type Definition = {
  vals: number[];
};

type ErrorBrand<Err extends string> = Readonly<{
  [k in Err]: void;
}>;

// Entry point for our builder. Unlike the value builder
// pattern example, we don't need a definition value storing the set of
// added numbers because we're going to stash them in a type and check
// them at compile time rather than runtime.
const makeAThing = () => {
  // Users can call addNumber as the next step in the builder.
  // Initialize the Nums typeset to empty set.
  return {
    addNumber: addNumber<never>(),
  };
};

type AddNumberBuilder<Nums extends number> = {
  // When the user calls addNumber(x: T), check that T doesn't
  // already exist in Nums. If it doesnt, continue the builder
  // and add T to the Nums set.
  addNumber: <T extends number>(
    x: T extends Nums ? ErrorBrand<"Number already declared"> : T
  ) => AddNumberBuilder<Nums | T>;

  // Finalize the builder, returning a function that asserts that x
  // exists in our Nums set.
  done: () => <T extends number>(
    x: T extends Nums ? T : ErrorBrand<"Not a legal number">
  ) => void;
};

// To implement the partial evaluation builder, the addNumber function
// returns a function that returns an AddNumberBuilder.
const addNumber = <Nums extends number>() => {
  return <T extends number>(
    x: T extends Nums ? ErrorBrand<"Number already declared"> : T
  ): AddNumberBuilder<Nums | T> => {
    return {
      addNumber: addNumber<Nums | T>(),
      done: done(),
    };
  };
};

// The done function returns a function that returns our validation
// function.
const done = <Nums extends number>() => {
  return () => {
    return <T extends number>(
      x: T extends Nums ? T : ErrorBrand<"Not a legal number">
    ) => {};
  };
};

const myBuilder = makeAThing().addNumber(7).addNumber(5).done();

myBuilder(5);
myBuilder(7);
myBuilder(8); // Argument of type 'number' is not assignable to parameter of type
// 'Readonly<{ "Not a legal number": void; }>'.(2345)

const myOther = makeAThing()
  .addNumber(7)
  .addNumber(5)
  .addNumber(5) // Argument of type 'number' is not assignable to parameter of
  // type 'Readonly<{ "Number already declared": void; }>'.(2345)
  .done();