-------------- Original message ---------------------- From: "Jonathan Lang" <[EMAIL PROTECTED]> > TSa wrote: > > Jonathan Lang wrote: > > > If at all possible, I would expect Complex to compose Num, thus > > > letting a Complex be used anywhere that a Num is requested. > > > > This will not work. The Num type is ordered the Complex type isn't. > > The operators <, <=, > and >= are not available in Complex. > > They can be: > > $A > $B if $A.x > $B.x | $A.y > $B.y; > $A < $B if $A.x < $B.x | $A.y < $B.y; > > This also allows you to unambiguously order any arbitrary set of > complex numbers. > > Pipe dream: it would be nice if something similar to the above > (faulty) code counted as valid Perl 6 logic programming.
That dosn't work. 1+2i < 2+1i then evaluates to (true | false) which is ambigious and can't be use to sort. Num."<=" as usually defined has certain properties: it's transitive: a<= && b<=c --> a <= c, it's reflexive: a<=a, it's anti-symetric: a<=b && b<=a --> a==b and it's total: one of a<=b or b<=a must hold. a<b is then defined to be a<=b && !(a==b). Note these are the properties needed sort a list of something. It is impossible to define "<=" on Complex so that is has all these properties and also that Nums compared using the Complex version of "<=" gives the same result as using the Num version of "<=". Note that you need this to work that way if you want Num to be a subtype of Complex. -- Mark Biggar [EMAIL PROTECTED] [EMAIL PROTECTED] [EMAIL PROTECTED]
