Linear Orderings
Linear orderings provide a strict order. The laws for
(<=)
for all <math>:
- reflexivity: <math>
- antisymmetry: <math>
- transitivity: <math>
and these "agree" with
<:
- x <= y = not (y > x)
- x >= y = not (y < x)
Unlike in the non-linear setting, a linear
compare doesn't
follow from
<= since it requires calls: one to
<= and one to
==. However, from a linear
compare it is easy to implement the others. Hence, the
minimal complete definition only contains
compare.