Here are the results of my research into program synthesis using genetic algorithms.

Using Artificial Intelligence to Write Self-Modifying/Improving Programs

http://www.primaryobjects.com/2013/01/27/using-artificial-in...

There is always a research paper, if you prefer the sciency format.

BF-Programmer: A Counterintuitive Approach to Autonomously Building Simplistic Programs Using Genetic Algorithms

http://www.primaryobjects.com/bf-programmer-2017.pdf