What is the method for defining a type as the complete set of combinations within a union type?

Summary:

In this scenario, I am looking to establish a comprehensive union of all possible combinations within a given set.

type Combinations<SomeUnion, T extends any[]> = /* Utilizing some mystical method */
//                          ^^^^^^^^^^^^^^^
//                       specifying the length of expected combinations.

// then


Combinations<string | number, ['x', 'y']> =
    [string, string] |
    [string, number] |
    [number, string] |
    [number, number] 

Combinations<string | number | boolean, ['x', 'y']> =
    [string, string]  |
    [string, number]  |
    [string, boolean] |
    [number, string]  |
    [number, number]  |
    [number, boolean] |
    [boolean, string] |
    [boolean, number] |
    [boolean, boolean]

Combinations<string | number, ['x', 'y', 'z']> =
    [string, string, string] |
    [string, string, number] |
    [string, number, string] |
    [string, number, number] |
    [number, string, string] |
    [number, string, number] |
    [number, number, string] |
    [number, number, number]

Details:

The aim is to create a method decorator that can guarantee, in a type-safe manner, that the number of arguments required by the decorated method matches the number of arguments provided to the decorator.



type FixedLengthFunction<T extends any[]> = (...args: { [k in keyof T]: any }) => void

function myDecorator<T extends any[]>(...args: T) {
    return <K extends string>(
        target: { [k in K]: FixedLengthFunction<T> },
        methodName: K,
        desc: any
    ) => {}
}


// Note: WAI => Works as intended
class Foo {
   @myDecorator()
   a() {}
   // Expected to be correct,
   // and indeed passes the type system.
   // WAI

   @myDecorator()
   b(x: number) {}
   // Expected to be incorrect since 'b' requires one more argument,
   // and detected by the type system.
   // WAI

   @myDecorator('m')
   c(x: number) {}
   // Expected to be correct,
   // and successfully passes the type system.
   // WAI

   @myDecorator('m')
   d() {}
   // Expected to be incorrect since 'd' demands one less argument,
   // but still passes the type system.
   // not WAI
}

This applies universally when the decorated method has fewer arguments than the decorator call.

The main issue lies in the fact that: (a: SomeType) => void aligns with (a: any, b: any) => void since any can also be undefined.

I proceeded to update FixedLengthFunction to:

type Defined = string | number | boolean | symbol | object
type FixedLengthFunction<T extends any[]> =
    (...args: { [k in keyof T]: Defined }) => void
//                              ^^^^^^^
//                      changes 'any' to 'Defined'

However, it resulted in a "false positive" complaint when:

@myDecorator('m')
c(x: number) {}

was flagged as incorrect.

This time, the issue was that (x: number) => void does not match (arg_0: Defined) => void. number represents a narrowed subset of Defined, violating the Liskov Substitution Principle (LSP).

The crux of the problem is:

FixedLengthFunction<['m', 'n']>
converts to
(...args: [Defined, Defined]) => void
, which further clarifies as
(arg_0: Defined, arg_1: Defined) => void
.

What is truly needed is:

(...args: 
    [number, number] |
    [string, number] |
    [boolean, string] 
    /* ...and so forth for all possible length 2 combinations */
) => void

Hence, the essential requirement here is the magical type Combinations featured at the beginning of this post.

Answer №1

Creating a union like that is not advisable as it can spiral out of control and lead to performance issues during compilation. While you may be able to achieve it using recursive type aliases, it's strongly recommended against (even if you can trick the compiler into accepting it, there's no guarantee it will work in the future).

However, I believe there might be a misunderstanding in the problem you've pointed out. You mentioned that a function with fewer parameters can be assigned to one with more parameters due to the use of any, which is incorrect. Generally, TypeScript permits a function with fewer parameters to be assigned where a function with more parameters is expected. The extra parameters are simply ignored by the function implementation and do not cause any issues:

let fn: (a: number) => void = function () { console.log("Don't care about your args!"); }

fn(1)// 1 is ignored but that is ok 

We can enforce strict equality of parameter numbers based on tuples having a length property and being able to infer the actual type of the class and extract the parameters from that type:

type FixedLengthFunction<T extends any[]> = (...args: { [k in keyof T]: any }) => void

type ErrorIfDifferentLength<TMethod, TExpected extends any[]> = 
    TMethod extends (...a: infer TParams) => any ? 
    TParams['length'] extends TExpected['length'] ? {}: { "!Error": "Number of parameters differ:", actual:  TParams['length'], expected: TExpected['length'] } : {}

function myDecorator<T extends any[]>(...a: T) {
    return <K extends string, TClass extends Record<K, FixedLengthFunction<T>>>(target: TClass & ErrorIfDifferentLength<TClass[K], T>, key: K): void => {

    }
}

// Note: WAI => Works as intended
class Foo {
    @myDecorator()
    a() {}
    // Expected to be correct,
    // and actually passed through the type system.
    // WAI

    @myDecorator()
    b(x: number) {}
    // Expected to be incorrect as 'b' has an additional argument,
    // and successfully flagged by the type system.
    // WAI

    @myDecorator('m')
    c(x: number) {}
    // Expected to be correct,
    // and validates with the type system.
    // WAI

    @myDecorator('m')
    d() {}
    // Argument of type 'Foo' is not assignable to parameter of type 'Foo & { "!Error": "Number of parameters differ:"; method: "d"; actual: 0; expected: 1; }'.
    // WAI
}

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