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All the Perl that's Practical to Extract and Report

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  • OK, I'm at a loss here. Naturals don't form a ring because they lack the number zero? Is that right? If so, that seems straightforward enough. However, I don't know what you mean when you wrote that even though Naturals are rings, you seem to have proven they are. I certainly don't know what that means in relation to the code you posted.

    Taking a guess, it seems what you're saying is that for a given set S which satisfies condition C, no arbitrary subset of S is necessarily guaranteed to satisfy C but you've accidentally implied that in your theory. Thus, any time you declare a subset of something, your theory implemenation must ensure that constraints the set obeys are also met by the subset?

    As for how roles fit into this, would the theory implementation also need to ensure that the roles can operate within said constraints? Hell, am I even making sense? I only have a tenuous grasp of what you're referring to and I suspect that a large stumbling block is my not understanding your syntax for theories. If you care to explain, please be gentle. It's been many years since I've honed my math skills :)

    • > Naturals don't form a ring because they lack the
      > number zero?

      This is somewhat beside the point, but that is one reason, yes. The other reason is that there are elements (namely, all of them :-) that don't have additive inverses.

      > Taking a guess, it seems what you're saying is
      > that for a given set S which satisfies condition
      > C, no arbitrary subset of S is necessarily
      > guaranteed to satisfy C but you've accidentally
      > implied that in your theory.

      Precisely. It turns out that that's h