[PPL-devel] Z-polytopes in PPL

[P M Hill]

On Thu, 18 Jun 2009, Michael Classen wrote:

> Hello,
>
> this might be a trivial question for some, but I just seem to have
> problems with it:
>
> I want to adapt our internal LooPo interface to use PPL Grids instead
> of Z-Polytopes. Now, Z-Polytopes were typically defined by a domain
> (or inequality system) and an affine function, which is applied to
> that domain (also alled Lattice).
>
> Now, in PPL, as far as I can see, you can only create Grids out of
> inequality systems, congruence systems or Grid generators. Is there an
> easy way (function, constructor) to generate a Grid from an inequality
> system + affine function, like in the old Polylib?

It appears as if you think that Grids can represent something akin to 
Z-polyhedra. This is not the case, the grids are just that "lattices". 
That is, only equalities and congruences are used to define a grid, not 
inequalities.

The details about the domain are in the documentation of the PPL and also, 
in a more theoretical form, in:
Proceedings of the 16th International Symposium on Logic-based Program 
Synthesis and Transformation (LOPSTR'06) (Venice, Italy, July 2006), 
volume 4407 of Lecture Notes in Computer Science, G. Puebla, Ed., pp. 
219-235, 2007
and available at
http://www.cs.unipr.it/ppl/Documentation/bibliography

What the PPL does also provide is a product domain as a templatic class 
(Partially_Reduced_Product). By instantiating the templatic arguments to 
Grid and C_Polyhedron (or NNC_Polyhedron), we can represent something like 
the Z-Polytopes in Polylib. There is a third templatic argument for this 
class for specifying a (partial) reduction procedure. If you let us know 
more exactly what you require for your Loopo interface, we can see if it 
is already available or if it would be straightforward to add the 
appropriate feature to the domain.

Best wishes,
   Pat


>
> thank you in advance!
>
> Greetings,
> Michael
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