[PPL-devel] Confusion about "space dimension"

[Roberto Bagnara]

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?

-- 
Prof. Roberto Bagnara
Computer Science Group
Department of Mathematics, University of Parma, Italy
http://www.cs.unipr.it/~bagnara/
mailto:bagnara at cs.unipr.it