The norm is I will forgive but I won't/can't forget. God says "your sins are forgiven and I will remember them no more". I think I wan't His kind of forgiving, not mine.
And as human beings, I think it is difficult if not impossible at times to forget. In fact, sometimes it is dangerous not to forget. We can forgive- no longer holding someone responsible. But ONLY our Heavenly Father forgives AND forgets our sins.
Should have read dangerous not to REMEMBER. Take for example an abuse victim. They can forgive the abuser, but putting themselves in a position where they can continue to be abused is not wise.