1. It's true that those specifications are clear (although you might also want to specify that multiset(sorted(lst)) == multiset(lst)), and sqrt should be allowed an error of half an ulp and perhaps required to be nonnegative and restricted in its domain to nonnegative numbers.) But they are not necessarily specifications that are easy to estimate, either. (I should have said "your very clear, easy-to-estimate specification", since writing specifications like the ones you have above is clearly not doing the development work.)
2. It is at least theoretically possible to automate the finding of programs that satisfy specifications like your two examples above. Given the knowledge that λx.x*x is strictly monotonic on nonnegative numbers, for example, you can apply a general binary chop routine to compute sqrt(x) in O(log numberofbits) time.
3. For your realistic example, it seems very likely that you could write software to build the scrapers rather than hiring a person. http://lists.canonical.org/pipermail/kragen-hacks/2004-Janua... represents a prototype solution to this problem from 2004, but without the knowledge of AI algorithms I have now, and of course with much less computational power than is available today.
1. It's true that those specifications are clear (although you might also want to specify that multiset(sorted(lst)) == multiset(lst)), and sqrt should be allowed an error of half an ulp and perhaps required to be nonnegative and restricted in its domain to nonnegative numbers.) But they are not necessarily specifications that are easy to estimate, either. (I should have said "your very clear, easy-to-estimate specification", since writing specifications like the ones you have above is clearly not doing the development work.)
2. It is at least theoretically possible to automate the finding of programs that satisfy specifications like your two examples above. Given the knowledge that λx.x*x is strictly monotonic on nonnegative numbers, for example, you can apply a general binary chop routine to compute sqrt(x) in O(log numberofbits) time.
3. For your realistic example, it seems very likely that you could write software to build the scrapers rather than hiring a person. http://lists.canonical.org/pipermail/kragen-hacks/2004-Janua... represents a prototype solution to this problem from 2004, but without the knowledge of AI algorithms I have now, and of course with much less computational power than is available today.