Curry a variadic function

Fixed-arity currying can watch fn.length to know when it has enough. A variadic function has fn.length of 0, so there is nothing to count towards, and the curried form needs an explicit end signal instead. The convention is a call with no arguments, which is also the trick behind the add(1)(2)(3) puzzle.

Implement variadicCurry(fn). It returns a collector function. Calling the collector with one or more arguments returns a new collector holding everything gathered so far, so arguments can be supplied one at a time or several at a time, over any number of calls. Calling a collector with no arguments invokes fn with all of the arguments gathered along that chain and returns its result — so variadicCurry(fn)() invokes fn with no arguments at all. Every collector is independent: branching off the same partially applied collector twice must give two separate results, with no arguments leaking between the branches.

const sum = variadicCurry((...nums) => nums.reduce((a, b) => a + b, 0));

sum(1)(2)(3)();     // 6
sum(1, 2)(3, 4)();  // 10
sum(1, 2, 3, 4)();  // 10
sum();              // 0 — immediate empty call still invokes fn

const sum = variadicCurry((...nums) => nums.reduce((a, b) => a + b, 0));
const startsWithThree = sum(1, 2);

startsWithThree(3)();  // 6
startsWithThree(10)(); // 13 — branches do not share arguments