On 5/20/05, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:
> > Mark A. Biggar wrote:
> > > Well the identity of % is +inf (also right side only).
> > I read $n % any( $n..Inf ) == $n. The point is there's no
> > unique right identity and thus (Num,%) disqualifies for a
> > Monoid. BTW, the above is a nice example where a junction
> > needn't be preserved :)
> If as usual the definition of a right identity value e is that a op e = a for
> all a,
> then only +inf works. Besdies you example should have been;
> $n % any (($n+1)..Inf), $n % $n = 0.
> > > E.g. if X<Y is left associative and returns Y when true then ...
> > Sorry, is it the case that $x = $y < $z might put something else
> > but 0 or 1 into $x depending on the order relation between $y and $z?
> Which is one reason why I siad that it might not make sense to define the
> chaining ops in terms of the associtivity of the binary ops, But as we are
> interested in what [<] over the empty list shoud return , the identity (left
> or right) of '<' is unimportant as I think that should return false as there
> is nothing to be less then anything else. Note that defaulting to undef
> therefore works in that case.
On the contrary a mathematician would say that the empty list is
monotonically increasing (vacuously) and the answer should be true.
"Computer Science is merely the post-Turing Decline of Formal Systems Theory."