This sounds like genetic algorithm programming (see my other comment below https://news.ycombinator.com/item?id=6080492). Writing a program consists of defining the end state. The GA then runs through thousands of epochs, getting closer and closer to the end state (determined by a fitness score for each program), until the solution is found.

I was able to achieve automated programs for printing text, simple math operations, string manipulation, and conditionals. After that, programming the fitness methods started getting complicated.

"Answer Set Programming" or more generally, Constraint Programming.