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Vesa Karvonen wrote:
<blockquote
cite="mid:9e43b9a0705080843i36936400x7702423831d4a91e@mail.gmail.com"
type="cite">On 5/8/07, Geoffrey Alan Washburn
<a class="moz-txt-link-rfc2396E" href="mailto:geoffw@cis.upenn.edu"><geoffw@cis.upenn.edu></a> wrote:
<br>
[...]
<br>
<blockquote type="cite"> While shorter is usually better, I'm not
sure I agree in this case. At
<br>
least I hypothesize that most times that someone would want to define a
<br>
partial order, they would find it more natural to define it in terms of
a
<br>
reflexive, transitive, anti-symmetric relation, rather than a
transitive,
<br>
anti-symmetric relation. For example, in one of my several structures
that
<br>
admits a partial order (but not a total order) is an ordering based
upon
<br>
subset inclusion. Therefore, I could define
<br>
<br>
val op <= = Set.isSubset
<br>
<br>
instead of
<br>
<br>
fun x < y = Set.isSubset (x, y) andalso not (Set.==(x, y))
<br>
<br>
furthermore in some cases equality will be defined in terms of <=
and
<br>
therefore writing something like the above may be a little awkward.
<br>
</blockquote>
<br>
Those are good points and I have to agree that <= is probably the
better
<br>
alternative for the partial order concept. Indeed, the table in my
previous
<br>
message doesn't apply to this case. I apparently made it under the
<br>
assumption of a total order.
<br>
</blockquote>
<br>
I was wondering about that, but in the few minutes I tried I
couldn't find a good example that contradicted your table.<br>
<br>
<pre class="moz-signature" cols="72">--
[Geoff Washburn|<a class="moz-txt-link-abbreviated" href="mailto:geoffw@cis.upenn.edu">geoffw@cis.upenn.edu</a>|<a class="moz-txt-link-freetext" href="http://www.cis.upenn.edu/~geoffw/">http://www.cis.upenn.edu/~geoffw/</a>]
</pre>
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