Summary  
This chapter covers higher-order functions, which are functions that accept other functions as arguments or return functions, enabling modular, reusable, and expressive code abstractions.  

General domain of usage  
Collection data transformation and filtering.

Higher-order functions are a cornerstone of functional programming. A **higher-order function** is any function that does at least one of the following: takes one or more functions as arguments, or returns a function as its result. This makes higher-order functions powerful tools for creating abstractions, reusing code, and building flexible software. By allowing functions to be passed around just like any other value, you can write code that is more modular and expressive.

 learn what higher-order functions are in Python and why they are important in functional programming. The video defines higher-order functions as functions that can take other functions as arguments or return them as results. You will see practical examples using Python's built-in `map` and `filter` functions, which show how you can pass functions like `double` or `is_even` to process and filter lists. The video also discusses how this approach leads to more modular, reusable, and expressive code. By the end, you will understand how to identify and use higher-order functions in your own Python programs. 120 - 150 wpm

## Key Points

- Higher-order functions either take one or more functions as arguments or return a function as a result;
- You can use higher-order functions to create reusable and flexible code;


def apply_to_list(func, items):
    result = []
    for item in items:
        result.append(func(item))
    return result

def double(x):
    return x * 2
    
numbers = [1, 2, 3, 4]
print(apply_to_list(double, numbers))

- Common built-in higher-order functions in Python include `map` and `filter`;
- `map` applies a function to every item in an iterable; 


def triple(x):
    return x * 3

numbers = [1, 2, 3, 4, 5]
result = list(map(triple, numbers))

print(result)

- `filter` selects items based on a condition;

def is_even(x):
    return x % 2 = 0

numbers = [1, 2, 3, 4, 5, 6]
result = list(filter(is_even, numbers))
print(result)

- Higher-order functions help you separate actions from data, making code more modular and expressive;
- Using higher-order functions reduces repetition and enables clearer communication of your intent.

Give an example of a built-in Python higher-order function.

In this course, you will learn advanced topics such as function arguments, iterators, generators, closures, and decorators. Dozens of practice exercises will help you grasp these topics.

Explore the art of packing and unpacking lists, tuples, and dictionaries to write more expressive and efficient Python code.

Delve into the world of higher-order functions, passing functions as arguments, and writing concise anonymous functions with lambda.

Unravel the mysteries of variable scope, and learn how nested functions and closures enable powerful encapsulation.

Delve into Python's iteration protocol, custom iterators, and generator functions for efficient data processing.

Understanding Higher-Order Functions

Key Points

1. What is a higher-order function?

2. Give an example of a built-in Python higher-order function.