Function application using Swift

FunctionApplication.playground

func fp<A, B, C>(fn:((A, B) -> C), arg:A) -> (B -> C) {
	func apply(b:B) -> C {
		return fn(arg, b)
	}
	return apply
}

func add(x: Int, y: Int) -> Int {
	return x + y
}

let addThree = fp(add, 3)

addThree(0)
addThree(1)
addThree(2)
addThree(3)

Nice partial application. Can it be extrapolated to work with unlimited arguments, though? For instance, typical implementations of partial application would permit:

func add(x: Int, y: Int, z: Int) -> Int { return x + y + z }
fp(add, 1)(2, 3) == (1 + 2 + 3)
// and
fp(fp(add, 1), 2)(3) == (1 + 2 + 3)
// or even
fp(add, 1, 2)(3) == (1 + 2 + 3)

(It's pretty clear that the original version of fp() only applies to dyadic functions.)