It's both! We are called to forgive and forget, yet we are not God and cannot blot out memories so easily with the sort of unconditional love He has for us.
I should live as far as possible as if I have forgotten.. that is the forgive seventy times seven bit. However, if someone has done something to destroy say my family, I may never be able to forget, but I have to live in an attitude of forgiveness, not just say it verbally.
My mind goes to people like Corrie Ten Boom, Graham Staines wife (missionary in India who with his two sons was burned alive.. his wife is now serving in India herself as a missionary alone), or Elizabeth Elliot and others of the families of the five missionaries martyred by the Aucas. They also returned to the same people and have seen a harvest for God.
I can't believe these people arn't daily reminded of their experiences or their losses at the hands of the very same people they are now working with, but forgiveness has in a sense become forgetfulness by their attitude and by the love and forgiveness God has given them. Active forgiveness speaks volumes over passive forgiveness which is often in name only.