[PPL-devel] Confusion about "space dimension"

[P M Hill]

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?
>
>