Unknown number of arguments in currying

Question

Hypothetical situation - can a currying function have an unknown number of arguments (kind of like varargs) Eg in Python:

addByCurrying(1)(2)(3)(4)

Should equal 10

addByCurrying(5)(6)

Should equal 11

How could I implement it?

• Sophie Swett: You can't do that in the most straightforward way. That would mean that addByCurrying(1)(2) is both a number and a function, which isn't possible.
• jscs: Have a look at Is it possible to have currying and variadic function at the same time?
• user6245072: Funny thing I discovered while playing around a bit: (lambda x: x (x)) ((lambda a: lambda b: lambda c: a (b)) (lambda x: x (x))) takes an argument and returns a new instance of itself, meaning you can pass as much arguments as you want.
• user6245072: @Tanner Swett could Church Encodings help on that?
• Frank: Possible duplicate of Is it possible to have currying and variadic function at the same time?

Answer 1

I recently answered a question on S.O regarding this exact situation. You can't do this with traditional functions in Python.

You can do this by taking advantage of callables though, overloading the __call__ dunder of an int subclass.

In short, return a new instance of your self with the updated value (+ here):

class addByCallable(int):
 def __call__(self, v):
 return type(self)(self + v)

Now, you call it and get this 'form' of currying:

addByCallable(1)(2)(3) # 6

Which is as close as you can get to doing this in Python.

• vikarjramun: Actually this is a great answer! Overloading call is a creative solution that I wouldn't have even thought of. So to do this for another class, I would just define a call function for it, that uses the value of self to return the same class, but also is a function! That's exactly what I was hoping for!
• Dimitris Fasarakis Hilliard: "but also is a function" isn't the exact terminology i'd use :-P. It is also callable, that is, it can behave as a function, that's really all we need here.

Answer 2

This is not possible since there is no way the function could know if it should return a number or a curried function.

There are various way of "cheating" to achieve some thing somewhat like this, for example you could call with no arguments in order to get the number rather than a function:

addByCurrying(1)(2) --> curried function
addByCurrying(1)(2)() --> the number 3

Which trick is most appropriate depends on what you are trying to achieve.

• vikarjramun: Can you define a lambada with an optional parameter? Or one with a default?
• JacquesB: @vikarjramun: Yes.