[seanhunter]

Just using set notation doesn't make an argument precise. You are begging some questions in your definition here.

For example, how do we know that a task solves a particular problem if we can't perform static analysis on it? It may give the appearance of working and then degrade radically under certain conditions. That really matters if you're using it for safety-critical applications and the problem space is large enough that it can't be exhaustively tested.