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The statement was categorically not fine to begin with. And there was no attempt on my part to twist the paragraph beyond what [it] really means. I was merely indulging in the fine art of deconstruction which basically operates on the premise that you can judge a writer s intent only by what he or she has actually said, not by what you might possibly think he or she might possibly have wanted to have possibly said, but didn t.
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Here are some quotes from another message: Circles and ellipses are not real world objects, they are mathematical objects. Oh dear. I think I can guess what the writer is getting at here, but if my guess is correct then I have to say I don t agree with it at all. Even if you think as I do not! that mathematics is not part of the real world, you must surely agree that much of mathematics is directly relevant to the real world. Mathematical objects are precisely what enable us to construct the appropriate theories that in turn let us construct real world applications of those theories (computer systems are surely one of the prize examples here, but there are literally thousands of others). Those theories rely hugely on abstractions of various kinds, and that s precisely what mathematical objects are (i.e., abstractions). It seems to me, therefore, that any decent, selfrespecting theory of type inheritance ought to be able to deal with mathematical objects as well as with real world ones (though, to repeat, I don t draw that distinction anyway). What s more, mathematical objects provide a rich source of good examples, examples that can be used to test the theory without getting sidetracked into distracting irrelevancies (as tends to happen if you use real world objects instead, such as employees and managers). In a nutshell, then, I think this criticism is completely off base. Thus, objects are not values ... Date is right that OO people ignore the difference between values and variables; that is because they do everything with variables and do not have real values. Yes, but you can t have the concept of variable without simultaneously having the concept of value (see my comments on the previous set of criticisms above). If OO people truly do not have real values, it just means they have a concept they don t properly recognize, or name. And they can t truly ignore the difference between values and variables; again, it just means there s a concept (in this case, a logical difference) that they fail to recognize and name properly. Objects are better models of real world objects than is a value. I can let out some string as I swing an object around my head, and its orbit (a circle) has just changed its radius. Yes, the concept of a variable is useful (see above). [My] summary of the paper ... is I don t like objects. I like relations better. To each his own. They are both Turing complete. But the disagreement is much more profound than ... Date seems to realize. I never said I don t like objects, and I never said I like relations better ; in fact, the word relation didn t appear in my original article at all. Objects and relations aren t directly comparable concepts. I do know that inside a database I need relations ( need, not just like, please note). I also know that relations need to be defined over types (aka domains). Since the object class
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concept seems to be vaguely related to the all-important type concept, it seems worthwhile to explore a possible marriage between the object and relational worlds, based on this putative connection (that s one of the things Darwen and I did, in depth and detail, in The Third Manifesto). But the crucial point is that we must have a very clear notion of just what types are including a very clear notion of what it means for one type to be a subtype of another. In The Third Manifesto, we do pin down these notions, very precisely. In the object world, by contrast, we find a great lack of precision and clear thinking in these very areas. My article on circles and ellipses was intended to draw people s attention to such issues.
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Some quotes from a message from CC: Perhaps the basic premise is flawed, and a circle is a subset of an ellipse (or in otherwords an ellipse a super type of a circle) Yes I know this is contrary, but it too can be argued ... Justifying this in an application-sense would provide examples of both type and object definition representations. What the condition of these two entities are in a mathematical realm is ambiguous if you are dealing with a system which does not obey those same syntactical scriptures. I suspect the first sentence in this quote is topsy-turvy; I think CC is trying to suggest that type ELLIPSE might be a subtype of type CIRCLE (but see my earlier remarks on deconstruction!). If so, then the suggestion is not new, of course; the idea is that (for example) circles and ellipses might both have a major semiaxis, but ellipses that aren t circles have a minor semiaxis as well. But this suggestion either violates substitutability or (perhaps more likely) violates the type graph as a good model of reality e.g., it might mean that we have to pretend that ellipses in general have a radius. I don t understand the last two sentences in this quote at all. An example of an ellipse as a type / subset of a circle is as follows Type Shape area position End of Type Type Circle Shape dimension1 End of Type Type Ellipse Circle dimension2 End of Type Note the phrasing ... an ellipse as a type / subset of a circle. One thing that makes this whole subject so difficult to get your head around, at least in spoken and written debate, is that people will insist on using, for example, the term circle to mean sometimes a type, sometimes a value, and sometimes a variable (not to mention sometimes an object, and possibly other
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