Welcome to this lesson on implementing a function that returns another function in Python. By the end of this lesson, you will understand how to create higher-order functions that can return other functions. This concept is useful in scenarios where you want to create customizable or deferred behavior in your programs, such as factory functions that generate specific functions at runtime.

Higher-order functions either take other functions as arguments or return them. They help create flexible, reusable code. When returning a function, consider it a "function generator" that can create specific functions based on runtime parameters.

This approach is valuable when you need functions with different behaviors based on parameters. Instead of writing multiple similar functions, you need only one generator function.

We'll use Python functions and lambda expressions to create a function that returns another function. This is often called a "factory function." Our example will generate incrementing functions based on a given increment value.

The incrementor function:

• Signature: The incrementor function takes an increment parameter and returns a lambda that adds this increment to its input.
• Return Statement: It returns a lambda that captures increment by value and takes an integer x, returning x + increment.

This way, this function creates another function, which increments its input value by increment and returns the result.

Let's consider the main function:

• Function Call: incrementor(3) returns a function that adds 3. We store it in the inc3 variable.
• Calling the Returned Function: inc3(5) increments 5 by 3, producing 8.

We can create as many such functions as we want. Here is another example:

This is why we call this function a factory!

You learned how to create functions that return other functions using Python's functions and lambda expressions. We discussed why and when to use such higher-order functions and walked through an example of an incrementor factory function. You now have a foundational understanding of creating dynamic and flexible code using Python.

Now that you've grasped the theory, it's time to solidify your knowledge through hands-on practice. You'll work on exercises to create functions that return other functions and use them in various scenarios. Let's get into the practice section to apply what you've learned!