On Tue, Aug 5, 2008 at 4:54 PM, Bill Page <[EMAIL PROTECTED]> wrote: > On Tue, Aug 5, 2008 at 4:20 PM, Gabriel Dos Reis wrote: >> >> >> 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 *partial ordering*, >> its spelling should not be tied to "<", or any other usual relational >> comparison because the interpreter (and the compiler in older >> versions of Axiom) do *syntactic* replacements of x >= y by >> not (x < y) -- and my other misguided syntactic transformations, >> -- which is true only if we had a total ordering. >> >> Thoughts? >> > > As you said: simple syntactic transformations of this kind are > "misguided". I think that first of all such transformations should be > eliminated.
Just eliminating the syntactic transformations in the interpreter does not solve the problem: you get new failures, and they need to be resolved. My proposal fort SetAggregate is to replace "<" with "part?". > On the other hand, it seems to me that the issue is not > the name of the operation but rather the category to which the > operation belongs. It has lot to do with the name. Most people expect "<" to be somehow related to ">=", and to denote total ordering -- and AXIOM certainly does that. > 'SetAggregate' does have an *attribute* named > 'partiallyOrderedSet'. I do not understand why this is an attribute > and not a category with specific exports. I don't think that is the fundamental problem here. Whether it is a category or attribute does not change the problem that "<" has already a well defined meaning established in the community. > > I agree that explicitly exporting '<' from SetAggregate is harmful. > Similarly explicitly exporting 'subset?' is also wrong. Could you elaborate on why the latter is wrong? > It is > conventional to use a symbol such as '<=' for partial ordering, Not in a context where it already means total ordering. > and I > think it would be usefully represented as an export of a category > 'PartiallyOrderedSet' that satisfies the axioms: I believe that is excessive overloading that does not mix well with OrderSet. Furthermore there can be simulatenously many operations that partially order a given set (think of usual "<" and divisibility on integers). In a sense we already know that the above scheme does not scale -- see `the monoid problem'. So just putting "<" is a separate category is no solution I fear -- unless we also solve the monoid problem. > > * 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 '=' and '~=' from BasicType). Similarly if some domain has > the category 'OrderedSet' and exports the symbols '<', '<=', '>' and > '>=' then it makes sense that a default implementation of 'x >= y' can > be given by 'not (x < y)'. > > 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 *if* (and I am not sure that this antecedent > really applies) there is some important optimization that could be > done if such knowledge if more directly available to either the > compiler or the interpreter, then I think it *might* be appropriate if > some built-in knowledge of the associated categories was assumed which > would enable such transformations. The syntactical transformations are supposed to optimize some indirect calls in some cases, but I think correctness should come first, ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ open-axiom-devel mailing list open-axiom-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
