Eventually though, software has to solve a real problem for a human being, and real problems (and humans) tend to be messy. A spec should model the problem and

Eventually though, software has to solve a real problem for a human being, and real problems (and humans) tend to be messy. A spec should model the problem and its solution, and will inevitably be sort of messy as a consequence. I also doubt that any spec survives implementation. Solutions must be adapted as the understanding of a problem and its appropriate solutions grow, and it is almost impossible to gain that understanding without experimentation (partial implementation).