Yea, you will invariably run into the halting problem and similar. But I think academics are too held back by that in general. The "program space" is very large

Yea, you will invariably run into the halting problem and similar. But I think academics are too held back by that in general. The "program space" is very large, and there's of course a lot of strange beasts out there, but only a very small subset of all possible programs are meaningful to create (in the sense that people want them or their output).