Feature: Generic Function Type Alias

Status: Background material. Normative text is now in dartLangSpec.tex.

This document is an informal specification of a feature supporting the definition of function type aliases using a more expressive syntax than the one available today, such that it also covers generic function types. The feature also introduces syntax for specifying function types directly, such that they can be used in type annotations etc. without going via a typedef.

In this document, a generic function type denotes the type of a function whose declaration includes a list of formal type parameters. It could also have been called a generic-function type, because it is “the type of a generic function”. Note that this differs from “a type parameterized name F whose instances F denote function types”, which might perhaps be called a generic function-type. In this document the latter is designated as a parameterized typedef. Examples clarifying this distinction are given below.

This feature introduces a new syntactic form of typedef declaration which includes an identifier and a type, connecting the two with an equals sign, =. The effect of such a declaration is that the name is declared to be an alias for the type. Type parameterization may occur in the declared type (declaring a generic function type) as well as on the declared name (declaring a parameterized typedef). This feature also introduces syntax for specifying function types directly, using a syntax which is similar to the header of a function declaration.

The motivation for adding this feature is that it allows developers to specify generic function types at all, and to specify function types everywhere a type is expected. That includes type annotations, return types, actual type arguments, and formal type parameter bounds. Currently there is no way to specify a function type directly in these situations. Even in the case where a function type can be specified (such as a type annotation for a formal parameter) it may be useful for readability to declare a name as an alias of a complex type, and use that name instead of the type.


Using the new syntax, a function type alias may be declared as follows:

typedef F = List<T> Function<T>(T);

This declares F to be the type of a function that accepts one type parameter T and one value parameter of type T whose name is unspecified, and returns a result of type List<T>. It is possible to use the new syntax to declare function types that we can already declare using the existing typedef declaration. For instance, G and H both declare the same type:

typedef G = List<int> Function(int); // New form.
typedef List<int> H(int i); // Old form.

Note that the name of the parameter is required in the old form, but the type may be omitted. In contrast, the type is required in the new form, but the name may be omitted.

The reason for having two ways to express the same thing is that the new form seamlessly covers non-generic functions as well as generic ones, and developers might prefer to use the new form everywhere, for improved readability.

There is a difference between declaring a generic function type and declaring a typedef which takes a type argument. The former is a declaration of a single type which describes a certain class of runtime entities: Functions that are capable of accepting some type arguments as well as some value arguments, both at runtime. The latter is a compile-time mapping from types to types: It accepts a type argument at compile time and returns a type, which may be used, say, as a type annotation. We use the phrase parameterized typedef to refer to the latter. Dart has had support for parameterized typedefs for a while, and the new syntax supports parameterized typedefs as well. Here is an example of a parameterized typedef, and a usage thereof:

typedef I<T> = List<T> Function(T); // New form.
typedef List<T> J<T>(T t); // Old form.
I<int> myFunction(J<int> f) => f;

In this example, we have declared two equivalent parameterized typedefs I and J, and we have used an instantiation of each of them in the type annotations on myFunction. Note that the type of myFunction does not include any generic types, it is just a function that accepts an argument and returns a result, both of which have a non-generic function type that we have obtained by instantiating a parameterized typedef. The argument type might as well have been declared using the traditional function signature syntax, and the return type (and the argument type, by the way) might as well have been declared using a regular, non-parameterized typedef:

typedef List<int> K(int i); // Old form, non-generic.
K myFunction2(List<int> f(int i)) => f; // Same as myFunction.

The new syntax allows for using the two kinds of type parameters together:

typedef L<T> = List<T> Function<S>(S, {T Function(int, S) factory});

This declares L to be a parameterized typedef; when instantiating L with an actual type argument as in L<String>, it becomes the type of a generic function that accepts a type argument S and two value arguments: one required positional argument of type S, and one named optional argument with name factory and type String Function(int, S); finally, it returns a value of type List<String>.


The new form of typedef declaration uses the following syntax (there are no deletions from the grammar; addition of a new rule or a new alternative in a rule is marked with NEW and modified rules are marked CHANGED):

  metadata 'typedef' typeAliasBody |
  metadata 'typedef' identifier typeParameters? '=' functionType ';' // NEW
functionType: // NEW
  returnType? 'Function' typeParameters? parameterTypeList
parameterTypeList: // NEW
  '(' ')' |
  '(' normalParameterTypes ','? ')' |
  '(' normalParameterTypes ',' optionalParameterTypes ')' |
  '(' optionalParameterTypes ')'
normalParameterTypes: // NEW
  normalParameterType (',' normalParameterType)*
normalParameterType: // NEW
  metadata (type | typedIdentifier)
optionalParameterTypes: // NEW
  optionalPositionalParameterTypes | namedParameterTypes
optionalPositionalParameterTypes: // NEW
  '[' normalParameterTypes ','? ']'
namedParameterTypes: // NEW
  '{' namedParameterType (',' namedParameterType)* ','? '}'
namedParameterType: // NEW
  metadata typedIdentifier
typedIdentifier: // NEW
  type identifier
type: // CHANGED
  typeWithoutFunction |
typeWithoutFunction: // NEW
  typeName typeArguments?
typeWithoutFunctionList: // NEW
  typeWithoutFunction (',' typeWithoutFunction)*
mixins: // CHANGED
  'with' typeWithoutFunctionList
interfaces: // CHANGED
  'implements' typeWithoutFunctionList
superclass: // CHANGED
  'extends' typeWithoutFunction
mixinApplication: // CHANGED
  typeWithoutFunction mixins interfaces?
newExpression: // CHANGED
  'new' typeWithoutFunction ('.' identifier)? arguments
constObjectExpression: // CHANGED
  'const' typeWithoutFunction ('.' identifier)? arguments
redirectingFactoryConstructorSignature: // CHANGED
  'const'? 'factory' identifier ('.' identifier)?
  formalParameterList '=' typeWithoutFunction ('.' identifier)?

The syntax relies on treating Function as a fixed element in a function type, similar to a keyword or a symbol (many languages use symbols like -> to mark function types).

The rationale for using this form is that it makes a function type very similar to the header in a declaration of a function with that type: Just replace Function by the name of the function, and add missing parameter names and default values.

The syntax differs from the existing function type syntax (functionSignature) in that the existing syntax allows the type of a parameter to be omitted, but the new syntax allows names of positional parameters to be omitted. The rationale for this change is that a function type where a parameter has a specified name and no type is very likely to be a mistake. For instance, int Function(int) should not be the type of a function that accepts an argument named “int” of type dynamic, it should specify int as the parameter type and allow the name to be unspecified. It is still possible to opt in and specify the parameter name, which may be useful as documentation, e.g., if several arguments have the same type.

The modification of the rule for the nonterminal type causes parsing ambiguities. The following disambiguation rule applies: If the parser is at a location L where the tokens starting at L may be a type or some other construct (e.g., in the body of a method, when parsing something that may be a statement and may also be a declaration), the parser must commit to parsing a type if it is looking at the identifier Function followed by < or (, or it is looking at a type followed by the identifier Function followed by < or (.

Note that this disambiguation rule does require parsers to have unlimited lookahead. However, if a parsing strategy is used where the token stream already contains references from each opening bracket (such as < or () to the corresponding closing bracket then the decision can be taken in a fixed number of steps: If the current token is Function then check the immediate successor (< or ( means yes, we are looking at a type, everything else means no) and we're done; if the first token is an identifier other than Function then we can check whether it is a qualified by looking at no more than the two next tokens, and we may then check whether the next token again is <; if it is not then we look for Function and the token after that, and if it is < then look for the corresponding > (we have now skipped a generic class type), and then the successor to that token again must be Function, and we finally check its successor (looking for < or ( again). This skips over the presumed type arguments to a generic class type without checking that they are actually type arguments, but we conjecture that there are no syntactically correct alternatives (for example, we conjecture that there is no syntactically correct statement, not a declaration, starting with SomeIdentifier<...> Function(... where the angle brackets are balanced).

Note that this disambiguation rule will prevent parsing some otherwise correct programs. For instance, the declaration of an asynchronous function named Function with an omitted return type (meaning dynamic) and an argument named int of type dynamic using Function(int) async {} will be a parse error, because the parser will commit to parsing a type after having seen “Function(” as a lookahead. However, we do not expect that it will be a serious problem for developers to be unable to write such programs.


Consider a typedef declaration as introduced by this feature, i.e., a construct on the form

metadata 'typedef' identifier typeParameters? '=' functionType ';'

This declaration introduces identifier into the enclosing library scope.

Consider a parameterized typedef, i.e., a construct on the form

metadata 'typedef' identifier typeParameters '=' functionType ';'

Note that in this case the typeParameters cannot be omitted. This construct introduces a scope known as the typedef scope. Each typedef scope is nested inside the library scope of the enclosing library. Every formal type parameter declared by the typeParameters in this construct introduces a type variable into its enclosing typedef scope. The typedef scope is the current scope for the typeParameters themselves, and for the functionType.

Consider a functionType specifying a generic function type, i.e., a construct on the form

returnType? 'Function' typeParameters parameterTypeList

Note again that typeParameters are present, not optional. This construct introduces a scope known as a function type scope. The function type scope is nested inside the current scope for the associated functionType. Every formal type parameter declared by the typeParameters introduces a type variable into its enclosing function type scope. The function type scope is the current scope for the entire functionType.

This implies that parameterized typedefs and function types are capable of specifying F-bounded type parameters, because the type parameters are in scope in the type parameter list itself.

Static Analysis

Consider a typedef declaration as introduced by this feature, i.e., a construct on the form

metadata 'typedef' identifier typeParameters? '=' functionType ';'

It is a compile-time error if a name N introduced into a library scope by a typedef has an associated functionType which depends directly or indirectly on N. It is a compile-time error if a bound on a formal type parameter in typeParameters is not a type. It is a compile-time error if a typedef has an associated functionType which is not a well-bounded type when analyzed under the assumption that every identifier resolving to a formal type parameter in typeParameters is a type satisfying its bound. It is a compile-time error if an instantiation F<T1..Tk> of a parameterized typedef is mal-bounded.

This implies that a typedef cannot be recursive. It can only introduce a name as an alias for a type which is already expressible as a functionType, or a name for a type-level function F where every well-bounded invocation F<T1..Tk> denotes a type which could be expressed as a functionType. In the terminology of kind systems, we could say that a typedef can define entities of kind * and of kind * -> *, and, when it is assumed that every formal type parameter of the typedef (if any) has kind *, it is an error if the right hand side of the declaration denotes an entity of any other kind than *; in particular, declarations of entities of kind * -> * cannot be curried.

*Note that the constraints required to ensure that the body of a typedef is well-bounded may not be expressible in the language with some otherwise reasonable declarations:

typedef F<X> = void Function(X);
class C<Y extends F<num>> {}
typedef G<Z> = C<F<Z>> Function();

The formal type parameter Z must be a supertype of num in order to ensure that F<Z> is a subtype of the bound F<num>, but we do not support lower bounds on type arguments in Dart. Consequently, a declaration like G is a compile-time error no matter which bound we specify for Z, because no bound will ensure that the body is well-bounded for all possible Z. Similarly, the body of a typedef may use a given type argument in two or more different covariant contexts, which may require a bound which is a subtype of the constraints needed for each of those usages; for nominal types we would need an intersection type constructor in order to express a useful constraint in this situation. A richer type algebra may be added to Dart in the future which could allow more of these complex typedefs, but it is not obvious that it is useful enough to justify the added complexity.*

It is a compile-time error if a name declared in a typedef, with or without actual type arguments, is used as a superclass, superinterface, or mixin. It is a compile-time error if a generic function type is used as a bound for a formal type parameter of a class or a function. It is a compile-time error if a generic function type is used as an actual type argument.

Generic function types can thus only be used in the following situations:

  • as a type annotation on an local, instance, static, or global variable.
  • as a function return or parameter type.
  • in a type test.
  • in a type cast.
  • in an on-catch clause.
  • as a parameter or return type in a function type.

The motivation for having this constraint is that it ensures that the Dart type system admits only predicative types. It does admit non-prenex types, e.g., int Function(T function<T>(T) f). From research into functional calculi it is well-known that impredicative types give rise to undecidable subtyping, e.g., (Pierce, 1993), and even though the Dart type system is very different from F-sub, we cannot assume that these difficulties are absent.

Dynamic Semantics

The addition of this feature does not change the dynamic semantics of Dart.


2017-May-31: Added constraint on usage of generic function types: They cannot be used as type parameter bounds nor as type arguments.

2017-Jan-04: Adjusted the grammar to require named parameter types to have a type (previously, the type was optional).

2016-Dec-21: Changed the grammar to prevent the new function type syntax in several locations (for instance, as a super class or as a mixin). The main change in the grammar is the introduction of typeWithoutFunction.

2016-Dec-15: Changed the grammar to prevent the old style function types (derived from functionSignature in the grammar) from occurring inside the new style (functionType).