Does Forgiveness Require Forgetting?

We started our new Faith Development discussion group March 6 and 10. One aspect of forgiveness that generated a stimulating conversation was whether forgiving necessitated forgetting as well. This is an important question. As I have reflected on this, I think for the most part forgiveness is an internal choice a person decides to make. I can choose to forgive, or not. Forgetting, on the other hand, seems to involve memories. Can I really choose to forget something? I suppose I can try. I can even deny in my mind that something happened. But in my personal experience I find my memories seem to present themselves involuntarily. Whether I want to or not, a memory of a past experience may come into my thoughts and feelings. So for me, I have been able to forgive someone/something that happened in the past while the memory still exists in my head and pops up involuntarily on occasion. What do you think? What are your experiences of forgiveness and forgetting (remembering)?