Thank you all for your thoughtful and useful comments. Since this has largely morphed into a discussion of my 3rd question, perhaps it would interest you to hear my reason for asking it.
John is just about spot on. Part of my research involves the enumeration and generation of various combinatorial objects using what are called "loopless" or "constant time" algorithms. (This means that the time required to move from one object to the next is bounded by a constant that is independent of the size of the object. It is related to following idea: If I generate all of the possible patterns expressible with N bits by simply counting in binary, as many as N bits may change from one pattern to the next. On the other hand if I use Gray code only one bit changes from each pattern to the next. If you are interested in this essentially useless (but fun) subject, the seminal paper by Gideon Ehrlich is here: http://portal.acm.org/citation.cfm?id=321781 ) Now, suppose that I want to generate, say, the set of all ordered trees with N nodes. I need to be able to represent the empty ordered tree, i.e. the tree with with zero nodes. There are a lot of ways I could do this. The problem is that I might tomorrow be looking instead at rooted trees, or free trees, or Young tableaux and in each case I will need to represent the empty rooted tree, or the empty free tree, or the empty Young tableau. In a very real sense, the empty Young tableau IS a Young tableau and the empty ordered tree IS an ordered tree. But in an equally real sense they are the same "ghost of a thing" looked at in different universes of discourse. So, what I would like is some sort of object that is a "kind of" everything but contains nothing, a unique minimal element of the partial ordering imposed on the set of classes by the inheritance heierarchy. Whilst I am not naive mathematically, I am relatively naive in the area of language design. In my naivete, it seemed to me that None could have been designed to be such a thing. Apparently that is incorrect. The matter is not urgent, there are oodles of workarounds. Indeed, having once found a particular loopless algorithm I don't necessarily publish an implementation of it, but rather a formal description and proof of correctness. Still, before I submit things for publication I generally prefer to implement them for myself just to convince myself that what I have proved correct in fact works at least for modest values of N. Paul ____________________________________ paul[dot]lafollette[at]gmail.com http://www.cis.temple.edu/~lafollet -- http://mail.python.org/mailman/listinfo/python-list
