Comment by gampleman

This is a valid definition in TypeScript:

    type Shape<T> = (
        circle: (x: number, y: number, r: number) => T,
        rectangle: (x: number, y: number, w: number, h: number) => T
    ) => T;

    function Circle<T>(x: number, y: number, r: number): Shape<T> {
        return (_Circle, _Rectangle) => _Circle(x, y, r);
    }

    function Rectangle<T>(x: number, y: number, w: number, h: number): Shape<T> {
        return (_Circle, _Rectangle) => _Rectangle(x, y, w, h);
    }

    const exampleCircle = Circle(2, 1.4, 4.5);
    const exampleRectangle = Rectangle(1.3, 3.1, 10.3, 7.7);

    function area(shape: Shape<unknown>): number {
        const s = shape as Shape<number>;
        return s(
            (x, y, r) => Math.PI * r * r,
            (x, y, w, h) => w * h
        );
    }

    export function main() {
        console.log(area(exampleCircle));
        console.log(area(exampleRectangle));
    }

Unfortunately I think the cast might be necessary, but happy to see another solution from someone with more typescript expertise.