higher kinded types

EDIT: I ended up releasing my idea as a library called TypeProps

Proof-of-concept:

type unknown = {} | null | undefined;

// Functor
interface StaticFunctor<G> {
    map<F extends Generic<G>, U>(
        transform: (a: Parameters<F>[0]) => U,
        mappable: F
    ): Generic<F, [U]>;
}

// Examples
const arrayFunctor: StaticFunctor<any[]> = {
    map: <A, B>(fn: (a: A) => B, fa: A[]): B[] => {
        return fa.map(fn);
    }
};
const objectFunctor: StaticFunctor<object> = {
    map: <A, B>(fn: (a: A) => B, fa: A): B => {
        return fn(fa);
    }
};
const nullableFunctor: StaticFunctor<object | null | undefined> = {
    map: <A, B>(
        fn: (a: A) => B,
        fa: A | null | undefined
    ): B | null | undefined => {
        return fa != undefined ? fn(fa) : fa;
    }
};

const doubler = (x: number) => x * 2;

const xs = arrayFunctor.map(doubler, [4, 2]); // xs: number[]
const x = objectFunctor.map(doubler, 42); // x: number
const xNull = nullableFunctor.map(doubler, null); // xNull: null
const xSome = nullableFunctor.map(doubler, 4 as number | undefined); // xSome: number | undefined

const functor: StaticFunctor<unknown | any[]> = {
    map(fn, fa) {
        return Array.isArray(fa)
            ? arrayFunctor.map(fn, fa)
            : fa != undefined
                ? objectFunctor.map(fn, fa)
                : nullableFunctor.map(fn, fa);
    }
};

const ys = functor.map(doubler, [4, 2]); // ys: number[]
const y = functor.map(doubler, 42); // y: number
const yNull = functor.map(doubler, null); // yNull: null
const ySome = functor.map(doubler, 42 as number | undefined); // ySome: number | undefined

// Plumbing
interface TypeProps<T = {}, Params extends ArrayLike<any> = never> {
    array: {
        infer: T extends Array<infer A> ? [A] : never;
        construct: Params[0][];
    };
    null: {
        infer: null extends T ? [never] : never;
        construct: null;
    };
    undefined: {
        infer: undefined extends T ? [never] : never;
        construct: undefined;
    };
    unfound: {
        infer: [NonNullable<T>];
        construct: Params[0];
    };
}

type Match<T> = T extends infer U
    ? ({} extends U ? any
        : TypeProps<U>[Exclude<keyof TypeProps, "unfound">]["infer"]) extends never
    ? "unfound"
    : {
        [Key in Exclude<keyof TypeProps, "unfound">]:
        TypeProps<T>[Key]["infer"] extends never
        ? never : Key
    }[Exclude<keyof TypeProps, "unfound">] : never;


type Parameters<T> = TypeProps<T>[Match<T>]["infer"];

type Generic<
    T,
    Params extends ArrayLike<any> = ArrayLike<any>,
    > = TypeProps<T, Params>[Match<T>]["construct"];

[SimonMeskens]

For those following along, I think this example (also posted to the TS github) more or less shows the power of my latest experiments:

type unknown = {} | null | undefined;

// Functor
interface StaticFunctor<G> {
    map<F extends Generic<G>, U>(
        transform: (a: Parameters<F>[0]) => U,
        mappable: F
    ): Generic<F, [U]>;
}

// Examples
const arrayFunctor: StaticFunctor<any[]> = {
    map: <A, B>(fn: (a: A) => B, fa: A[]): B[] => {
        return fa.map(fn);
    }
};
const objectFunctor: StaticFunctor<object> = {
    map: <A, B>(fn: (a: A) => B, fa: A): B => {
        return fn(fa);
    }
};
const nullableFunctor: StaticFunctor<object | null | undefined> = {
    map: <A, B>(
        fn: (a: A) => B,
        fa: A | null | undefined
    ): B | null | undefined => {
        return fa != undefined ? fn(fa) : fa;
    }
};

const doubler = (x: number) => x * 2;

const xs = arrayFunctor.map(doubler, [4, 2]); // xs: number[]
const x = objectFunctor.map(doubler, 42); // x: number
const xNull = nullableFunctor.map(doubler, null); // xNull: null
const xSome = nullableFunctor.map(doubler, 4 as number | undefined); // xSome: number | undefined

const functor: StaticFunctor<unknown | any[]> = {
    map(fn, fa) {
        return Array.isArray(fa)
            ? arrayFunctor.map(fn, fa)
            : fa != undefined
                ? objectFunctor.map(fn, fa)
                : nullableFunctor.map(fn, fa);
    }
};

const ys = functor.map(doubler, [4, 2]); // ys: number[]
const y = functor.map(doubler, 42); // y: number
const yNull = functor.map(doubler, null); // yNull: null
const ySome = functor.map(doubler, 42 as number | undefined); // ySome: number | undefined

// Plumbing
interface TypeProps<T = {}, Params extends ArrayLike<any> = never> {
    array: {
        infer: T extends Array<infer A> ? [A] : never;
        construct: Params[0][];
    };
    null: {
        infer: null extends T ? [never] : never;
        construct: null;
    };
    undefined: {
        infer: undefined extends T ? [never] : never;
        construct: undefined;
    };
    unfound: {
        infer: [NonNullable<T>];
        construct: Params[0];
    };
}

type Match<T> = T extends infer U
    ? ({} extends U ? any
        : TypeProps<U>[Exclude<keyof TypeProps, "unfound">]["infer"]) extends never
    ? "unfound"
    : {
        [Key in Exclude<keyof TypeProps, "unfound">]:
        TypeProps<T>[Key]["infer"] extends never
        ? never : Key
    }[Exclude<keyof TypeProps, "unfound">] : never;


type Parameters<T> = TypeProps<T>[Match<T>]["infer"];

type Generic<
    T,
    Params extends ArrayLike<any> = ArrayLike<any>,
    > = TypeProps<T, Params>[Match<T>]["construct"];

This one doesn’t have the mapping stuff yet of TypeProps proper, but it has some new tricks up its sleeve. For mapping, I’m looking at finding a way to get closer to Haskell, where you can define an instance type like Maybe (Either e)

[SimonMeskens]

TypeProps just reached stable alpha, I just typed some really complex examples, including Haskell-style instance types. I’m going to close this issue down.

Next step is publishing on NPM and making a new repo to provide Fantasy-land, Static-land and some other varieties

Thanks for the help Tycho 😃