[Haskell-cafe] What puts False before True?

Steve Downey sdowney at gmail.com
Tue Jun 5 19:31:37 EDT 2007

Well, traditionally, a boolean algebra is a ring, which means it has
two operations corresponding to plus and times, and a zero such that a
plus zero is a, and a one such that a times one is a. Also by
longstanding tradition, zero is less than one.

Now, in most programming languages, a boolean type is an element of
the two valued boolean algebra, but not all boolean algebras are two
valued. Four valued boolean algebra, for example, introduces m and not
m (which must be distinct).  There the ordering is typically false,
not m, m, true.

Overall, you might as well ask why 'b' is greater than 'a'.

Consistent and useful.

On 6/5/07, Albert Y. C. Lai <trebla at vex.net> wrote:
> PR Stanley wrote:
> > What do the ≤ symbols represent?
> I see you are still stuck in ISO-8859-1 and deprived of international
> characters and symbols. (And this reply in ISO-8859-1 too accordingly;
> normally I use UTF-8.) Unicode and UTF-8 FTW! :)
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