What makes the specification superior in principle to the program? For some domains, you can write a specification that has value in itself, it will be shorter

What makes the specification superior in principle to the program? For some domains, you can write a specification that has value in itself, it will be shorter and easier to review. For other domains, the program itself is the best specification for the desired behavior. There is nothing special about a specification that makes it inherently more correct than a program. The specification may be large enough and detailed enough that it is essentially just as hard to review as the program output. The specification can have subtle bugs, just like a program. Even worse, the specification itself is harder to test, especially for corner cases. It can be very easy to produce an excellent specification that solves a different problem than expected, especially for complex problems with many moving parts and many possible use-cases.