On Wednesday, November 29, 2006, at 07:54AM, "Maarten Kronenburg" <M.Kronenburg@inter.nl.net> wrote:
The unsigned integer inherits from the signed one. While this does model arithmetics correctly (a natural number is an integer, after all), it is the unsigned integer that has richer functionality. It's clumsy and not extensible to use inheritance in such a case.
The normal and the unsigned integer have the same functionality, only the implementation is slightly different.
I've heard this often enough since the beginning of this discussion, and imho it's a major source of confusion and problems in the design. Google "Liskov Substitution Principle", "ISA Relationship" or other similar keywords, for more information. The famous example is Shape/Rectangle/Square (read http://www.objectmentor.com/resources/articles/lsp.pdf for a good discussion). So I have to say this loud and clear: a natural number <NOT> "is a" </NOT> integer. It is not, no more than a modular one is. Try subtracting 1 to 0, and you will not get the same behavior in either three types. This violates the LSP (Liskov Subst. Princ. mentioned above) However, a const_unsigned_integer "IsA" const_integer, so long as you can't modify the value. Thus if you think of integer as a value semantic type, all is well in your relationships, but the presence of operator--, etc. dictates that unsigned_integer and integer should be unrelated classes. There is a hierarchy, equivalent to the famous example of Shape/Square/Rectangle, where (loosely speaking, and without syntactic rigor): class const_integer; class const_unsigned_integer : public const_integer; // a natural number is an integer, when talking about value semantics class integer : public const_integer; class unsigned_integer : public const_unsigned integer; But note that the fourth side of the rectangle (unsigned_integer: public integer) is *not* provided. The same goes even more drastically with modular_integer where some operations (operator<) don't make real sense. I think this was mentioned back in June, perhaps not in such details, but I remember some people objecting to the inheritance back then. I think you should think about this seriously, Maarten, since imho it's a major flaw in your design, not taking any position on allocators or other issues. I don't have a particular opinion about how to fix the proposal, but I just want this forum to be at least aware of the issues. Regards, -- Herve Bronnimann