tmp.ts

function handleNull<A, B, C, D>(middleware: Middleware<A, B, C, D>)

function applyMiddleware<A, B, C, D>(
  middleware: Middleware<A, B, C, D>,
  b_c: Fn<B, C>
): Fn<A, D | null> {
  return a => {
    const  res = middleware(a);
    if (!res) {
      return null;
    }
    const [b, c_d] = res;
    return c_d(b_c(b));
  };
}

function composeMiddleware<A, B, C, D, E, F>(
  l: Middleware<A, B, C, D>,
  r: Middleware<B, E, F, C>
): Middleware<A, E, F, D> {
  return (a) => {
    const lRes = l(a)
    if (!lRes) {
      return null;
    }
    const [b, c_d] = lRes;
    const rRes = r(b);
    if (!rRes) {
      return null;
    }
    const [e, f_c] = rRes;
    return [e, f => c_d(f_c(f))]
  } 
}

type WithCost<T> = T & { cost: number };

function incrementCostMiddleware<B, C>(): Middleware<
  WithCost<B>,
  B,
  C,
  WithCost<C>
> {
  return ({ cost, ...rest }) => [rest as any, u => ({ cost: cost + 1, ...u })];
}

function parseURL

const fn = applyMiddleware(
  incrementCostMiddleware(),
  ({ a }: { a: number }) => ({ a, b: "hi" })
);

const res = fn({ a: 10, cost: 50 });