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Improving operator requirements in protocols


When a type conforms to a protocol that declares an operator as a requirement, that operator must be implemented as a global function defined outside of the conforming type. This can lead both to user confusion and to poor type checker performance since the global namespace is overcrowded with a large number of operator overloads. This proposal mitigates both of those issues by proposing that operators in protocols be declared statically (to change and clarify where the conforming type implements it) and that Swift use universal lookup for operators that finds candidates both at the global scope and within types.

Swift-evolution thread: Discussion about operators and protocols in the context of FloatingPoint


The proposal came about as a result of discussion about SE-0067: Enhanced Floating Point Protocols. To implement the numerous arithmetic and comparison operators, this protocol defined named instance methods for them and then implemented the global operator functions to delegate to them. For example,

public protocol FloatingPoint {
  func adding(rhs: Self) -> Self
  // and others

public func + <T: FloatingPoint>(lhs: T, rhs: T) -> T {
  return lhs.adding(rhs)

One of the motivating factors for these named methods was to make the operators generic and reduce the number of concrete global overloads, which would improve the type checker's performance compared to individual concrete overloads for each conforming type. Some concerns were raised about the use of named methods:

  • They bloat the public interface. Every floating point type would expose mutating and non-mutating methods for each arithmetic operation, as well as non-mutating methods for the comparisons. We don't expect users to actually call these methods directly but they must be present in the public interface because they are requirements of the protocol. Therefore, they would clutter API documentation and auto-complete lists and make the properties and methods users actually want to use less discoverable.
  • Swift's naming guidelines encourage the use of "terms of art" for naming when it is appropriate. In this case, the operator itself is the term of art. It feels odd to elevate (2.0).adding(2.0).isEqual(to: 4.0) to the same first-class status as 2.0 + 2.0 == 4.0; this is the situation that overloaded operators were made to prevent.
  • Devising good names for the operators is tricky; the swift-evolution list had a fair amount of bikeshedding about the naming and preposition placement of isLessThanOrEqual(to:) in order to satisfy API guidelines, for example.
  • Having both an adding method and a + operator provides two ways for the user to do the same thing. This may lead to confusion if users think that the two ways of adding have slightly different semantics.

Some contributors to the discussion list have expressed concerns about operators being members of protocols at all. I feel that removing them entirely would be a step backwards for the Swift language; a protocol is not simply a list of properties and methods that a type must implement, but rather a higher-level set of requirements. Just as properties, methods, and associated types are part of that requirement set, it makes sense that an arithmetic type, for example, would declare arithmetic operators among its requirements as well.

Inconsistency in the current operator design with protocols

When a protocol declares an operator as a requirement, that requirement is located inside the protocol definition. For example, consider Equatable:

protocol Equatable {
  func ==(lhs: Self, rhs: Self) -> Bool

However, since operators are global functions, the actual implementation of that operator for a conforming type must be made outside the type definition. This can look particularly odd when extending an existing type to conform to an operator-only protocol:

extension Foo: Equatable {}

func ==(lhs: Foo, rhs: Foo) -> Bool {
  // Implementation goes here

This is an odd inconsistency in the Swift language, driven by the fact that operators must be global functions. What's worse is that every concrete type that conforms to Equatable must provide the operator function at global scope. As the number of types conforming to this protocol increases, so does the workload of the compiler to perform type checking.

Proposed solution

When a protocol wishes to declare operators that conforming types must implement, we propose adding the ability to declare operator requirements as static members of the protocol:

protocol Equatable {
  static func ==(lhs: Self, rhs: Self) -> Bool

Types conforming to a protocol that contains static operators would implement the operators as static methods (or class methods for class types) defined within the type:

struct Foo: Equatable {
  let value: Int

  static func ==(lhs: Foo, rhs: Foo) -> Bool {
    return lhs.value == rhs.value

let f1 = Foo(value: 5)
let f2 = Foo(value: 10)
let eq = (f1 == f2)

We initially considered requiring users to declare a global "trampoline" operator for each operator inside their protocols. This operator would be generic and constrained to that protocol type and would use the static types of its actual arguments to dispatch to the correct implementation. However, this is a burden on protocol authors to provide these stub functions that are purely an implementation detail.

Instead, Swift should always perform operator lookup universally such that it sees all operators defined at either module scope or within a type/extension of a type. This gives us the syntactic improvements immediately and the natural Swift thing of defining your functionality within the type or an extension thereof just works.

While it may seem odd that operators will be the only place where Swift does such universal lookup, operators can be considered a special case. This is a cleaner approach than requiring the user to manually provide trampoline operators. There is really no way to avoid it: we simply don’t want normal lexical name lookup for operators when they can be defined in types.

This approach does not (directly) give any of the type checker performance/QoI improvements mentioned above. The key insight here is that we don't want to consider both a generic operator based on some protocol (for example, + for Arithmetic types) and the operator functions used to satisfy that requirement.

Therefore, we can achieve the performance improvements by making that insight part of the semantic model: when we find all operators, we also find the operators in the protocols themselves. The operators in the protocols are naturally generic; e.g., the Arithmetic + effectively has a generic function type like this:

<Self: Arithmetic>(Self, Self) -> Self

Then, we say that we do not consider an operator function if it implements a protocol requirement, because the requirement is a generalization of all of the operator functions that satisfy that requirement. With this rule, we’re effectively getting the same effects as if users had declared trampoline operators, but it's automatic.

Benefits of this approach

By using the name of the operator itself as the method, this approach avoids bloating the public interfaces of protocols and conforming types with additional named methods, reducing user confusion. This also will lead to better consistency going forward, as various authors of such protocols will not be providing their own method names.

This approach also significantly reduces the number of symbols in the global namespace. Consider a protocol like Equatable, which requires a global definition of == for every type that conforms to it. The approach described above with universal lookup will ignore all of the implementations of == on types where it satisfies the Equatable conformance, which leaves only the single operator on Equatable itself to be considered instead. (This assumes that nobody implements == while not conforming to Equatable; while this is certainly possible, it is likely to be rare enough that it would not negatively impact performance.)

Other kinds of operators (prefix, postfix, assignment)

Static operator methods have the same signatures as their global counterparts. So, for example, prefix and postfix operators as well as assignment operators would be defined the way one would expect:

protocol SomeProtocol {
  static func +=(lhs: inout Self, rhs: Self)
  static prefix func ~(value: Self) -> Self

  // These are deprecated, of course, but used here just to serve as an
  // example.
  static prefix func ++(value: inout Self) -> Self
  static postfix func ++(value: inout Self) -> Self

Class types and inheritance

While this approach works well for value types, it has the same limitations that today's global operators have with regard to class types; namely that they are dispatched based on the static type of the operands rather than their dynamic types. This can lead to surprises when using base class references.

This is not a regression from current behavior and we leave that problem open for a future dedicated design. For now, we require that operators implemented in a class are either static or final class methods.

We do note, however, that the common case of "Subclass uses the result of Superclass's operator in its computation" has a quite elegant solution in this design that does not involve overriding. Consider this example:

protocol Equatable {
  static func ==(lhs: Self, rhs: Self) -> Bool

class Superclass: Equatable {
  var foo: Int

  static func ==(lhs: Superclass, rhs: Superclass) -> Bool {
    return ==

class Subclass: Superclass {
  var bar: String

  static func ==(lhs: Subclass, rhs: Subclass) -> Bool {
    guard lhs as Superclass == rhs as Superclass else {
      return false
    return ==

Since the operators are dispatched based on the static types of the operands, the explicit up-casts to the superclass allows us to reuse its implementation as part of our subclass's computation.

Removal of non-static protocol operators

Because the proposed solution serves as a replacement and improvement for the existing syntax used to declare operator requirements in protocols, we propose that the non-static operator method syntax be removed in Swift 3. Going forward, static member operators should be the only way to define operators that are required for protocol conformance. This is a breaking change for existing code, but supporting two kinds of operators with different declaration and use syntax would lead to significant user confusion.

Global operator functions would be unaffected by this change. Users would still be able to define them as before.

Detailed design

Currently, the Swift language allows the use of operators as the names of global functions and of functions in protocols. This proposal is essentially asking to extend that list to include static/class methods of protocols and concrete types.

Interestingly, the production rules themselves of the Swift grammar for function declarations already appear to support declaring static functions inside a protocol or other type with names that are operators. In fact, declaring a static operator function in a protocol works today (that is, the static modifier is ignored).

However, defining such a function in a concrete type fails with the error operators are only allowed at global scope. This area of Parser::parseDeclFunc appears to be the likely place to make a change to allow this.

Restrictions on methods with operator names

Since methods with operator names are now found as part of a universal lookup, we restrict a few characteristics of their declarations as follows:

  • Methods with operator names must be static (or alternatively final class inside classes). Non-static methods with operator names are an error.

  • Methods with operator names must satisfy the same function signature requirements as global operator functions (infix operators take two arguments, prefix/postfix operators take one argument, and so forth).

Impact on existing code

The ability to declare operators as static/class functions inside a type is a new feature and would not affect existing code.

Changing the way operators are declared in protocols (static instead of non-static) is a breaking change. As described above, we propose removing it entirely in Swift 3.

Applying this change to the protocols already in the Swift standard library (such as Equatable) would be a breaking change, because it would change the way by which subtypes conform to that protocol. It might be possible to implement a quick fix that hoists a global operator function into the subtype's definition, either by making it static and moving the code itself or by wrapping it in an extension.

Alternatives considered

One alternative would be to do nothing. This would leave us with the problems cited above:

  • Concrete types either provide their own global operator overloads, potentially exploding the global namespace and increasing the workload of the type checker...
  • ...or they define generic operators that delegate to named methods, but those named methods bloat the public interface of the type.
  • Furthermore, there is no consistency required for these named methods among different types; each can define its own, and subtle differences in naming can lead to user confusion.

Another alternative would be that instead of using static methods, operators could be defined as instance methods on a type. For example,

protocol SomeProtocol {
  func +(rhs: Self) -> Self

struct SomeType: SomeProtocol {
  func +(rhs: SomeType) -> SomeType { ... }

func + <T: SomeProtocol>(lhs: T, rhs: T) -> T {
  return lhs.+(rhs)

There is not much to be gained by doing this, however. It does not solve the dynamic dispatch problem for classes described above, and it would require writing operator method signatures that differ from those of the global operators because the first argument instead becomes the implicit self. As a matter of style, when it doesn't necessarily seem appropriate to elevate one argument of an infix operator—especially one that is commutative—to the special status of "receiver" while the other remains an argument.

Likewise, commutative operators with heterogeneous arguments are more awkward to implement if operators are instance methods. Consider a contrived example of a CustomStringProtocol type that supports concatenation with Character using the + operator, commutatively. With static operators, both versions of the operator are declared in CustomStringProtocol, as one would expect:

protocol CustomStringProtocol {
  static func +(lhs: Self, rhs: Character) -> Self
  static func +(lhs: Character, rhs: Self) -> Self

Likewise, the implementation of both operators would be contained entirely within the conforming types. If these were instance methods, it's unclear how the version that has the Character argument on the left-hand side would be expressed in the protocol, or how it would be implemented if an instance of Character were the receiver. Would it be an extension on the Character type? This would split the implementation of an operation that logically belongs to CustomStringProtocol across two different locations in the code, which is something we're trying to avoid.


Thanks to Chris Lattner and Dave Abrahams for contributing to the early discussions, particularly regarding the need to improve type checker performance by genericizing protocol-based operators. Thanks also to Doug Gregor who provided some incredibly valuable insight near the end of the review process that was significant enough that I consider him now a coäuthor of the proposal.