Higher order function - Python

Question

I have an assignment to write a code in high order function (Function 1). However, I do not know why I should write it like that instead of normal one (Function 2). I would really appreciate if someone could show me when High order function is better.

# Function 1 (High order):
def high_function (L):
    def function (x):
        total = 0
        for i in range(len(L)):
            total = total + x **(len(L) - 1 - i) * L[i]
        return total
    return function

# Function 2 (Normal):
def high_function (L, x):
    total = 0
    for i in range(len(L)):
        total = total + x **(len(L) - 1 - i) * L[i]
    return total

Answer 1

First, give your functions a better name, so the usage is more clearly:

def polynomial(factors):
    def eval(x):
        result = 0
        for factor in factors:
            result = x * result + factor
        return result
    return eval

So the function is used to define a polynomial, which can be used to evaluate for different x :

parabola = polynomial([1, 0, 0])

And to use it somewhere else:

value = parabola(0.4)

Answer 2

I lack formal knowledge of functional programming, but in essence, having higher order functions allows you to create functions as needed and pass them to other higher order functions.

Just like objects can take in other objects, languages that treat functions as first class citizens allow functions to be passed into other functions.

Consider this example,

def add(a):
    def func(b):
      return a + b

    return func 

This add function can be used to create functions as needed

twoMore = add(2)
x = 10
xPlusTwo = twoMore(x)

Note that when you create a function within a function, the inner function is within a closure and has access to the scope of the outer function. In the case of the add function, the inner func has access to a when it returned by add and used in twoMore .

Just to conclude my point about passing functions around, consider this other example

def filter_list(valid, list):
    return [item for item in list
                if valid(item)]

def is_greater_than(value):
    def func(item):
        return item > value

    return func

my_list = [1,2,3,4,5,6,7]
gt5 = is_greater_than(5)
new_list = filter_list(gt5, my_list)