I don't know if my thoughts here are relevant - this discussion seems a little strange to me! So I may be missing the point.
I thought that all objects seen by the user had a semantic interpretation and whatever information that we returned was semantic - in the context of the object itself. We do not want to give the syntactic representation in the PPl as the meaning of the object.
I feel that we should not try and decide if this object semantic or syntactic but what the semantics of the object are.
polyhedra, grids, BDS are clear to me - they denote points in some n-dimensional space.
What about a constraint system? Is this a set of hyperplanes - or should it have the same semantics as the polyhedron it describes? Probably the latter - but I am not really sure of the issues.
and so on
then linear expressions could have the semantics of the expression as an algebraic construct so that A + A is the same as 2*A - but then we should not say they have a space dimension; or, maybe the semantics could be the vector of the coordinates - then we can talk about the smallest space in which the vector could have a meaning - but then why say A + C has space dimension 2 while A + B has space dimension 2? Also the inhomogeneous term would not fit into this picture.
Ciao, Pat
On Wed, 1 Feb 2006, Roberto Bagnara wrote:
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?