missing 'xor' Boolean operator

[Wayne Brehaut]

On Tue, 14 Jul 2009 11:47:41 -0700 (PDT), Mark Dickinson
<dickinsm at gmail.com> wrote:

>On Jul 14, 7:25 pm, "Dr. Phillip M. Feldman" <pfeld... at verizon.net>
>wrote:
>> Current Boolean operators are 'and', 'or', and 'not'.  It would be nice to
>> have an 'xor' operator as well.
>
>Hmm.  I don't think 'nice' is sufficient.  You'd need to make the case
>that it's sufficiently useful to justify adding a new keyword 'xor' to
>the language;  I suspect that would be an uphill struggle. :)
>
>I'll just note that:
>
>(1) It's easy to emulate xor:  'x xor y' <-> bool(x) != bool(y)
>
>(2) 'and' and 'or' are special in that they have useful short-
>circuiting behaviour; xor doesn't have this property (that is, you
>always need to evaluate *both* operands to determine the result).
>
>I'd also guess that 'xor' would be much less used than 'and' or 'or',
>but maybe that's just a reflection of the sort of code that I tend to
>write.

You're right about that!. It's used everywhere in:

- coding and encryption theory (and practice) (e.g.,
http://www.mathcs.emory.edu/~whalen/Hash/Hash_Articles/IEEE/XOR-based%20hash%20functions.pdf)
- emulation and simulation of hardware (since all but the most trivial
logic circuits are likely to include XOR-gates)
- hence, for design of new architectures or simulators or virtual
machines and simplification of existing ones--(e.g.,
http://www.date-conference.com/archive/conference/proceedings/PAPERS/1999/DATE99/PDFFILES/05A_6.PDF)
and
http://bochs.sourceforge.net/Virtualization_Without_Hardware_Final.pdf
which includes:

"The answer relies on the observation that subtracting an integer
value from 0xFFFFFFFF gives the same result as XOR-ing that same value
to 0xFFFFFFFF."

And, perhaps the most useful use of all, for Bouton's solution of the
game of Nim--both for the proof that his strategy "solves" the game
and for an easy implementation of a Nim-playing program--and the only
operator needed is XOR (e.g., http://www.wordiq.com/definition/Nim).

wayne