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/******************************************************************************
* Top contributors (to current version):
* Mudathir Mohamed, Daniel Larraz, Andres Noetzli
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2025 by the authors listed in the file AUTHORS
* in the top-level source directory and their institutional affiliations.
* All rights reserved. See the file COPYING in the top-level source
* directory for licensing information.
* ****************************************************************************
*
* A simple demonstration of reasoning about relations with cvc5 via Java API.
*/
import static io.github.cvc5.Kind.*;
import io.github.cvc5.*;
public class Relations
{
public static void main(String[] args) throws CVC5ApiException
{
TermManager tm = new TermManager();
Solver solver = new Solver(tm);
{
// Set the logic
solver.setLogic("ALL");
// options
solver.setOption("produce-models", "true");
// we need finite model finding to answer sat problems with universal
// quantified formulas
solver.setOption("finite-model-find", "true");
// we need sets extension to support set.universe operator
solver.setOption("sets-exp", "true");
// (declare-sort Person 0)
Sort personSort = tm.mkUninterpretedSort("Person");
// (Tuple Person)
Sort tupleArity1 = tm.mkTupleSort(new Sort[] {personSort});
// (Relation Person)
Sort relationArity1 = tm.mkSetSort(tupleArity1);
// (Tuple Person Person)
Sort tupleArity2 = tm.mkTupleSort(new Sort[] {personSort, personSort});
// (Relation Person Person)
Sort relationArity2 = tm.mkSetSort(tupleArity2);
// empty set
Term emptySetTerm = tm.mkEmptySet(relationArity1);
// empty relation
Term emptyRelationTerm = tm.mkEmptySet(relationArity2);
// universe set
Term universeSet = tm.mkUniverseSet(relationArity1);
// variables
Term people = tm.mkConst(relationArity1, "people");
Term males = tm.mkConst(relationArity1, "males");
Term females = tm.mkConst(relationArity1, "females");
Term father = tm.mkConst(relationArity2, "father");
Term mother = tm.mkConst(relationArity2, "mother");
Term parent = tm.mkConst(relationArity2, "parent");
Term ancestor = tm.mkConst(relationArity2, "ancestor");
Term descendant = tm.mkConst(relationArity2, "descendant");
Term isEmpty1 = tm.mkTerm(EQUAL, males, emptySetTerm);
Term isEmpty2 = tm.mkTerm(EQUAL, females, emptySetTerm);
// (assert (= people (as set.universe (Relation Person))))
Term peopleAreTheUniverse = tm.mkTerm(EQUAL, people, universeSet);
// (assert (not (= males (as set.empty (Relation Person)))))
Term maleSetIsNotEmpty = tm.mkTerm(NOT, isEmpty1);
// (assert (not (= females (as set.empty (Relation Person)))))
Term femaleSetIsNotEmpty = tm.mkTerm(NOT, isEmpty2);
// (assert (= (set.inter males females)
// (as set.empty (Relation Person))))
Term malesFemalesIntersection = tm.mkTerm(SET_INTER, males, females);
Term malesAndFemalesAreDisjoint = tm.mkTerm(EQUAL, malesFemalesIntersection, emptySetTerm);
// (assert (not (= father (as set.empty (Relation Person Person)))))
// (assert (not (= mother (as set.empty (Relation Person Person)))))
Term isEmpty3 = tm.mkTerm(EQUAL, father, emptyRelationTerm);
Term isEmpty4 = tm.mkTerm(EQUAL, mother, emptyRelationTerm);
Term fatherIsNotEmpty = tm.mkTerm(NOT, isEmpty3);
Term motherIsNotEmpty = tm.mkTerm(NOT, isEmpty4);
// fathers are males
// (assert (set.subset (rel.join father people) males))
Term fathers = tm.mkTerm(RELATION_JOIN, father, people);
Term fathersAreMales = tm.mkTerm(SET_SUBSET, fathers, males);
// mothers are females
// (assert (set.subset (rel.join mother people) females))
Term mothers = tm.mkTerm(RELATION_JOIN, mother, people);
Term mothersAreFemales = tm.mkTerm(SET_SUBSET, mothers, females);
// (assert (= parent (set.union father mother)))
Term unionFatherMother = tm.mkTerm(SET_UNION, father, mother);
Term parentIsFatherOrMother = tm.mkTerm(EQUAL, parent, unionFatherMother);
// (assert (= ancestor (rel.tclosure parent)))
Term transitiveClosure = tm.mkTerm(RELATION_TCLOSURE, parent);
Term ancestorFormula = tm.mkTerm(EQUAL, ancestor, transitiveClosure);
// (assert (= descendant (rel.transpose ancestor)))
Term transpose = tm.mkTerm(RELATION_TRANSPOSE, ancestor);
Term descendantFormula = tm.mkTerm(EQUAL, descendant, transpose);
// (assert (forall ((x Person)) (not (set.member (tuple x x) ancestor))))
Term x = tm.mkVar(personSort, "x");
Term xxTuple = tm.mkTuple(new Term[] {x, x});
Term member = tm.mkTerm(SET_MEMBER, xxTuple, ancestor);
Term notMember = tm.mkTerm(NOT, member);
Term quantifiedVariables = tm.mkTerm(VARIABLE_LIST, x);
Term noSelfAncestor = tm.mkTerm(FORALL, quantifiedVariables, notMember);
// formulas
solver.assertFormula(peopleAreTheUniverse);
solver.assertFormula(maleSetIsNotEmpty);
solver.assertFormula(femaleSetIsNotEmpty);
solver.assertFormula(malesAndFemalesAreDisjoint);
solver.assertFormula(fatherIsNotEmpty);
solver.assertFormula(motherIsNotEmpty);
solver.assertFormula(fathersAreMales);
solver.assertFormula(mothersAreFemales);
solver.assertFormula(parentIsFatherOrMother);
solver.assertFormula(descendantFormula);
solver.assertFormula(ancestorFormula);
solver.assertFormula(noSelfAncestor);
// check sat
Result result = solver.checkSat();
// output
System.out.println("Result = " + result);
System.out.println("people = " + solver.getValue(people));
System.out.println("males = " + solver.getValue(males));
System.out.println("females = " + solver.getValue(females));
System.out.println("father = " + solver.getValue(father));
System.out.println("mother = " + solver.getValue(mother));
System.out.println("parent = " + solver.getValue(parent));
System.out.println("descendant = " + solver.getValue(descendant));
System.out.println("ancestor = " + solver.getValue(ancestor));
}
Context.deletePointers();
}
}
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