Question

I am studying the properties of functions in Python and I came across an exercise that asks to:

Write a function which returns de power of a number. Conditions: The function may only take 1 argument and must use another function to return the value of the power of a given number.

The code that solves this exercise is:

def power(x):
    return lambda y: y**x

For example, if we would like to know the value of the power: 2^3, we would call the function like this: power(3)(2)

Here is what I would like to know:

Is there any way to write a function that, when called, has a similar structure: function()()().
In other words, is it possible to write a function, that requires three or more parentheses ()()() when called?
If it is possible, could you please give me an example code of that function and briefly explain it?

Also:

def power(x):
    def power_extra(y):
        return y

    def power_another(z):
        return z

    return power_extra and power_another

Possible?

Answer 1

Sure you can:

def power_times(k):
    """use as power_times(k)(x)(y) => k * y^x"""
    return lambda x: lambda y: k * y**x

print power_times(2)(3)(4)  # returns 2 * 4^3 = 128

When you call this function with argument 2 (power_times(2)), it returns a lambda function that works like lambda x: lambda y: 2 * y ** x (that is, like your original function, only with an extra “times 2”).

You can stack as many lambdas on top of each other as you like:

def many_lambdas(x):
    """many_lambdas(x)(y)(z)(q) => x + y * z^q"""
    return lambda y: lambda z: lambda q: x + y * z ** q

print many_lambdas(1)(2)(3)(4) # prints 163

Indeed, it might be even clearer if you skipped using def at all, and just wrote:

many_lambdas = lambda x: lambda y: lambda z: lambda q: x + y * z ** q

Or, alternatively, you could skip using lambda ever and just use them as nested functions:

def many_funcs(x):
    def many_funcs_y(y):
        def many_funcs_z(z):
            def many_funcs_q(q):
                return x + y * z ** q
            return many_funcs_q
        return many_funcs_z
    return many_funcs_y

print many_funcs(1)(2)(3)(4)  # prints 163