7.2.40 LinkingEnd principle

• identifier: principle.linkingEnd
• dimension variables: D1, D2, D3
• argument variables:
  End: vec(label(D1) iset(label(D2)))
• default values:
  End: ^.D3.entry.end
• model record: empty
• constraints: LinkingEnd (priority 100)
• edge constraints: none

This principle assumes that the Graph principle (Graph) is used on dimensions D1 and D2.

This principle is from the family of linking principles. The constraint for all edges from v to v' labeled l on D1 is:

• if End(l) is not empty, then on D2, the incoming edge label of v' must be in End(l).

Here is the definition of the LinkingEnd 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'
   Opti(isIn) at 'Opti.ozf'
export
   Constraint
define
   proc {Constraint Nodes G Principle FD FS Select}
      DVA2DIDA = Principle.dVA2DIDA
      ArgRecProc = Principle.argRecProc
      %%
      D1DIDA = {DVA2DIDA 'D1'}
      D2DIDA = {DVA2DIDA 'D2'}
      DIDA2LabelLat = G.dIDA2LabelLat
      D1LabelLat = {DIDA2LabelLat D1DIDA}
      D1LAs = D1LabelLat.constants
   in
      if {Helpers.checkModel 'LinkingEnd.oz' Nodes
	  [D1DIDA#daughtersL
	   D2DIDA#labels]} then
	 for Node1 in Nodes do
	    for Node2 in Nodes do
	       for LA in D1LAs do
		  if {Not {Opti.isIn Node2.index Node1.D1DIDA.model.daughtersL.LA}=='out'} then
		     %% LinkingEnd
		     %%
		     %% m -l->1 d =>
		     %%   End(l) neq emptyset =>
		     %%     -End(l)->2 d
		     EndLALMRec =
		     {ArgRecProc 'End' o('^': Node1)}
		     EndLM = EndLALMRec.LA
		  in
		     {FD.impl
		      {FS.reified.include Node2.index Node1.D1DIDA.model.daughtersL.LA}
		      {FD.impl
		       {FD.nega {FS.reified.equal EndLM FS.value.empty}}
		       {FD.reified.greater
			{FS.card {FS.intersect Node2.D2DIDA.model.labels EndLM}} 0}} 1}
		  end
	       end
	    end
	 end
      end
   end
end