Typescript: ReturnType of overloaded function

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As Matt McCutchen points this is a limitation of ReturnType and in general conditional types and multiple overload signatures.

We can however construct a type that will return all overloaded return types for up to an arbitrary number of overloads:

function applyChanges1(input: string): number
function applyChanges1(input: number): string
function applyChanges1(input: number | string): number | string {
return typeof input === "number" ? input.toString() : input.length
}

function applyChanges2(input: number): string
function applyChanges2(input: string): number
function applyChanges2(input: number | string): number | string {
return typeof input === "number" ? input.toString() : input.length
}


type OverloadedReturnType<T> = 
    T extends { (...args: any[]) : infer R; (...args: any[]) : infer R; (...args: any[]) : infer R ; (...args: any[]) : infer R } ? R  :
    T extends { (...args: any[]) : infer R; (...args: any[]) : infer R; (...args: any[]) : infer R } ? R  :
    T extends { (...args: any[]) : infer R; (...args: any[]) : infer R } ? R  :
    T extends (...args: any[]) => infer R ? R : any


type RetO1 = OverloadedReturnType<typeof applyChanges1> // string | number 
type RetO2 = OverloadedReturnType<typeof applyChanges2> // number | string

The version above will work for up to 4 overload signatures (whatever they may be) but can easily (if not prettily) be extended to more.

We can even get a union of possible argument types in the same way: 

type OverloadedArguments<T> = 
    T extends { (...args: infer A1) : any; (...args: infer A2) : any; (...args: infer A3) : any ; (...args: infer A4) : any } ? A1|A2|A3|A4  :
    T extends { (...args: infer A1) : any; (...args: infer A2) : any; (...args: infer A3) : any } ? A1|A2|A3 :
    T extends { (...args: infer A1) : any; (...args: infer A2) : any } ? A1|A2  :
    T extends (...args: infer A) => any ? A : any


type RetO1 = OverloadedArguments<typeof applyChanges1> // [string] & [number]
type RetO2 = OverloadedArguments<typeof applyChanges2>  // [number] & [string]

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