Ralf Hemmecke wrote:
>
> Well, there are also "strict partial orders", which are then
> irreflexive. But instead of antisymmetric, they are assymetric.
> (See for example: Bronstein/Semendrajew: "Taschenbuch der Mathematik"
> under "Halbordnung".)
> http://de.wikipedia.org/wiki/Taschenbuch_der_Mathematik
>
> The Aldor library seems to build on the concept of an irreflexive
> partial order.
> https://github.com/pippijn/aldor/blob/master/aldor/lib/aldor/src/base/sal_order.as#L56
>
> Note in particular that it defines
>
> (a:%) > (b:%):Boolean == ~(a <= b)
>
I did not look at Bronstein/Semendrajew, but if the aim is to
have general partial order, then the above is wrong (or uses
confusingly nonstandard definition of '>'). I am affraid that
the above is just a fancy definition of linear order (which
is OK in such case).
> in contrast to
>
> (a:%) > (b:%):Boolean == b < a
This is common definition, valid regardless of of order beeing
a partial one or linear one.
--
Waldek Hebisch
[email protected]
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