7.2.61 Projectivity principle

• identifier: principle.projectivity
• dimension variables: D
• argument variables: none
• default values: none
• model record: empty
• constraints: Projectivity (priority 130)
• edge constraints: none

This principle assumes that the Graph principle (Graph) is used on dimension D.

The operation of this principle depends on whether on D, a principle is used that introduces the yield feature, i.e., typically an order principle. If the yield feature is present, then the principle states that for each node on D, its yield set must be convex (i.e. without holes), otherwise, the eqdown set must be convex.

Here is the definition of the Projectivity constraint functor:

%% Copyright 2001-2008
%% by Ralph Debusmann <rade@ps.uni-sb.de> (Saarland University) and
%%    Denys Duchier <duchier@ps.uni-sb.de> (LIFO, Orleans) and
%%    Jorge Marques Pelizzoni <jpeliz@icmc.usp.br> (ICMC, Sao Paulo) and
%%    Jochen Setz <info@jochensetz.de> (Saarland University)
%%
functor
import
%   System(show)
   
   Helpers(checkModel) at 'Helpers.ozf'
export
   Constraint
define
   proc {Constraint Nodes G Principle FD FS Select}
      DVA2DIDA = Principle.dVA2DIDA
      %%
      DIDA = {DVA2DIDA 'D'}
   in
      %% check features
      if {Helpers.checkModel 'Projectivity.oz' Nodes
	  [DIDA#eqdown]} then
	 for Node in Nodes do
	    if {HasFeature Node.DIDA.model yield} then
	       {FS.int.convex Node.DIDA.model.yield}
	    else
	       {FS.int.convex Node.DIDA.model.eqdown}
	    end
	 end
      end
   end
end