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/******************************************************************************
* Top contributors (to current version):
* Mudathir Mohamed, Aina Niemetz, Mathias Preiner
*
* 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 via the C++ API.
*/
#include <cvc5/cvc5.h>
#include <iostream>
using namespace cvc5;
int main()
{
TermManager tm;
Solver 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({personSort});
// (Relation Person)
Sort relationArity1 = tm.mkSetSort(tupleArity1);
// (Tuple Person Person)
Sort tupleArity2 = tm.mkTupleSort({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(Kind::EQUAL, {males, emptySetTerm});
Term isEmpty2 = tm.mkTerm(Kind::EQUAL, {females, emptySetTerm});
// (assert (= people (as set.universe (Relation Person))))
Term peopleAreTheUniverse = tm.mkTerm(Kind::EQUAL, {people, universeSet});
// (assert (not (= males (as set.empty (Relation Person)))))
Term maleSetIsNotEmpty = tm.mkTerm(Kind::NOT, {isEmpty1});
// (assert (not (= females (as set.empty (Relation Person)))))
Term femaleSetIsNotEmpty = tm.mkTerm(Kind::NOT, {isEmpty2});
// (assert (= (set.inter males females)
// (as set.empty (Relation Person))))
Term malesFemalesIntersection = tm.mkTerm(Kind::SET_INTER, {males, females});
Term malesAndFemalesAreDisjoint =
tm.mkTerm(Kind::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(Kind::EQUAL, {father, emptyRelationTerm});
Term isEmpty4 = tm.mkTerm(Kind::EQUAL, {mother, emptyRelationTerm});
Term fatherIsNotEmpty = tm.mkTerm(Kind::NOT, {isEmpty3});
Term motherIsNotEmpty = tm.mkTerm(Kind::NOT, {isEmpty4});
// fathers are males
// (assert (set.subset (rel.join father people) males))
Term fathers = tm.mkTerm(Kind::RELATION_JOIN, {father, people});
Term fathersAreMales = tm.mkTerm(Kind::SET_SUBSET, {fathers, males});
// mothers are females
// (assert (set.subset (rel.join mother people) females))
Term mothers = tm.mkTerm(Kind::RELATION_JOIN, {mother, people});
Term mothersAreFemales = tm.mkTerm(Kind::SET_SUBSET, {mothers, females});
// (assert (= parent (set.union father mother)))
Term unionFatherMother = tm.mkTerm(Kind::SET_UNION, {father, mother});
Term parentIsFatherOrMother =
tm.mkTerm(Kind::EQUAL, {parent, unionFatherMother});
// (assert (= ancestor (rel.tclosure parent)))
Term transitiveClosure = tm.mkTerm(Kind::RELATION_TCLOSURE, {parent});
Term ancestorFormula = tm.mkTerm(Kind::EQUAL, {ancestor, transitiveClosure});
// (assert (= descendant (rel.transpose descendant)))
Term transpose = tm.mkTerm(Kind::RELATION_TRANSPOSE, {ancestor});
Term descendantFormula = tm.mkTerm(Kind::EQUAL, {descendant, transpose});
// (assert (forall ((x Person)) (not (set.member (tuple x x) ancestor))))
Term x = tm.mkVar(personSort, "x");
Term xxTuple = tm.mkTuple({x, x});
Term member = tm.mkTerm(Kind::SET_MEMBER, {xxTuple, ancestor});
Term notMember = tm.mkTerm(Kind::NOT, {member});
Term quantifiedVariables = tm.mkTerm(Kind::VARIABLE_LIST, {x});
Term noSelfAncestor =
tm.mkTerm(Kind::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
std::cout << "Result = " << result << std::endl;
std::cout << "people = " << solver.getValue(people) << std::endl;
std::cout << "males = " << solver.getValue(males) << std::endl;
std::cout << "females = " << solver.getValue(females) << std::endl;
std::cout << "father = " << solver.getValue(father) << std::endl;
std::cout << "mother = " << solver.getValue(mother) << std::endl;
std::cout << "parent = " << solver.getValue(parent) << std::endl;
std::cout << "descendant = " << solver.getValue(descendant) << std::endl;
std::cout << "ancestor = " << solver.getValue(ancestor) << std::endl;
}
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