Andrew Barnert via Python-ideas writes:
...
Is there any commonly used or even imaginable useful type that uses
them in weirder ways than set and float (which are both partially
ordered) or np? array (where they aren’t even Boolean-values)?
I've had occasion (a class for outcomes in two-player games) to define
both < and <= as complete preorders, with "symmetry" in the sense that
A < B iff B > A and A <= B iff B >= A, but < and <= were completely
independent: they could be identical ("game of pure coordination"),
they could be inverse ("game of pure competition"), and they could be
anything else (eg, "prisoners' dilemma"). This system took a little
getting used to, but writing "A > B and A >= B and A != B" [1] to
implement "A Pareto dominates B" was one expressive convenience among
others.
I'm not sure this is "weird" in the sense you mean, and I greatly
doubt this is sufficiently common to deserve an ABC :-), but it's a
real example (long since archived on a disc whose exact location has
slipped from memory ;-) that shows how flexible "ordering" in Python
can be.
Footnotes:
[1] How the class, and specifically "A != B", were implemented is
left for the reader who knows game theory to imagine. ;-)
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