type E1<X> = <T>() => T extends X ? 0 : 1
type E2<X> = <T>() => T extends X ? 0 : 1

type IsEqual<X, Y> = E1<X> extends E2<Y> ? true : false

/**
 * Whether or not T includes U as an element.
 */
type Includes<T extends readonly unknown[], U> = true extends {
  [key in keyof T]: IsEqual<T[key], U>
}[number] ? true : false

A non-recursive type-level Includes operator in Typescript

Introduction

Includes is a type-level operator that determines whether a given type T includes a given type U as an element. In other words, it returns true if T is a subtype of U.

This operator is implemented using a simple helper function, IsEqual, which compares two types X and Y and returns true if they are equal.

Implementation

IsEqual

The IsEqual function is implemented as follows:

type IsEqual<X, Y> = E1<X> extends E2<Y> ? true : false

where E1 and E2 are helper functions that take a type T and return 0 if T is equal to X, and 1 otherwise.

Thus, IsEqual<X, Y> returns true if E1<X> is equal to E2<Y>, and false otherwise.

E1 and E2

The E1 and E2 functions are implemented as follows:

type E1<X> = <T>() => T extends X ? 0 : 1
type E2<X> = <T>() => T extends X ? 0 : 1

These functions take a type T and return 0 if T is equal to X, and 1 otherwise. These functions exploit deep behavior around generics to implement a “true type-level equality check”, which will even distinguish readonly attributes from non-readonly attributes.

The deep behavior needed to distinguish readonly attributes does not work without both type declarations, despite the equivalence. The internal type-checking behavior seems to depend on comparing two separate type identifiers.

Includes

The Includes function is implemented as follows:

type Includes<T extends readonly unknown[], U> = true extends {
  [key in keyof T]: IsEqual<T[key], U>
}[number] ? true : false

First, note that Includes takes two type parameters: T, which is a readonly array type, and U, which is the element type that we want to check for inclusion in T. We do not introduce a constraint whereby U must be an element of T, since the whole purpose of the function is to determine whether or not U is an element of T.

Next, we define a helper type, R, which is a mapped type. This is a type whose properties are determined by mapping a given type T to another type U. In this case, we are mapping each element of T to the result of IsEqual<T[key], U>.

Thus, R is a type with one property for each element of T, whose value is true if the element is equal to U, and false otherwise.

Finally, we return true if R has a property with value true, and false otherwise.

Advantages

The Includes operator has a number of advantages over other implementations.

First, it is non-recursive. This means that it will not suffer from exponential typechecking, which is a problem with other implementations of Includes.

Second, it is type-safe. This means that it will only return true if U is actually an element of T. Other implementations may return true even if U is not an element of T.

Third, it is efficient. This means that it will not introduce unnecessary type-checking constraints. Other implementations may introduce such constraints, which can lead to slow type-checking.

Conclusion

The Includes operator is a simple, efficient, and type-safe way to determine whether a given type T includes a given type U as an element.