design

Trait headers

Trait headers are written according to the following grammar:

TRAIT_HEADER =
  'trait' IDENT [ '<' INPUT_PARAMS '>' ] [ ':' BOUNDS ] [ WHERE_CLAUSE ]

INPUT_PARAMS = INPUT_PARAM { ',' INPUT_PARAM }* [ ',' ]
INPUT_PARAM  = IDENT [ ':' BOUNDS ]

BOUNDS = BOUND { '+' BOUND }* [ '+' ]
BOUND  = IDENT [ '<' ARGS '>' ]

ARGS   = INPUT_ARGS
       | OUTPUT_CONSTRAINTS
       | INPUT_ARGS ',' OUTPUT_CONSTRAINTS

INPUT_ARGS = TYPE { ',' TYPE }*

OUTPUT_CONSTRAINTS = OUTPUT_CONSTRAINT { ',' OUTPUT_CONSTRAINT }*
OUTPUT_CONSTRAINT  = IDENT '=' TYPE

NOTE: The grammar for WHERE_CLAUSE and BOUND is explained in detail in the subsection “Constraining associated types” below.

All type parameters to a trait are considered inputs, and can be used to select an impl; conceptually, each distinct instantiation of the types yields a distinct trait. More details are given in the section “The input/output type distinction” below.

Trait bodies: defining associated items

Trait bodies are expanded to include three new kinds of items: consts, types, and lifetimes:

TRAIT = TRAIT_HEADER '{' TRAIT_ITEM* '}'
TRAIT_ITEM =
  ... <existing productions>
  | 'const' IDENT ':' TYPE [ '=' CONST_EXP ] ';'
  | 'type' IDENT [ ':' BOUNDS ] [ WHERE_CLAUSE ] [ '=' TYPE ] ';'
  | 'lifetime' LIFETIME_IDENT ';'

Traits already support associated functions, which had previously been called “static” functions.

The BOUNDS and WHERE_CLAUSE on associated types are obligations for the implementor of the trait, and assumptions for users of the trait:

trait Graph {
    type N: Show + Hash;
    type E: Show + Hash;
    ...
}

impl Graph for MyGraph {
    // Both MyNode and MyEdge must implement Show and Hash
    type N = MyNode;
    type E = MyEdge;
    ...
}

fn print_nodes<G: Graph>(g: &G) {
    // here, can assume G::N implements Show
    ...
}

Namespacing/shadowing for associated types

Associated types may have the same name as existing types in scope, except for type parameters to the trait:

struct Foo { ... }

trait Bar<Input> {
    type Foo; // this is allowed
    fn into_foo(self) -> Foo; // this refers to the trait's Foo

    type Input; // this is NOT allowed
}

By not allowing name clashes between input and output types, keep open the possibility of later allowing syntax like:

Bar<Input=u8, Foo=uint>

where both input and output parameters are constrained by name. And anyway, there is no use for clashing input/output names.

In the case of a name clash like Foo above, if the trait needs to refer to the outer Foo for some reason, it can always do so by using a type alias external to the trait.

Defaults

Notice that associated consts and types both permit defaults, just as trait methods and functions can provide defaults.

Defaults are useful both as a code reuse mechanism, and as a way to expand the items included in a trait without breaking all existing implementors of the trait.

Defaults for associated types, however, present an interesting question: can default methods assume the default type? In other words, is the following allowed?

trait ContainerKey : Clone + Hash + Eq {
    type Query: Hash = Self;
    fn compare(&self, other: &Query) -> bool { self == other }
    fn query_to_key(q: &Query) -> Self { q.clone() };
}

impl ContainerKey for String {
    type Query = str;
    fn compare(&self, other: &str) -> bool {
        self.as_slice() == other
    }
    fn query_to_key(q: &str) -> String {
        q.into_string()
    }
}

impl<K,V> HashMap<K,V> where K: ContainerKey {
    fn find(&self, q: &K::Query) -> &V { ... }
}

In this example, the ContainerKey trait is used to associate a “Query” type (for lookups) with an owned key type. This resolves the thorny “equiv” problem in HashMap, where the hash map keys are Strings but you want to index the hash map with &str values rather than &String values, i.e. you want the following to work:

// H: HashMap<String, SomeType>
H.find("some literal")

rather than having to write

H.find(&"some literal".to_string())`

The current solution involves duplicating the API surface with _equiv methods that use the somewhat subtle Equiv trait, but the associated type approach makes it easy to provide a simple, single API that covers the same use cases.

The defaults for ContainerKey just assume that the owned key and lookup key types are the same, but the default methods have to assume the default associated types in order to work.

For this to work, it must not be possible for an implementor of ContainerKey to override the default Query type while leaving the default methods in place, since those methods may no longer typecheck.

We deal with this in a very simple way:

• If a trait implementor overrides any default associated types, they must also override all default functions and methods.

• Otherwise, a trait implementor can selectively override individual default methods/functions, as they can today.

Trait implementations

Trait impl syntax is much the same as before, except that const, type, and lifetime items are allowed:

IMPL_ITEM =
  ... <existing productions>
  | 'const' IDENT ':' TYPE '=' CONST_EXP ';'
  | 'type' IDENT' '=' 'TYPE' ';'
  | 'lifetime' LIFETIME_IDENT '=' LIFETIME_REFERENCE ';'

Any type implementation must satisfy all bounds and where clauses in the corresponding trait item.

Referencing associated items

Associated items are referenced through paths. The expression path grammar was updated as part of UFCS, but to accommodate associated types and lifetimes we need to update the type path grammar as well.

The full grammar is as follows:

EXP_PATH
  = EXP_ID_SEGMENT { '::' EXP_ID_SEGMENT }*
  | TYPE_SEGMENT { '::' EXP_ID_SEGMENT }+
  | IMPL_SEGMENT { '::' EXP_ID_SEGMENT }+
EXP_ID_SEGMENT   = ID [ '::' '<' TYPE { ',' TYPE }* '>' ]

TY_PATH
  = TY_ID_SEGMENT { '::' TY_ID_SEGMENT }*
  | TYPE_SEGMENT { '::' TY_ID_SEGMENT }*
  | IMPL_SEGMENT { '::' TY_ID_SEGMENT }+

TYPE_SEGMENT = '<' TYPE '>'
IMPL_SEGMENT = '<' TYPE 'as' TRAIT_REFERENCE '>'
TRAIT_REFERENCE = ID [ '<' TYPE { ',' TYPE * '>' ]

Here are some example paths, along with what they might be referencing

// Expression paths ///////////////////////////////////////////////////////////////

a::b::c         // reference to a function `c` in module `a::b`
a::<T1, T2>     // the function `a` instantiated with type arguments `T1`, `T2`
Vec::<T>::new   // reference to the function `new` associated with `Vec<T>`
<Vec<T> as SomeTrait>::some_fn
                // reference to the function `some_fn` associated with `SomeTrait`,
                //   as implemented by `Vec<T>`
T::size_of      // the function `size_of` associated with the type or trait `T`
<T>::size_of    // the function `size_of` associated with `T` _viewed as a type_
<T as SizeOf>::size_of
                // the function `size_of` associated with `T`'s impl of `SizeOf`

// Type paths /////////////////////////////////////////////////////////////////////

a::b::C         // reference to a type `C` in module `a::b`
A<T1, T2>       // type A instantiated with type arguments `T1`, `T2`
Vec<T>::Iter    // reference to the type `Iter` associated with `Vec<T>
<Vec<T> as SomeTrait>::SomeType
                // reference to the type `SomeType` associated with `SomeTrait`,
                //   as implemented by `Vec<T>`

Ways to reference items

Next, we’ll go into more detail on the meaning of each kind of path.

For the sake of discussion, we’ll suppose we’ve defined a trait like the following:

trait Container {
    type E;
    fn empty() -> Self;
    fn insert(&mut self, E);
    fn contains(&self, &E) -> bool where E: PartialEq;
    ...
}

impl<T> Container for Vec<T> {
    type E = T;
    fn empty() -> Vec<T> { Vec::new() }
    ...
}

Via an ID_SEGMENT prefix

When the prefix resolves to a type

The most common way to get at an associated item is through a type parameter with a trait bound:

fn pick<C: Container>(c: &C) -> Option<&C::E> { ... }

fn mk_with_two<C>() -> C where C: Container, C::E = uint {
    let mut cont = C::empty();  // reference to associated function
    cont.insert(0);
    cont.insert(1);
    cont
}

For these references to be valid, the type parameter must be known to implement the relevant trait:

// Knowledge via bounds
fn pick<C: Container>(c: &C) -> Option<&C::E> { ... }

// ... or equivalently,  where clause
fn pick<C>(c: &C) -> Option<&C::E> where C: Container { ... }

// Knowledge via ambient constraints
struct TwoContainers<C1: Container, C2: Container>(C1, C2);
impl<C1: Container, C2: Container> TwoContainers<C1, C2> {
    fn pick_one(&self) -> Option<&C1::E> { ... }
    fn pick_other(&self) -> Option<&C2::E> { ... }
}

Note that Vec<T>::E and Vec::<T>::empty are also valid type and function references, respectively.

For cases like C::E or Vec<T>::E, the path begins with an ID_SEGMENT prefix that itself resolves to a type: both C and Vec<T> are types. In general, a path PREFIX::REST_OF_PATH where PREFIX resolves to a type is equivalent to using a TYPE_SEGMENT prefix <PREFIX>::REST_OF_PATH. So, for example, following are all equivalent:

fn pick<C: Container>(c: &C) -> Option<&C::E> { ... }
fn pick<C: Container>(c: &C) -> Option<&<C>::E> { ... }
fn pick<C: Container>(c: &C) -> Option<&<<C>::E>> { ... }

The behavior of TYPE_SEGMENT prefixes is described in the next subsection.

When the prefix resolves to a trait

However, it is possible for an ID_SEGMENT prefix to resolve to a trait, rather than a type. In this case, the behavior of an ID_SEGMENT varies from that of a TYPE_SEGMENT in the following way:

// a reference Container::insert is roughly equivalent to:
fn trait_insert<C: Container>(c: &C, e: C::E);

// a reference <Container>::insert is roughly equivalent to:
fn object_insert<E>(c: &Container<E=E>, e: E);

That is, if PREFIX is an ID_SEGMENT that resolves to a trait Trait:

• A path PREFIX::REST resolves to the item/path REST defined within Trait, while treating the type implementing the trait as a type parameter.

• A path <PREFIX>::REST treats PREFIX as a (DST-style) type, and is hence usable only with trait objects. See the UFCS RFC for more detail.

Note that a path like Container::E, while grammatically valid, will fail to resolve since there is no way to tell which impl to use. A path like Container::empty, however, resolves to a function roughly equivalent to:

fn trait_empty<C: Container>() -> C;

Via a TYPE_SEGMENT prefix

The following text is slightly changed from the UFCS RFC.

When a path begins with a TYPE_SEGMENT, it is a type-relative path. If this is the complete path (e.g., <int>), then the path resolves to the specified type. If the path continues (e.g., <int>::size_of) then the next segment is resolved using the following procedure. The procedure is intended to mimic method lookup, and hence any changes to method lookup may also change the details of this lookup.

Given a path <T>::m::...:

1. Search for members of inherent impls defined on T (if any) with the name m. If any are found, the path resolves to that item.

2. Otherwise, let IN_SCOPE_TRAITS be the set of traits that are in scope and which contain a member named m:

   • Let IMPLEMENTED_TRAITS be those traits from IN_SCOPE_TRAITS for which an implementation exists that (may) apply to T.
     • There can be ambiguity in the case that T contains type inference variables.
   • If IMPLEMENTED_TRAITS is not a singleton set, report an ambiguity error. Otherwise, let TRAIT be the member of IMPLEMENTED_TRAITS.
   • If TRAIT is ambiguously implemented for T, report an ambiguity error and request further type information.
   • Otherwise, rewrite the path to <T as Trait>::m::... and continue.

Via a IMPL_SEGMENT prefix

The following text is somewhat different from the UFCS RFC.

When a path begins with an IMPL_SEGMENT, it is a reference to an item defined from a trait. Note that such paths must always have a follow-on member m (that is, <T as Trait> is not a complete path, but <T as Trait>::m is).

To resolve the path, first search for an applicable implementation of Trait for T. If no implementation can be found – or the result is ambiguous – then report an error. Note that when T is a type parameter, a bound T: Trait guarantees that there is such an implementation, but does not count for ambiguity purposes.

Otherwise, resolve the path to the member of the trait with the substitution Self => T and continue.

This apparently straightforward algorithm has some subtle consequences, as illustrated by the following example:

trait Foo {
    type T;
    fn as_T(&self) -> &T;
}

// A blanket impl for any Show type T
impl<T: Show> Foo for T {
    type T = T;
    fn as_T(&self) -> &T { self }
}

fn bounded<U: Foo>(u: U) where U::T: Show {
    // Here, we just constrain the associated type directly
    println!("{}", u.as_T())
}

fn blanket<U: Show>(u: U) {
    // the blanket impl applies to U, so we know that `U: Foo` and
    // <U as Foo>::T = U (and, of course, U: Show)
    println!("{}", u.as_T())
}

fn not_allowed<U: Foo>(u: U) {
    // this will not compile, since <U as Trait>::T is not known to
    // implement Show
    println!("{}", u.as_T())
}

This example includes three generic functions that make use of an associated type; the first two will typecheck, while the third will not.

• The first case, bounded, places a Show constraint directly on the otherwise-abstract associated type U::T. Hence, it is allowed to assume that U::T: Show, even though it does not know the concrete implementation of Foo for U.

• The second case, blanket, places a Show constraint on the type U, which means that the blanket impl of Foo applies even though we do not know the concrete type that U will be. That fact means, moreover, that we can compute exactly what the associated type U::T will be, and know that it will satisfy Show. Coherence guarantees that that the blanket impl is the only one that could apply to U. (See the section “Impl specialization” under “Unresolved questions” for a deeper discussion of this point.)

• The third case assumes only that U: Foo, and therefore nothing is known about the associated type U::T. In particular, the function cannot assume that U::T: Show.

The resolution rules also interact with instantiation of type parameters in an intuitive way. For example:

trait Graph {
    type N;
    type E;
    ...
}

impl Graph for MyGraph {
    type N = MyNode;
    type E = MyEdge;
    ...
}

fn pick_node<G: Graph>(t: &G) -> &G::N {
    // the type G::N is abstract here
    ...
}

let G = MyGraph::new();
...
pick_node(G) // has type: <MyGraph as Graph>::N = MyNode

Assuming there are no blanket implementations of Graph, the pick_node function knows nothing about the associated type G::N. However, a client of pick_node that instantiates it with a particular concrete graph type will also know the concrete type of the value returned from the function – here, MyNode.

Scoping of trait and impl items

Associated types are frequently referred to in the signatures of a trait’s methods and associated functions, and it is natural and convenient to refer to them directly.

In other words, writing this:

trait Graph {
    type N;
    type E;
    fn has_edge(&self, &N, &N) -> bool;
    ...
}

is more appealing than writing this:

trait Graph {
    type N;
    type E;
    fn has_edge(&self, &Self::N, &Self::N) -> bool;
    ...
}

This RFC proposes to treat both trait and impl bodies (both inherent and for traits) the same way we treat mod bodies: all items being defined are in scope. In particular, methods are in scope as UFCS-style functions:

trait Foo {
    type AssocType;
    lifetime 'assoc_lifetime;
    const ASSOC_CONST: uint;
    fn assoc_fn() -> Self;

    // Note: 'assoc_lifetime and AssocType in scope:
    fn method(&self, Self) -> &'assoc_lifetime AssocType;

    fn default_method(&self) -> uint {
        // method in scope UFCS-style, assoc_fn in scope
        let _ = method(self, assoc_fn());
        ASSOC_CONST // in scope
    }
}

// Same scoping rules for impls, including inherent impls:
struct Bar;
impl Bar {
    fn foo(&self) { ... }
    fn bar(&self) {
        foo(self); // foo in scope UFCS-style
        ...
    }
}

Items from super traits are not in scope, however. See the discussion on super traits below for more detail.

These scope rules provide good ergonomics for associated types in particular, and a consistent scope model for language constructs that can contain items (like traits, impls, and modules). In the long run, we should also explore imports for trait items, i.e. use Trait::some_method, but that is out of scope for this RFC.

Note that, according to this proposal, associated types/lifetimes are not in scope for the optional where clause on the trait header. For example:

trait Foo<Input>
    // type parameters in scope, but associated types are not:
    where Bar<Input, Self::Output>: Encodable {

    type Output;
    ...
}

This setup seems more intuitive than allowing the trait header to refer directly to items defined within the trait body.

It’s also worth noting that trait-level where clauses are never needed for constraining associated types anyway, because associated types also have where clauses. Thus, the above example could (and should) instead be written as follows:

trait Foo<Input> {
    type Output where Bar<Input, Output>: Encodable;
    ...
}

Constraining associated types

Associated types are not treated as parameters to a trait, but in some cases a function will want to constrain associated types in some way. For example, as explained in the Motivation section, the Iterator trait should treat the element type as an output:

trait Iterator {
    type A;
    fn next(&mut self) -> Option<A>;
    ...
}

For code that works with iterators generically, there is no need to constrain this type:

fn collect_into_vec<I: Iterator>(iter: I) -> Vec<I::A> { ... }

But other code may have requirements for the element type:

• That it implements some traits (bounds).
• That it unifies with a particular type.

These requirements can be imposed via where clauses:

fn print_iter<I>(iter: I) where I: Iterator, I::A: Show { ... }
fn sum_uints<I>(iter: I) where I: Iterator, I::A = uint { ... }

In addition, there is a shorthand for equality constraints:

fn sum_uints<I: Iterator<A = uint>>(iter: I) { ... }

In general, a trait like:

trait Foo<Input1, Input2> {
    type Output1;
    type Output2;
    lifetime 'a;
    const C: bool;
    ...
}

can be written in a bound like:

T: Foo<I1, I2>
T: Foo<I1, I2, Output1 = O1>
T: Foo<I1, I2, Output2 = O2>
T: Foo<I1, I2, Output1 = O1, Output2 = O2>
T: Foo<I1, I2, Output1 = O1, 'a = 'b, Output2 = O2>
T: Foo<I1, I2, Output1 = O1, 'a = 'b, C = true, Output2 = O2>

The output constraints must come after all input arguments, but can appear in any order.

Note that output constraints are allowed when referencing a trait in a type or a bound, but not in an IMPL_SEGMENT path:

• As a type: fn foo(obj: Box<Iterator<A = uint>> is allowed.
• In a bound: fn foo<I: Iterator<A = uint>>(iter: I) is allowed.
• In an IMPL_SEGMENT: <I as Iterator<A = uint>>::next is not allowed.

The reason not to allow output constraints in IMPL_SEGMENT is that such paths are references to a trait implementation that has already been determined – it does not make sense to apply additional constraints to the implementation when referencing it.

Output constraints are a handy shorthand when using trait bounds, but they are a necessity for trait objects, which we discuss next.

Trait objects

When using trait objects, the Self type is “erased”, so different types implementing the trait can be used under the same trait object type:

impl Show for Foo { ... }
impl Show for Bar { ... }

fn make_vec() -> Vec<Box<Show>> {
    let f = Foo { ... };
    let b = Bar { ... };
    let mut v = Vec::new();
    v.push(box f as Box<Show>);
    v.push(box b as Box<Show>);
    v
}

One consequence of erasing Self is that methods using the Self type as arguments or return values cannot be used on trait objects, since their types would differ for different choices of Self.

In the model presented in this RFC, traits have additional input parameters beyond Self, as well as associated types that may vary depending on all of the input parameters. This raises the question: which of these types, if any, are erased in trait objects?

The approach we take here is the simplest and most conservative: when using a trait as a type (i.e., as a trait object), all input and output types must be provided as part of the type. In other words, only the Self type is erased, and all other types are specified statically in the trait object type.

Consider again the following example:

trait Foo<Input1, Input2> {
    type Output1;
    type Output2;
    lifetime 'a;
    const C: bool;
    ...
}

Unlike the case for static trait bounds, which do not have to specify any of the associated types, lifetimes, or consts, (but do have to specify the input types), trait object types must specify all of the types:

fn consume_foo<T: Foo<I1, I2>>(t: T) // this is valid
fn consume_obj(t: Box<Foo<I1, I2>>)  // this is NOT valid

// but this IS valid:
fn consume_obj(t: Box<Foo<I1, I2, Output1 = O2, Output2 = O2, 'a = 'static, C = true>>)

With this design, it is clear that none of the non-Self types are erased as part of trait objects. But it leaves wiggle room to relax this restriction later on: trait object types that are not allowed under this design can be given meaning in some later design.

Inherent associated items

All associated items are also allowed in inherent impls, so a definition like the following is allowed:

struct MyGraph { ... }
struct MyNode { ... }
struct MyEdge { ... }

impl MyGraph {
    type N = MyNode;
    type E = MyEdge;

    // Note: associated types in scope, just as with trait bodies
    fn has_edge(&self, &N, &N) -> bool {
        ...
    }

    ...
}

Inherent associated items are referenced similarly to trait associated items:

fn distance(g: &MyGraph, from: &MyGraph::N, to: &MyGraph::N) -> uint { ... }

Note, however, that output constraints do not make sense for inherent outputs:

// This is *not* a legal type:
MyGraph<N = SomeNodeType>

The input/output type distinction

When designing a trait that references some unknown type, you now have the option of taking that type as an input parameter, or specifying it as an output associated type. What are the ramifications of this decision?

Coherence implications

Input types are used when determining which impl matches, even for the same Self type:

trait Iterable1<A> {
    type I: Iterator<A>;
    fn iter(self) -> I;
}

// These impls have distinct input types, so are allowed
impl Iterable1<u8> for Foo { ... }
impl Iterable1<char> for Foo { ... }

trait Iterable2 {
    type A;
    type I: Iterator<A>;
    fn iter(self) -> I;
}

// These impls apply to a common input (Foo), so are NOT allowed
impl Iterable2 for Foo { ... }
impl Iterable2 for Foo { ... }

More formally, the coherence property is revised as follows:

• Given a trait and values for all its type parameters (inputs, including Self), there is at most one applicable impl.

In the trait reform RFC, coherence is guaranteed by maintaining two other key properties, which are revised as follows:

Orphan check: Every implementation must meet one of the following conditions:

1. The trait being implemented (if any) must be defined in the current crate.

2. At least one of the input type parameters (including but not necessarily Self) must meet the following grammar, where C is a struct or enum defined within the current crate:

   T = C
     | [T]
     | [T, ..n]
     | &T
     | &mut T
     | ~T
     | (..., T, ...)
     | X<..., T, ...> where X is not bivariant with respect to T
   

Overlapping instances: No two implementations can be instantiable with the same set of types for the input type parameters.

See the trait reform RFC for more discussion of these properties.

Type inference implications

Finally, output type parameters can be inferred/resolved as soon as there is a matching impl based on the input type parameters. Because of the coherence property above, there can be at most one.

On the other hand, even if there is only one applicable impl, type inference is not allowed to infer the input type parameters from it. This restriction makes it possible to ensure crate concatenation: adding another crate may add impls for a given trait, and if type inference depended on the absence of such impls, importing a crate could break existing code.

In practice, these inference benefits can be quite valuable. For example, in the Add trait given at the beginning of this RFC, the Sum output type is immediately known once the input types are known, which can avoid the need for type annotations.

Limitations

The main limitation of associated items as presented here is about associated types in particular. You might be tempted to write a trait like the following:

trait Iterable {
    type A;
    type I: Iterator<&'a A>; // what is the lifetime here?
    fn iter<'a>(&'a self) -> I;  // and how to connect it to self?
}

The problem is that, when implementing this trait, the return type I of iter must generally depend on the lifetime of self. For example, the corresponding method in Vec looks like the following:

impl<T> Vec<T> {
    fn iter(&'a self) -> Items<'a, T> { ... }
}

This means that, given a Vec<T>, there isn’t a single type Items<T> for iteration – rather, there is a family of types, one for each input lifetime. In other words, the associated type I in the Iterable needs to be “higher-kinded”: not just a single type, but rather a family:

trait Iterable {
    type A;
    type I<'a>: Iterator<&'a A>;
    fn iter<'a>(&self) -> I<'a>;
}

In this case, I is parameterized by a lifetime, but in other cases (like map) an associated type needs to be parameterized by a type.

In general, such higher-kinded types (HKTs) are a much-requested feature for Rust, and they would extend the reach of associated types. But the design and implementation of higher-kinded types is, by itself, a significant investment. The point of view of this RFC is that associated items bring the most important changes needed to stabilize our existing traits (and add a few key others), while HKTs will allow us to define important traits in the future but are not necessary for 1.0.

Encoding higher-kinded types

That said, it’s worth pointing out that variants of higher-kinded types can be encoded in the system being proposed here.

For example, the Iterable example above can be written in the following somewhat contorted style:

trait IterableOwned {
    type A;
    type I: Iterator<A>;
    fn iter_owned(self) -> I;
}

trait Iterable {
    fn iter<'a>(&'a self) -> <&'a Self>::I where &'a Self: IterableOwned {
        IterableOwned::iter_owned(self)
    }
}

The idea here is to define a trait that takes, as input type/lifetimes parameters, the parameters to any HKTs. In this case, the trait is implemented on the type &'a Self, which includes the lifetime parameter.

We can in fact generalize this technique to encode arbitrary HKTs:

// The kind * -> *
trait TypeToType<Input> {
    type Output;
}
type Apply<Name, Elt> where Name: TypeToType<Elt> = Name::Output;

struct Vec_;
struct DList_;

impl<T> TypeToType<T> for Vec_ {
    type Output = Vec<T>;
}

impl<T> TypeToType<T> for DList_ {
    type Output = DList<T>;
}

trait Mappable
{
    type E;
    type HKT where Apply<HKT, E> = Self;

    fn map<F>(self, f: E -> F) -> Apply<HKT, F>;
}

While the above demonstrates the versatility of associated types and where clauses, it is probably too much of a hack to be viable for use in libstd.

Associated consts in generic code

If the value of an associated const depends on a type parameter (including Self), it cannot be used in a constant expression. This restriction will almost certainly be lifted in the future, but this raises questions outside the scope of this RFC.

Staging

Associated lifetimes are probably not necessary for the 1.0 timeframe. While we currently have a few traits that are parameterized by lifetimes, most of these can go away once DST lands.

On the other hand, associated lifetimes are probably trivial to implement once associated types have been implemented.

Other interactions

Interaction with implied bounds

As part of the implied bounds idea, it may be desirable for this:

fn pick_node<G>(g: &G) -> &<G as Graph>::N

to be sugar for this:

fn pick_node<G: Graph>(g: &G) -> &<G as Graph>::N

But this feature can easily be added later, as part of a general implied bounds RFC.

Future-proofing: specialization of impls

In the future, we may wish to relax the “overlapping instances” rule so that one can provide “blanket” trait implementations and then “specialize” them for particular types. For example:

trait Sliceable {
    type Slice;
    // note: not using &self here to avoid need for HKT
    fn as_slice(self) -> Slice;
}

impl<'a, T> Sliceable for &'a T {
    type Slice = &'a T;
    fn as_slice(self) -> &'a T { self }
}

impl<'a, T> Sliceable for &'a Vec<T> {
    type Slice = &'a [T];
    fn as_slice(self) -> &'a [T] { self.as_slice() }
}

But then there’s a difficult question:

fn dice<A>(a: &A) -> &A::Slice where &A: Sliceable {
    a // is this allowed?
}

Here, the blanket and specialized implementations provide incompatible associated types. When working with the trait generically, what can we assume about the associated type? If we assume it is the blanket one, the type may change during monomorphization (when specialization takes effect)!

The RFC does allow generic code to “see” associated types provided by blanket implementations, so this is a potential problem.

Our suggested strategy is the following. If at some later point we wish to add specialization, traits would have to opt in explicitly. For such traits, we would not allow generic code to “see” associated types for blanket implementations; instead, output types would only be visible when all input types were concretely known. This approach is backwards-compatible with the RFC, and is probably a good idea in any case.

Alternatives

Multidispatch through tuple types

This RFC clarifies trait matching by making trait type parameters inputs to matching, and associated types outputs.

A more radical alternative would be to remove type parameters from traits, and instead support multiple input types through a separate multidispatch mechanism.

In this design, the Add trait would be written and implemented as follows:

// Lhs and Rhs are *inputs*
trait Add for (Lhs, Rhs) {
    type Sum; // Sum is an *output*
    fn add(&Lhs, &Rhs) -> Sum;
}

impl Add for (int, int) {
    type Sum = int;
    fn add(left: &int, right: &int) -> int { ... }
}

impl Add for (int, Complex) {
    type Sum = Complex;
    fn add(left: &int, right: &Complex) -> Complex { ... }
}

The for syntax in the trait definition is used for multidispatch traits, here saying that impls must be for pairs of types which are bound to Lhs and Rhs respectively. The add function can then be invoked in UFCS style by writing

Add::add(some_int, some_complex)

Advantages of the tuple approach:

• It does not force a distinction between Self and other input types, which in some cases (including binary operators like Add) can be artificial.

• Makes it possible to specify input types without specifying the trait: <(A, B)>::Sum rather than <A as Add<B>>::Sum.

Disadvantages of the tuple approach:

• It’s more painful when you do want a method rather than a function.

• Requires where clauses when used in bounds: where (A, B): Trait rather than A: Trait<B>.

• It gives two ways to write single dispatch: either without for, or using for with a single-element tuple.

• There’s a somewhat jarring distinction between single/multiple dispatch traits, making the latter feel “bolted on”.

• The tuple syntax is unusual in acting as a binder of its types, as opposed to the Trait<A, B> syntax.

• Relatedly, the generics syntax for traits is immediately understandable (a family of traits) based on other uses of generics in the language, while the tuple notation stands alone.

• Less clear story for trait objects (although the fact that Self is the only erased input type in this RFC may seem somewhat arbitrary).

On balance, the generics-based approach seems like a better fit for the language design, especially in its interaction with methods and the object system.

A backwards-compatible version

Yet another alternative would be to allow trait type parameters to be either inputs or outputs, marking the inputs with a keyword in:

trait Add<in Rhs, Sum> {
    fn add(&Lhs, &Rhs) -> Sum;
}

This would provide a way of adding multidispatch now, and then adding associated items later on without breakage. If, in addition, output types had to come after all input types, it might even be possible to migrate output type parameters like Sum above into associated types later.

This is perhaps a reasonable fallback, but it seems better to introduce a clean design with both multidispatch and associated items together.

Unresolved questions

Super traits

This RFC largely ignores super traits.

Currently, the implementation of super traits treats them identically to a where clause that bounds Self, and this RFC does not propose to change that. However, a follow-up RFC should clarify that this is the intended semantics for super traits.

Note that this treatment of super traits is, in particular, consistent with the proposed scoping rules, which do not bring items from super traits into scope in the body of a subtrait; they must be accessed via Self::item_name.

Equality constraints in where clauses

This RFC allows equality constraints on types for associated types, but does not propose a similar feature for where clauses. That will be the subject of a follow-up RFC.

Multiple trait object bounds for the same trait

The design here makes it possible to write bounds or trait objects that mention the same trait, multiple times, with different inputs:

fn mulit_add<T: Add<int> + Add<Complex>>(t: T) -> T { ... }
fn mulit_add_obj(t: Box<Add<int> + Add<Complex>>) -> Box<Add<int> + Add<Complex>> { ... }

This seems like a potentially useful feature, and should be unproblematic for bounds, but may have implications for vtables that make it problematic for trait objects. Whether or not such trait combinations are allowed will likely depend on implementation concerns, which are not yet clear.

Generic associated consts in match patterns

It seems desirable to allow constants that depend on type parameters in match patterns, but it’s not clear how to do so while still checking exhaustiveness and reachability of the match arms. Most likely this requires new forms of where clause, to constrain associated constant values.

For now, we simply defer the question.

Generic associated consts in array sizes

It would be useful to be able to use trait-associated constants in generic code.

// Shouldn't this be OK?
const ALIAS_N: usize = <T>::N;
let x: [u8; <T>::N] = [0u8; ALIAS_N];
// Or...
let x: [u8; T::N + 1] = [0u8; T::N + 1];

However, this causes some problems. What should we do with the following case in type checking, where we need to prove that a generic is valid for any T?

let x: [u8; T::N + T::N] = [0u8; 2 * T::N];

We would like to handle at least some obvious cases (e.g. proving that T::N == T::N), but without trying to prove arbitrary statements about arithmetic. The question of how to do this is deferred.