Typescript infer type of higher-order function that executes optional function parameters with same argument signatures

Question

Let's say I have a function that takes two functions f and g as arguments and returns a function that executes f and g and returns an object with the results. I also want to enforce that f and g have the same signature. This is easy enough with conditional types:

type ArgumentTypes<F extends Function> = F extends (...args: infer A) => any ? A : never;
function functionPair<
    F extends (...args: any[]) => any,
    G extends (...args: ArgumentTypes<F>) => any
>
(f: F, g: G): (...args: ArgumentTypes<F>) => { f: ReturnType<F>, g: ReturnType<G> }
{
    return (...args: ArgumentTypes<F>) => ({ f: f(...args), g: g(...args) });
}

functionPair((foo: string) => foo, (bar: number) => bar); // Error, incompatible signatures, as expected
functionPair((foo: string) => foo, (bar: string) => bar.length); // (foo: string) => { f: string; g: number; }, as expected

Now, what if I want to make f and g optional , and have the shape of the returned object change as a result? That is, if f or g is undefined , their key should be missing from the resulting object:

functionPair(); // Should be () => {}
functionPair(undefined, undefined); // Should be () => {}
functionPair((foo: string) => foo); // Should be (foo: string) => { f: string }
functionPair(undefined, (bar: string) => foo.length); // Should be (bar: string) => { g: number }
functionPair((foo: string) => foo, (bar: string) => foo.length); // Should be (foo: string) => { f: string, g: number }, as before

I've been trying to accomplish this with conditional types, but I'm having some trouble with conditionally enforcing the shape of the resulting function. Here's what I have so far (strict null checks are off):

function functionPair<
    A extends F extends undefined ? G extends undefined ? [] : ArgumentTypes<G> : ArgumentTypes<F>,
    F extends (...args: any[]) => any = undefined,
    G extends F extends undefined ? (...args: any[]) => any : (...args: ArgumentTypes<F>) => any = undefined
>
(f?: F, g?: G): (...args: A) =>
    F extends undefined
    ? G extends undefined ? {} : { g: ReturnType<G> }
    : G extends undefined ? { f: ReturnType<F> } : { f: ReturnType<F>, g: ReturnType<G> }
{ /* implementation... */ }

const a = functionPair(); // () => {}, as expected
const b = functionPair((foo: string) => foo); // (foo: string) => { f: string; }, as expected
const c = functionPair((foo: string) => foo, (bar: number) => bar); // Error, incompatible signatures, as expected
const d = functionPair((foo: string) => foo, (bar: string) => bar.length); // (foo: string) => { f: string; g: number; }, as expected

const e = functionPair(undefined, undefined); // INCORRECT! Expected () => {}, got (...args: unknown[] | []) => {} | { f: any; } | { g: any; } | { f: any; g: any; }
const f = functionPair(undefined, (bar: string) => bar.length); // INCORRECT! Expected (bar: string) => { g: number; } but got (...args: unknown[] | [string]) => { g: number; } | { f: any; g: number; }

---

By the way, I know that this is technically possible with overloads, as below, but I'd really like to understand how to do it without them.

function functionPairOverloaded(): () => {}
function functionPairOverloaded(f: undefined, g: undefined): () => {}
function functionPairOverloaded<F extends (...args: any[]) => any>(f: F): (...args: ArgumentTypes<F>) => { f: ReturnType<F> }
function functionPairOverloaded<G extends (...args: any[]) => any>(f: undefined, g: G): (...args: ArgumentTypes<G>) => { g: ReturnType<G> }
function functionPairOverloaded<F extends (...args: any[]) => any, G extends (...args: ArgumentTypes<F>) => any>(f: F, g: G): (...args: ArgumentTypes<F>) => { f: ReturnType<F>, g: ReturnType<G> }
function functionPairOverloaded<F extends (...args: any[]) => any, G extends (...args: any[]) => any>(f?: F, g?: G) { /* implementation... */ }

Answer 1

Assuming you have --strictNullChecks turned on, I guess I'd do it this way:

type Fun = (...args: any[]) => any;
type FunFrom<F, G> = F extends Fun ? F : G extends Fun ? G : () => {};
type IfFun<F, T> = F extends Fun ? T : never;
type Ret<T> = T extends (...args: any[]) => infer R ? R : never

declare function functionPair<
  F extends Fun | undefined = undefined,
  G extends ((...args: (F extends Fun ? Parameters<F> : any[])) => any) 
    | undefined = undefined
>(
  f?: F, 
  g?: G
): (...args: Parameters<FunFrom<F, G>>) => {
  [K in IfFun<F, 'f'> | IfFun<G, 'g'>]: K extends 'f' ? Ret<F> : Ret<G> 
};

That's fairly ugly, but it does give you the behavior you're looking for:

const a = functionPair(); // () => {}, as expected
const b = functionPair((foo: string) => foo); // (foo: string) => { f: string; }, as expected
const c = functionPair((foo: string) => foo, (bar: number) => bar); // Error, incompatible signatures, as expected
const d = functionPair((foo: string) => foo, (bar: string) => bar.length); // (foo: string) => { f: string; g: number; }, as expected
const e = functionPair(undefined, undefined); // () => {}, as expected
const f = functionPair(undefined, (bar: string) => bar.length); // (bar: string) => { g: number; }, as expected

I decided to go with just two type parameters F and G and instead of A use Parameters<FunFrom<F, G>> . Note that Parameters is a built-in type function similar to your ArgumentTypes .

Also, for the return type of the returned function I do a somewhat ugly mapped type. I first was planning to do something like IfFun<F, {f: Ret<F>}> & IfFun<G, {g: Ret<G>}> , which is (I believe) more understandable, but the resulting type {f: X, g: Y} is nicer than the intersection {f: X} & {g: Y} .

Anyway, hope that helps. Good luck!

---

If you want to be able to turn --strictNullChecks off, then the definitions get even hairier:

type Fun = (...args: any[]) => any;
type AsFun<F> = [F] extends [Fun] ? F : never
type FunFrom<F, G> = AsFun<IfFun<F, F, IfFun<G, G, () => {}>>>;
type IfFun<F, Y, N=never> = F extends undefined ? N : 
  0 extends (1 & F) ? N : F extends Fun ? Y : N;
type Ret<T> = T extends (...args: any[]) => infer R ? R : never

declare function functionPair<
  F extends Fun | undefined = undefined,
  G extends ((...args: IfFun<F, Parameters<F>, any[]>) => any)
  | undefined = undefined
  >(
    f?: F,
    g?: G
  ): (...args: Parameters<FunFrom<F, G>>) => {
    [K in IfFun<F, 'f'> | IfFun<G, 'g'>]: K extends 'f' ? Ret<F> : Ret<G>
  };

The difference is that IfFun<> needs to be able to distinguish functions from undefined and any , both of which pop up in unfortunate places when you turn off --strictNullChecks . That's because undefined extends Function ? true : false undefined extends Function ? true : false starts returning true , and any starts getting inferred when you pass the manual undefined value into the functions. Distinguishing undefined is reasonably straightforward since Function extends undefined ? true : false Function extends undefined ? true : false is still false , but distinguishing any is annoying and involves some funny business .

Good luck again!