term rewrite system

Imagine you are playing with blocks that have different letters on each side. Let's say you have the block with the letter "a" on one side and the block with the letter "b" on the other side. You also have another block with the letter "c" on one side and the letter "d" on the other side.

Now, let's say you want to change the side of the block with the letter "a" to the side with the letter "b". You can simply flip the block over and now it will have "b" on the top instead of "a". This is kind of like what a term rewrite system does.

In computer programming, there are often a lot of complicated rules and equations that need to be simplified or rewritten in a different way. This is where term rewrite systems come in. They are like a set of blocks with different rules or equations written on them.

When a term is given to the term rewrite system, it checks to see if any of its rules or equations apply to that term. If they do, it rewrites the term to make it simpler or to match a different format.

For example, imagine you have the term (x + 1) + 2. The term rewrite system might have a rule that says "if you see (a + b) + c, you can rewrite it as a + (b + c)". So, the term rewrite system would rewrite our example as x + (1 + 2) which is simpler and easier to work with.

Overall, a term rewrite system is like a set of blocks with different rules on them that can be used to simplify and rewrite complex equations or rules.