[PPL-devel] Confusion about "space dimension"
P M Hill
hill at comp.leeds.ac.uk
Wed Feb 1 16:46:07 CET 2006
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
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.
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
> 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
> Constraint_System outght to be another thing. Notice that I am not
> 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
> 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
>> What is the "space dimension" of this object? The maximum of the "space
>> dimensions" of the objects it contains?
>> 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?
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