Is there an Algorithm that can code itself? Suppose there is algorithm that has a strong NLP module. Could it use the NLP module to read text books such as http://www.amazon.in/Artificial-Intelligence-Modern-Approach-Prentice/dp/0136042597 in text form, parse it, understand the semantics and then use the knowledge to improve the very code it's written in ?
Like a virtual computer scientist? Is any research group working on it or even thought of that idea?
While there are no program synthesizers that can synthesize themselves in their entirety, plenty of synthesizers can synthesize pieces of themselves. Rohit Singh, for instance, has a project using the Sketch synthesizer to optimize many logical solvers, including that of Sketch itself.