Now, let's delve into the assumptions and definitions surrounding the T
in our Set<T>
type, which will always consist of a combination of string literal types. Assuming you will utilize the --strict
compiler option, we proceed to define the variables and types as follows:
const A = "A"; type A = typeof A;
const B = "B"; type B = typeof B;
This particular question holds great interest for me due to its complexity. Firstly, it is important to note that Set
s cannot be directly compared for equality. Therefore, traditional methods like switch
/case
are not applicable here. Instead, I present to you a type guard function that enables checking if a specific type of Set<T>
is indeed a subset of another type Set<U>
where U extends T
.
function isSubset<T extends string, U extends T[]>(
set: Set<T>,
...subsetArgs: U
): set is Set<U[number]> {
const otherSet = new Set(subsetArgs);
if (otherSet.size !== set.size) return false;
for (let v of otherSet.values()) {
if (!set.has(v)) return false;
}
return true;
}
You have the flexibility to customize this function to suit your needs. Essentially, it verifies that an element exists in set
only if it also exists in subsetArgs
. Here is an illustration of how to implement it:
declare const set: Set<A | B>; // a set containing elements 'A' or 'B'
if isSubset(set) { // no additional arguments, checking for emptiness
set; // narrowed down to Set<never>
} else if isSubset(set, A) { // checking for presence of 'A' only
set; // narrowed down to Set<A>
}
Observe how the type guard refines the type of set
with each condition? Instead of using switch
/case
, we employ if
/else
constructs.
The subsequent challenge revolves around the automatic expansion of the type Set<A | B>
to encompass all conceivable subset types such as Set<never>
, Set<A>
, Set<B>
, and Set<A | B>
. This manual expansion can be achieved through the following technique:
// notice the expanded union of types represented by 'subset'
function show(subset: Set<never> | Set<A> | Set<B> | Set<A | B>): string {
if (isSubset(subset)) {
return "Empty";
} else if (isSubset(subset, A)) {
return "This is A";
} else if (isSubset(subset, B)) {
return "This is B";
} else if (isSubset(subset, A, B)) {
return "Something in German I guess";
} else {
return assertUnreachable(subset); // prevents errors
}
}
console.log(show(new Set([A]))); // output: "This is A"
console.log(show(new Set([A, B]))); // output: "Something in German I guess"
console.log(show(new Set([A, B, "C"])); // compile time error, unexpected "C"
console.log(show(new Set())); // output: "Empty"
This configuration compiles successfully. However, one potential pitfall arises when the TypeScript compiler views Set<A>
as a subtype of Set<A | B>
. The order of type guard clauses becomes critical—ensuring proper narrowing from narrower to broader types to avoid erroneous compilation conclusions.
function badShow(subset: PowerSetUnion<A | B>): string {
if (isSubset(subset, A, B)) {
return "Something in German I guess";
} else {
return assertUnreachable(subset); // now triggers an error as expected!
}
}
Careful sequencing of checks mitigates the aforementioned issue. Alternatively, a more intricate approach involves encapsulating Set<T>
within InvariantSet<T>
objects to circumvent subtyping relationships:
type InvariantSet<T> = {
set: Set<T>;
"**forceInvariant**": (t: T) => T;
}
By enveloping all instances of Set<T>
inside InvariantSet<T>
, the problem associated with subtype relations between sets is resolved. Nonetheless, this solution introduces increased complexity.
Furthermore, there may arise the necessity to automatically generate all possible subset types from a union type like A | B
, resulting in definitions such as
Set<never> | Set<A> | Set<B> | Set<A | B>
. This concept aligns with the notion of a
power set.
While achieving an exact power set definition is challenging due to circular dependencies, a workaround can be implemented through extensive yet similar individual definitions limited by a predefined recursion depth. This method accounts for unions up to a specified number of constituents, preventing overwhelming scenarios where managing unions becomes unwieldy. Here is a practical implementation:
type PowerSetUnion<U, V = U> = Set<U> | (V extends any ? (PSU0<Exclude<U, V>>) : never);
// Additional PSUs follow...
type PSUX<U> = Set<U>; // terminating point
Utilizing these distributive conditional types yields the desired outcome for various use cases:
type PowerSetAB = PowerSetUnion<A | B>; // returns the complete power set of 'A | B'
type PowerSetOhBoy = PowerSetUnion<1 | 2 | 3 | 4 | 5 | 6>; // exemplifies power set generation for multiple elements
Feel free to modify the show()
signature to accommodate PowerSetUnion<T>
for enhanced functionality.
Phew! That was quite a journey, but I trust it provides clarity and guidance for your project endeavors. Best of luck!