But not actually. Program synthesis is hard even if you have perfect formal requirements. In practice, gathering formal requirements is by far the most difficult task. You're probably better off building a system using modern development practices than trying to collect formal requirements Let alone translating those requirements into code, which is easier than coming up with the requirements but still difficult.

> Recently AI has proved...

FYI, it's not as if the program synthesis folks haven't heard of neural nets... you're giving researchers who actually do this stuff all day surprisingly little credit.