Doctor Moon
The Doctor Moon was an artificial moon which was built by Felman Lux, Strackman Lux's grandfather, to protect CAL, his youngest daughter who became the Library's computer and was given an imaginary world in which to play while in control of the Library. He was built has a virus checker desighned to monitor CAL's systems and her spiritual wellbeing. He continued to perform these functions even during the Vasda Narada crisis. His presense is enough to stop the Doctor'soic screwdriver working which he did has nightfall arived and his phisical body came in range.
In Charlotte's imaginary world Doctor Moon was in human form and was treating her. He protected her and gave her advice to save the others in the Library. That was until she was in an overload and temporarily switched him off. When the Doctor saved River Song into CAL's imaginary world, the Doctor Moon was back online once more, protecting CAL, River and the rest of the team, minus Strackman Lux who had not died in the Library. (DW: Silence in the Library/ Forest of the Dead)
Doctor Moon's function in the virtual world was apparently to keep both Charlotte and others downloaded into it from realising the unreality of the world they were in, possibly to help them keep sane. The virtual world was modelled after early 21st Century Earth (or something similar to it).
In the virtul world he can control people's memories including CAL's using the simple sentance "And then" followed by whatever comanned he wished from forgetting something to remembering something. Unlike CAL who could be considered to have gone mad thanks to the Vasda nerada insident Doctor Moon was still quite sane though very logic bound.