iff with more than two arguments: the arguments after the second one are ignored #74

With three arguments, the constraint iff is handled by cosoco 2.6.1 as if only its first two arguments were given.

<instance format="XCSP3" type="CSP">
  <variables>
    <var id="a"> 0 1 </var>
    <var id="b"> 0 1 </var>
    <var id="c"> 0 1 </var>
  </variables>
  <constraints>
    <intension> iff(a,b,c) </intension>
  </constraints>
</instance>

Observed: with cosoco model.xml -model=2 -nbsols=0, the solutions are:

<values> 0 0 0 </values>
<values> 0 0 1 </values>
<values> 1 1 0 </values>
<values> 1 1 1 </values>

that is to say all the tuples where a = b, whatever the value of c.

Expected: the value of c should be taken into account. The specification writes x1 ⇔ ... ⇔ xr (Table 4.1 of XCSP3-Core); ACE considers that all the arguments must be equivalent (solutions 0 0 0 and 1 1 1), and CHOCO computes a ⇔ (b ⇔ c) (solutions 0 0 1, 0 1 0, 1 0 0, 1 1 1). The semantics is discussed in xcsp3team/pycsp3#102, but in both cases, c matters.

In PyCSP3: satisfy(iff(x > 0, y > 0, b)).

Tests: test_xor_iff_imply[COSOCO-iff(x > 0, y > 0, b)] in pycsp3/tests/test_constraints_intension.py of xcsp3team/pycsp3.

Results of the other solvers

On the instance above (with java -jar ACE-2.6.jar model.xml -s=all -xe -xc=false and java -cp choco-parsers-4.10.15-beta.jar org.chocosolver.parser.xcsp.ChocoXCSP model.xml -a -f -flt):

• ACE gives 2 solutions: (0, 0, 0), (1, 1, 1) (all the arguments are equivalent);
• CHOCO gives 4 solutions: (0, 0, 1), (0, 1, 0), (1, 0, 0), (1, 1, 1) (a ⇔ (b ⇔ c)).

Both take the third argument into account, but they do not agree on the semantics (see xcsp3team/pycsp3#102).

This issue was found by the unit tests of PyCSP3: xcsp3team/pycsp3#66