I think if you're doing your spec as a combination of high level set theory or algebra and some prose, then it should be easier than writing the program itself

I think if you're doing your spec as a combination of high level set theory or algebra and some prose, then it should be easier than writing the program itself (assuming you know a bit about math and how to write a spec). The question is how much time is it worth putting into writing a detailed spec. I think the answer is that it really depends on the size and complexity of your software. I think the idea is that programmers have to be comfortable with writing something down, even if it's not perfect. A half-baked spec is better than no spec, basically. Otherwise you will likely end up with spaghetti code that needs to be rewritten or scrapped.