Without type assertions, can I give an interface’s function a private parameter? Here’s what I mean by “private”:

1. This parameter can be passed within the current module.
2. External to the current module, that parameter cannot be used.

This code demonstrates what I’d like to be able to do:

export interface PublicInterface {
  publicFunction1: (foo: string) => string;
  publicFunction2: () => string;
}

export const implementation: PublicInterface = {
  publicFunction1: function (foo: string | number): string {
    return "abc";
  },
  publicFunction2: function (): string {
    return implementation.publicFunction1(123); // I'd like this to compile without a type assertion
  },
};

// another-file.ts
implementation.publicFunction1("xyz");
implementation.publicFunction1(123); // I'd like this to continue to error

I tried to accomplish this with function overloads instead of an interface, but I got an error when I did not export every overload: “Overload signatures must all be exported or non-exported.” This leads me to believe this isn’t possible without a type assertion, but I thought I would ask anyway. If there is a way to do this I’d like to learn it.