The category SetAggregate? exports a partial ordering operation for
set inclusion under the name "<". I consider this harmful. The
principal reason is that since set inclusion is a Thoughts?
It is conventional to use a symbol such as - a <= a (reflexivity);
- if a <= b and b <= a then a = b (antisymmetry);
- if a <= b and b <= c then a <= c (transitivity).
for all a, b, and c in P, where P has PartiallyOrderedSet. Then
SetAggregate should be a subcategory of PartiallyOrderedSet which in
turn is a subcategory of SetCategory (which provides the equivalence
relations It seems to me that this sort of mathematical knowledge (semantics) is
correctly captured by the appropriate design of the Axiom library. In
general I think it should not be built-in to either the compiler or
the interpreter. But Certainly the relationship between partial orders and total ordering is well understood and essential to mathematics. http://en.wikipedia.org/wiki/Totally_ordered_set A more common notation might be "s <= t returns true if all elements of set aggregate s are also elements of set aggregate t", i.e. a partial ordering given by set inclusion. http://en.wikipedia.org/wiki/Partial_order Similarly, the documentation says Apparently the documentation in 'SetAggregate': ++ s < t returns true if all elements of set aggregate s are also ++ elements of set aggregate t. is wrong? I guess that is the case since I see that the definition of
s < t == #s < #t and s = intersect(s,t) So the intention of SetAggregate is that http://en.wikipedia.org/wiki/Subset But then
I forgot to say in my original email that for full disclosure I ran into the problem I reported precisely because I removed the syntactic transformations and hit lot of regressions. So, it does not look to me that just removing the syntactic transformations is that simple. It does expose a fundamental problem that needs to be addressed: -- How many are aware that somewhere in AXIOM input files there is an expression such as: s >= t where s and t are both Multiset, which relies on the fact that the interpreter is doing misguided syntactic transformations? (I would not have guessed without actually trying it).
I have seen this kind of thing before because I was interested in the subject of the proper treatment of inequalities and inequations. See the following: http://axiom-wiki.newsynthesis.org/SandBoxInequation The following is an attempt to implement |

...--test1, Tue, 09 Apr 2013 18:25:17 +0000 reply