Bill Page <[email protected]> writes:

[...]

| > It is an obscure binary relation, much of which not related to
| > the actual mathematics that OpenAxiom wants to deal with.
| > That is part of the reasons why it is not glorified into a category
| > of its own.
| 
| In OpenAxiom 'before?' is exported by SetCategory
| 
| (1) -> )di op before?
| 
| There is one exposed function called before? :
|    [1] (D,D) -> Boolean from D if D has SETCAT
| 
| In FriCAS it is exported by the category 'Comparable'
| 
| (1) -> )di op smaller?
| 
| There is one unexposed function called smaller? :
|    [1] (D,D) -> Boolean from D if D has COMPAR
| 
| and it is inherit by OrderedSet it from Comparable. Note: In FriCAS
| not all domains in OrderedSet are Comparable.

OpenAxiom did not introduce a dedicated category just for 'before?', as you
would find elsewhere.  And most domains just don't care about 'before?'

If a domain has a natural ordering, then the implementation of before?
will use that -- without the author ever having to notice.  Otherwise,
we do something else he does not need to know about.  It is a purely
implementation detail artifact, which in an ideal world no OpenAxiom
user should ever have to hear of.  And I would like to keep it that way.

| > It is an obscure relation that is best ignored by most users
| > (including library writers.)  Only OpenAxiom *runtime system*
| > developers (not the library developers) have to care about it.
| >
| 
| Could you explain why you say only run-time system developers have to
| care about it?  Are you claiming that this order relation it is not
| important for "mathematical" algorithms?

It is not important for their mathematical semantics.  The only times it
matters is when we a particular algorithm happens to critically depend
on that ordering.  But, in that case, I would look twice at the
algorithm instead of trying to glorify 'before?'

-- Gaby

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