[MLton-user] Extended Basis Library: Partial order concept

[Geoffrey Alan Washburn]

Vesa Karvonen wrote:
> On 5/8/07, Geoffrey Alan Washburn <geoffw at cis.upenn.edu> wrote:
> [...]
>>      While shorter is usually better, I'm not sure I agree in this 
>> case.  At
>> least I hypothesize that most times that someone would want to define a
>> partial order, they would find it more natural to define it in terms 
>> of a
>> reflexive, transitive, anti-symmetric relation, rather than a 
>> transitive,
>> anti-symmetric relation.  For example, in one of my several 
>> structures that
>> admits a partial order (but not a total order) is an ordering based upon
>> subset inclusion.  Therefore, I could define
>>
>>      val op <= = Set.isSubset
>>
>>  instead of
>>
>>      fun x < y = Set.isSubset (x, y) andalso not (Set.==(x, y))
>>
>>  furthermore in some cases equality will be defined in terms of <= and
>> therefore writing something like the above may be a little awkward.
>
> Those are good points and I have to agree that <= is probably the better
> alternative for the partial order concept.  Indeed, the table in my 
> previous
> message doesn't apply to this case.  I apparently made it under the
> assumption of a total order.

    I was wondering about that, but in the few minutes I tried I 
couldn't find a good example that contradicted your table.

-- 
[Geoff Washburn|geoffw at cis.upenn.edu|http://www.cis.upenn.edu/~geoffw/]

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