This is a tag-on to the previous prompt (read that one first). Now, that chapter opens up the possibility that while River has been saved from the Library and lives, there is also some embodiment of her conscience or personality in the datacore. We saw the Tenth Doctor upload her and then we saw River in the datacore with CAL, Dr Moon, her friends from the expedition and her 'children.' So does this mean there are now two River Songs (sort of)? It would certainly explain why time jumps around so much and occurs in flashes in the datacore. Also, it could explain how River was able to maintain a connection with Clara during the Name of the Doctor. I just thought that I would explore this idea a bit further here.
River returned to Luna University and her colleagues were none the wiser about what happened at the Library. To be fair, Professor River Song was a law unto herself. She organised expeditions on a whim, without consulting others, and her colleagues just let her get on with it; partly because she was a valued, successful and brilliant academic at the university and partly because they wanted a quiet life and it was easy to let River do what she wanted to do (she'd only end up doing it anyway). Even though she was exhausted, she still greeted colleagues and students cordially as she made her way to her office. Once there, she collapsed onto the sofa and fell into a fitful sleep.
She stood amidst neatly trimmed grass. A large house was behind her. She looked down at herself and noticed that she was wearing a cream dress and her hair was down. When she looked back up, a man and a young girl were walking towards her. She knew the young girl was CAL, the computer from the Library but she couldn't call her that not when the girl looked so real. She would have to call her Charlotte.
"It's okay. You're safe," Charlotte said reassuringly. "You'll always be safe here. The Doctor fixed the datacore. This is a good place now. But I was worried you might be lonely, so I brought you some friends. Aren't I a clever girl?"
"Aren't we all?" A female voice rang loud and clear.
She turned around to see her lost friends from the Library. With a smile, she remarked, "Oh, for heaven's sake. He just can't do it, can he? That man. That impossible man. He just can't give in."
She ran towards her friends and hugged them all.
River woke up suddenly. It was such a vivid dream clearly brought on as a result of her recent adventure. She settled back down. Within seconds, she was asleep. She dreamt once again that she was in the datacore.
From then on, every time that River fell asleep, she witnessed snapshots of a life in the datacore. She thought that they would have stopped after a few days but the dreams continued. She always remembered every detail of her dreams and quickly came to the conclusion that she was living another parallel life in the datacore. She didn't know why this was happening but she was able to accept it, seeing as she had seen and done plenty of strange things as a time traveller. She also figured that these 'dreams' were a small price to pay if it meant that she could continue to live.
A few days later, she worked out how she was living two separate lives. Her sonic screwdriver. After the Doctor had given it to her, because she was naturally curious, she studied it closely and found a neural relay hidden in the screwdriver. Obviously, the Doctor, the one with the spiky hair who hardly knew her, had seen the neural relays at work, decided to make one for River and then uploaded her conscience, or something, to save her. She was filled with hope and love for that impossible man, the man who wanted nothing more than for everybody to live. That night, River dreamt that she was telling her children in the datacore all about running with the Doctor and what happens when he comes to call.