[EMAIL PROTECTED] wrote:
I see here another case of a common erroneous approach to problem-solving. People are trying to enumerate definitions to impose on something, rather than starting with the thing at hand and exhausting any clues it may provide before moving on. This can lead to serious and, in hindsight, embarrassing mistakes.
In this case, we are dealing with '^^', a meaningless unpronounceable symbol. Oh, but wait ... we also spell it 'xor', which I suppose is often pronounced "ex or", which might be the source of the difficulty. Because 'xor' stands for ... ... 'exclusive or'. Exclusive? It's not hard to figure out what that means. Here are some of the relevant dictionary definitions:
Not allowing something else; incompatible: mutually exclusive conditions Not accompanied by others; single or sole
So what does that say about proposing that xor(p1,p2,...) is true if an odd number of p[i] are true? Other than that people should pronounce these operators out loud more often?
Clearly, xor is true iff *exactly* one of its arguments is true, and of course it should return that argument (or bool::false if no argument is true).
That should now be so blatantly obvious that everyone should be embarrassed for not having seen it immediately. But don't run from embarrassment (or become defensive and attack the messenger) -- it's a powerful tool (which is why we evolved to have it). It should cause one to question one's thought processes and consider how to improve upon them, which is all to the good, isn't it?
Except that xor or ^^ is only a binary operation, there is no
"xor(p1,p2,...)", only "p1 xor p2 xor ..." which can really only be understood if you add () to disambiguate the order that the binary ops are performed. Fortunately, xor is associative so it doesn't matter how you add the (), you get the same answer. Try it out, you will discover
that "p1 xor p2 xor ..." is true iff an odd number of the p's are true. As long as you build "p1 xor p2 xor ..." out of binary xor ops that is the result you get. Computing parity is much more common that your multi-arg operation. Besides, all the literature about logic and circuit design define "p1 xor p2 xor ..." in terms of binary xor, so your trying to buck hundreds of years of consensus.
-- [EMAIL PROTECTED] [EMAIL PROTECTED]
