Free variables and bound variables

Okay kiddo, imagine you have a toy box. Inside that toy box, you have some toys that you can play with, like blocks and stuffed animals. Now, let's pretend you want to talk about those toys to your friend.

When you start talking about your toys with your friend, you'll use some words to point to those toys. Those words can be thought of as variables.

Now, there are two types of variables: free variables and bound variables.

A free variable is like a toy that's not stuck in the toy box - you can take it out and play with it whenever you want. It's something that's not restricted by anything.

For example, let's say you have a red ball in your toy box, and you want to talk about it to your friend. You might say something like, "I have a red ball." The word "ball" in this sentence is a free variable because you haven't put any rules or restrictions on it. You could say "red ball," "big ball," "round ball," and so on. The variable "ball" is free to vary in any way you want.

On the other hand, a bound variable is like a toy that's stuck in the toy box - it's not free to vary. It's something that's restricted or defined by something else.

For example, let's say you have a toy car in your toy box with a red roof. You might say something like, "The car with the red roof is in the toy box." In this sentence, the variable "car" is bound because you've defined it as the one with the red roof - you can't talk about any other car in the toy box because you've already specified which one you're referring to.

So, to sum it up:

- Free variables are like toys in the toy box that you can play with in any way you want.
- Bound variables are like toys that you've defined or restricted in some way, and you can't talk about them in any other way.