Enea Zaffanella wrote:
When considering systems of semantic objects, all the object in a system will have the same space dimension. They can be reordered and modified as long as the semantics of the system stays the same. We can add/remove redundant objects in the multiset.
Systems of semantic objects seem redundant to me: a finite system of semantic objects is a semantic object, and I see little value in calling it with two names. In other words, a system of hyperplanes and halfspaces is a polyhedron: Constraint_System outght to be another thing. Notice that I am not insisting on a religious view of "syntax" (as usual, we do not distinguish between syntactically different constraints defining the same affine half-space so that, for example, x >= 2 and 2x >= 4 are the same constraint).
In contrast, a system of syntactic objects is a list of syntactic objects: should reordering and/or semantics-preserving modifications be allowed on it?
We can negotiate. But this does not seem a big problem to me. Reordering: why not? Normalization: why not? Let us take an "abstract syntax view" and forget about all the syntactic sugar.
What is the "space dimension" of this object? The maximum of the "space dimensions" of the objects it contains?
Yes.
To keep it short, I think that this change of perspective has to be carefully considered, one facet at a time, striving for maximum consistency and clarity. It will take some time to foresee all of the possible consequences of any design change in this respect ...
Yes, but it cannot take ages: work on the foreign interfaces has to start soon. In order to do this, we must come up with an abstract view of our objects (syntactic and semantic ones) that has a chance of surviving the additions we have already made (grids, bd-shapes, powersets) and that we are about to make.
However, before attacking Constraint_System, let us start from the easy example in my message: is
A + B has space dimension 3
somehow defensible?