Higher-order type functions in TypeScript?

For you and others searching for a workaround, you can try a simple idea based on placeholders (see this comment in the discussion mentioned by jcalz):

type Placeholder = {'aUniqueKey': unknown};
type Replace<T, X, Y> = {
  [k in keyof T]: T[k] extends X ? Y : T[k];
};

So, your function would look like follows:

type HigherOrderTypeFn<T, M> = T extends (...) ? Replace<M, Placeholder, T> : never;

and be called for example like that:

type M<U> = U[];
type X = HigherOrderTypeFn<number, M<Placeholder>> // is number[] (if ... is number)

For people coming across this, there's this nice example floating around on the TypeScript discord server:

export interface Hkt<I = unknown, O = unknown> {
  [Hkt.isHkt]: never,
  [Hkt.input]: I,
  [Hkt.output]: O,
}

export declare namespace Hkt {
  const isHkt: unique symbol
  const input: unique symbol
  const output: unique symbol

  type Input<T extends Hkt<any, any>> =
    T[typeof Hkt.input]

  type Output<T extends Hkt<any, any>, I extends Input<T>> =
    (T & { [input]: I })[typeof output]

  interface Compose<O, A extends Hkt<any, O>, B extends Hkt<any, Input<A>>> extends Hkt<Input<B>, O>{
    [output]: Output<A, Output<B, Input<this>>>,
  }

  interface Constant<T, I = unknown> extends Hkt<I, T> {}
}

Which can be used as follows. The snippet below defines a SetFactory, where you specify the type the desired set type when creating a factory, e.g. typeof FooSet or typeof BarSet . typeof FooSet is the constructor for a FooSet and is like a higher kinded type, the constructor type takes any T and returns a FooSet<T>. The SetFactory contains several methods such as createNumberSet, which returns a new set of the given type, with the type parameters set to number.

interface FooSetHkt extends Hkt<unknown, FooSet<any>> {
    [Hkt.output]: FooSet<Hkt.Input<this>>
}
class FooSet<T> extends Set<T> {
    foo() {} 
    static hkt: FooSetHkt;
}

interface BarSetHkt extends Hkt<unknown, BarSet<any>> {
    [Hkt.output]: BarSet<Hkt.Input<this>>;
}
class BarSet<T> extends Set<T> { 
    bar() {} 
    static hkt: BarSetHkt;
}

class SetFactory<Cons extends {
    new <T>(): Hkt.Output<Cons["hkt"], T>;
    hkt: Hkt<unknown, Set<any>>;
}> {
    constructor(private Ctr: Cons) {}
    createNumberSet() { return new this.Ctr<number>(); }
    createStringSet() { return new this.Ctr<string>(); }
}

// SetFactory<typeof FooSet>
const fooFactory = new SetFactory(FooSet);
// SetFactory<typeof BarSet>
const barFactory = new SetFactory(BarSet);

// FooSet<number>
fooFactory.createNumberSet();
// FooSet<string>
fooFactory.createStringSet();

// BarSet<number>
barFactory.createNumberSet();
// BarSet<string>
barFactory.createStringSet();

Short explanation of how this works (with FooSet and number as an example):

• The main type to understand is Hkt.Output<Const["hkt"], T>. With our example types substituted this becomes Hkt.Output<(typeof FooSet)["hkt"], number>. The magic now involves turning this into a FooSet<number>
• First we resolve (typeof FooSet)["hkt"] to FooSetHkt. A lot of the magic lies here, by storing the info about how to create a FooSet in the static hkt property of FooSet. You need to do this for each supported class.
• Now we have Hkt.Output<FooSetHkt, number>. Resolving the Hkt.Output type alias, we get (FooSetHkt & { [Hkt.input]: number })[typeof Hkt.output]. The unique symbols Hkt.input / Hkt.output help for creating unique properties, but we could have also used unique string constants.
• Now we need to access the Hkt.output property of FooSetHkt. This is different for each class and contains the details on how to construct a concrete type with the type argument. FooSetHkt defines the output property to be of type FooSet<Hkt.Input<this>>.
• Finally, Hkt.Input<this> just acceses the Hkt.input property of FooSetHkt. It would resolve to unknown, but by using the intersection FooSetHkt & { [Hkt.input]: number }, we can change the Hkt.input property to number. And so if we've reached our goal, Hkt.Input<this> resolves to number and FooSet<Hkt.Input<this>> resolves to FooSet<number>.

For the example from the question, Hkt.Output is essentially what was being asked for, just with the type parameters reversed:

interface List<T> {}
interface ListHkt extends Hkt<unknown, List<any>> {
    [Hkt.output]: List<Hkt.Input<this>>
}
type HigherOrderTypeFn<T, M extends Hkt> = Hkt.Output<M, T>;
// Gives you List<number>
type X = HigherOrderTypeFn<number, ListHkt>;

There's an implementation of HKTs (leveraging module augmentation) in fp-ts.

The workaround for Higher Kinded Types as documented here by its author is:

export interface HKT<URI, A> {
  readonly _URI: URI;
  readonly _A: A;
}

And can be used like this:

export interface Foldable<F> {
  readonly URI: F;
  reduce: <A, B>(fa: HKT<F, A>, b: B, f: (b: B, a: A) => B) => B;
}

Check it out this question: higher kinded type in typescript from fp-ts and URI

Maybe that can shed some light?

Cheers