partial application in typescript

partial-application.ts

export default function createPartialApplication<T extends any[], R>(
    fn: (...args: T) => R,
): PartialApplication<T, R> {
    return function accumulator(...args1: any[]): any {
        return args1.length >= fn.length
            ? fn(...(args1 as T))
            : (...args2: any[]) => accumulator(...args1.concat(args2));
    };
}

type PartialApplication<T extends readonly any[], R> = <A extends Partial<T>>(
    ...args: A
) => Length<A> extends Length<T>
    ? R
    : PartialApplication<ShiftN<T, Length<A>>, R>;

type Length<T extends readonly any[]> = T["length"];

type ShiftNMap<T extends readonly any[]> = {
    0: T;
    1: ShiftOne<T>;
    2: ShiftOne<ShiftOne<T>>;
    3: ShiftOne<ShiftOne<ShiftOne<T>>>;
    4: ShiftOne<ShiftOne<ShiftOne<ShiftOne<T>>>>;
    5: ShiftOne<ShiftOne<ShiftOne<ShiftOne<ShiftOne<T>>>>>;
};

type ShiftN<T extends readonly any[], N> = N extends keyof ShiftNMap<T>
    ? ShiftNMap<T>[N]
    : N extends number
    ? any[]
    : never;

type ShiftOne<T extends readonly any[]> = T extends [any, ...infer U]
    ? U
    : never;