Subsets & Subtypes

 

What is a subtype?

A type like number, boolean, or string describes a set of possible values. A number describes every possible number, so a single number (such as 42) would be a subtype of the number type.

If we want to know whether one type is the subtype of another, we need to look at all the possible values for both types and figure out if the other has a subset of the values.

For example, if we had a TypeA which described the numbers 1 through 3, and a TypeB which described the numbers 1 through 5: TypeA would be considered a subtype of TypeB, because TypeA is a subset of TypeB.

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type TypeA = 1 | 2 | 3;
type TypeB = 1 | 2 | 3 | 4 | 5;

Consider a TypeLetters which described the strings: “A”, “B”, “C”, and a TypeNumbers which described the numbers: 1, 2, 3. Neither of them would be a subtype of the other, as they each contain a completely different set of values.

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type TypeLetters = "A" | "B" | "C";
type TypeNumbers =  1  |  2  |  3;

Finally, if we had a TypeA which described the numbers 1 through 3, and a TypeB which described the numbers 3 through 5. Neither of them would be a subtype of the other. Even though they both have 3 and describe numbers, they each have some unique items.

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type TypeA = 1 | 2 | 3;
type TypeB =         3 | 4 | 5;

When are subtypes used?

Most of the work that Flow does is comparing types against one another.

For example, in order to know if you are calling a function correctly, Flow needs to compare the arguments you are passing with the parameters the function expects.

This often means figuring out if the value you are passing in is a subtype of the value you are expecting.

So if I write a function that expects the numbers 1 through 5, any subtype of that set will be acceptable.

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// @flow
function f(param: 1 | 2 | 3 | 4 | 5) {
  // ...
}

declare var oneOrTwo: 1 |  2; // Subset of the input parameters type.
declare var fiveOrSix: 5 | 6; // Not a subset of the input parameters type.

f(oneOrTwo); // Works!
// $ExpectError
f(fiveOrSix); // Error!
number literal `6` This type is incompatible with the expected param type of number enum

Subtypes of complex types

Flow needs to compare more than just sets of primitive values, it also needs to be able to compare objects, functions, and every other type that appears in the language.

Subtypes of objects

You can start to compare two objects by their keys. If one object contains all the keys of another object, then it may be a subtype.

For example, if we had an ObjectA which contained the key foo, and an ObjectB which contained the keys foo and bar. Then it’s possible that ObjectB is a subtype of ObjectA.

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// @flow
type ObjectA = { foo: string };
type ObjectB = { foo: string, bar: number };

let objectB: ObjectB = { foo: 'test', bar: 42 };
let objectA: ObjectA = objectB; // Works!

But we also need to compare the types of the values. If both objects had a key foo but one was a number and the other was a string, then one would not be the subtype of the other.

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// @flow
type ObjectA = { foo: string };
type ObjectB = { foo: number, bar: number };

let objectB: ObjectB = { foo: 1, bar: 2 };
// $ExpectError
let objectA: ObjectA = objectB; // Error!
object type This type is incompatible with object type object type This type is incompatible with object type

If these values on the object happen to be other objects, we would have to compare those against one another. We need to compare every value recursively until we can decide if we have a subtype or not.

Subtypes of functions

Subtyping rules for functions are more complicated. So far, we’ve seen that A is a subtype of B if B contains all possible values for A. For functions, it’s not clear how this relationship would apply. To simplify things, you can think of a function type A as being a subtype of a function type B if functions of type A can be used wherever a function of type B is expected.

Let’s say we have a function type and a few functions. Which of the functions can be used safely in code that expects the given function type?

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type FuncType = (1 | 2) => "A" | "B";

let f1: (1 | 2) => "A" | "B" | "C" = (x) => /* ... */
let f2: (1 | null) => "A" | "B" = (x) => /* ... */
let f3: (1 | 2 | 3) => "A" = (x) => /* ... */
  • f1 can return a value that FuncType never does, so code that relies on FuncType might not be safe if f1 is used. Its type is not a subtype of FuncType.
  • f2 can’t handle all the argument values that FuncType does, so code that relies on FuncType can’t safely use f2. Its type is also not a subtype of FuncType.
  • f3 can accept all the argument values that FuncType does, and only returns values that FuncType does, so its type is a subtype of FuncType.

In general, the function subtyping rule is this: A function type B is a subtype of a function type A if and only if B’s inputs are a superset of A’s, and B’s outputs are a subset of A’s. The subtype must accept at least the same inputs as its parent, and must return at most the same outputs.

The decision of which direction to apply the subtyping rule on inputs and outputs is governed by variance, which is the topic of the next section.


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