Intersection Types

Sometimes it is useful to create a type which is all of a set of other types. For example, you might want to write a function which accepts an object which is the combination of other object types. For this, Flow supports intersection types.

// @flow
type A = { a: number };
type B = { b: boolean };
type C = { c: string };

function method(value: A & B & C) {
  // ...

// $ExpectError
method({ a: 1 }); // Error!
// $ExpectError
method({ a: 1, b: true }); // Error!
method({ a: 1, b: true, c: 'three' }); // Works!

Intersection type syntax

Intersection types are any number of types which are joined by an ampersand &.

Type1 & Type2 & ... & TypeN

You may also add a leading ampersand which is useful when breaking intersection types onto multiple lines.

type Foo =
  & Type1
  & Type2
  & ...
  & TypeN

Each of the members of a intersection type can be any type, even another intersection type.

type Foo = Type1 & Type2;
type Bar = Type3 & Type4;

type Baz = Foo & Bar;

Intersection types require all in, but one out

Intersection types are the opposite of union types. When calling a function that accepts an intersection type, we must pass in all of those types. But inside of our function we only have to treat it as any one of those types.

// @flow
type A = { a: number };
type B = { b: boolean };
type C = { c: string };

function method(value: A & B & C) {
  var a: A = value;
  var b: B = value;
  var c: C = value;

Even as we treat our value as just one of the types, we do not get an error because it satisfies all of them.

Intersection of function types

A common use of intersection types is to express functions that return different results based on the input we pass in. Suppose for example that we want to write the type of a function that

  • returns a string, when we pass in the value "string",
  • returns a number, when we pass in the value "number", and
  • returns any possible type (mixed), when we pass in any other string.

The type of this function will be

type Fn =
  & ((x: "string") => string)
  & ((x: "number") => number)
  & ((x: string) => null);

Each line in the above definition is called an overload, and we say that functions of type Fn are overloaded.

Note the use of parentheses around the arrow types. These are necessary to override the precedence of the “arrow” constructor over the intersection.

Calling an overloaded function

Using the above definition we can declare a function fn that has the following behavior:

declare var fn: Fn;
var n: string = fn("string"); // okay
var n: number = fn("number"); // okay
var n: boolean = fn("boolean"); // error: null is incompatible with number

Flow achieves this behavior by matching the type of the argument to the first overload with a compatible parameter type. Notice for example that the argument "string" matches both the first and the last overload. Flow will just pick the first one. If no overload matches, Flow will raise an error at the call site.

Declaring overloaded functions

An equivalent way to declare the same function fn would be by using consecutive “declare function” statements

declare function fn(x: "string"): string;
declare function fn(x: "number"): number;
declare function fn(x: string): null;

A limitation in Flow is that it can’t check the body of a function against an intersection type. In other words, if we provided the following implementation for fn right after the above declarations

function fn(x) {
  if (x === "string") { return ""; }
  else if (x === "number") { return 0; }
  else { return null; }

Flow silently accepts it (and uses Fn as the inferred type), but does not check the implementation against this signature. This makes this kind of declaration a better suited candidate for library definitions, where implementations are omitted.

Intersections of object types

When you create an intersection of object types, you merge all of their properties together.

For example, when you create an intersection of two objects with different sets of properties, it will result in an object with all of the properties.

// @flow
type One = { foo: number };
type Two = { bar: boolean };

type Both = One & Two;

var value: Both = {
  foo: 1,
  bar: true

When you have properties that overlap by having the same name, Flow follows the same strategy as with overloaded functions: it will return the type of the first property that matches this name.

For example, if you merge two objects with a property named prop, first with a type of number and second with a type of boolean, accessing prop will return number.

type One = { prop: number };
type Two = { prop: boolean };

declare var both: One & Two;

var prop1: number = both.prop; // okay
var prop2: boolean = both.prop; // Error: number is incompatible with boolean

Note: When it comes to objects, the order-specific way in which intersection types are implemented in Flow, may often seem counterintuitive from a set theoretic point of view. In sets, the operands of intersection can change order arbitrarily (commutative property). For this reason, it is a better practice to define this kind of operation over object types using the spread operator, e.g. { ...One, ...Two }, where the ordering semantics are better specified.

Impossible intersection types

Using intersection types, it is possible to create types which are impossible to create at runtime. Intersection types will allow you to combine any set of types, even ones that conflict with one another.

For example, you can create an intersection of a number and a string.

// @flow
type NumberAndString = number & string;

function method(value: NumberAndString) {
  // ...

// $ExpectError
method(3.14); // Error!
// $ExpectError
method('hi'); // Error!

But you can’t possibly create a value which is both a number and a string, but you can create a type for it. There’s no practical use for creating types like this, but it’s a side effect of how intersection types work.

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