> 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. -- Mark Biggar [EMAIL PROTECTED] [EMAIL PROTECTED] [EMAIL PROTECTED]
