To forgive is to substitute a happy feeling for a sad and angry feeling, it seems to me. As long as you can do that, then you are forgiving the person. What do you think of this?
You seem to have part of the essence of forgiveness correct and yet there is more depth to it. When a person goes through the process of forgiveness, then he or she (usually slowly) transforms negative emotions (anger, discouragement, resentment) into more positive ones (happiness, joy, love). Because this is a process that can take time, we probably should not use the word “substitute” to describe the emotional transformation because “substitute” sounds as if we just quickly switch out one set of emotions for another.
Besides a transformation of emotions, the forgiver transforms thoughts from negative to more positive and behaviors also to the more positive. Besides all of this, as a person forgives, he or she grows more competent and consistent in the practice of forgiveness, sometimes reaching the goal of forgiveness more quickly after the 100th attempt compared with the first attempt. I point out all of these characteristics so that you are not left with the view that forgiveness is primarily emotional and that the change typically occurs quickly, which it does not for most people who are deeply hurt by another’s hurtful actions.