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?
-- ts
