cvc5/examples/api/java/Relations.java

/*********************                                                        */
/*! \file Relations.java
 ** \verbatim
 ** Top contributors (to current version):
 **   Mudathir Mahgoub
 ** This file is part of the CVC4 project.
 ** Copyright (c) 2009-2020 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.\endverbatim
 **
 ** \brief Reasoning about relations with CVC4 via Java API.
 **
 ** A simple demonstration of reasoning about strings with CVC4 via Jave API.
 **/

import edu.stanford.CVC4.*;

/*
This file uses the API to make a sat call equivalent to the following benchmark:
(set-logic ALL)
(set-option :finite-model-find true)
(set-option :produce-models true)
(set-option :sets-ext true)
(set-option :output-language "smt2")
(declare-sort Person 0)
(declare-fun people () (Set (Tuple Person)))
(declare-fun males () (Set (Tuple Person)))
(declare-fun females() (Set (Tuple Person)))
(declare-fun father () (Set (Tuple Person Person)))
(declare-fun mother () (Set (Tuple Person Person)))
(declare-fun parent () (Set (Tuple Person Person)))
(declare-fun ancestor () (Set (Tuple Person Person)))
(declare-fun descendant () (Set (Tuple Person Person)))

(assert (= people (as univset (Set (Tuple Person)))))
(assert (not (= males (as emptyset (Set (Tuple Person))))))
(assert (not (= females (as emptyset (Set (Tuple Person))))))
(assert (= (intersection males females) (as emptyset (Set (Tuple Person)))))

; father relation is not empty
(assert (not (= father (as emptyset (Set (Tuple Person Person))))))
; mother relation is not empty
(assert (not (= mother (as emptyset (Set (Tuple Person Person))))))

; fathers are males
(assert (subset (join father people) males))
; mothers are females
(assert (subset (join mother people) females))

; parent
(assert (= parent (union father mother)))

; no self ancestor
(assert (forall ((x Person)) (not (member (mkTuple x x) ancestor))))

; descendant
(assert (= descendant (tclosure parent)))

; ancestor
(assert (= ancestor (transpose descendant)))

(check-sat)
(get-model)
 */

public class Relations {
  public static void main(String[] args) {
    System.loadLibrary("cvc4jni");

    ExprManager manager = new ExprManager();
    SmtEngine smtEngine = new SmtEngine(manager);

    // Set the logic
    smtEngine.setLogic("ALL");

    // options
    smtEngine.setOption("produce-models", new SExpr(true));
    smtEngine.setOption("finite-model-find", new SExpr(true));
    smtEngine.setOption("sets-ext", new SExpr(true));
    smtEngine.setOption("output-language", new SExpr("smt2"));

    // (declare-sort Person 0)
    Type personType = manager.mkSort("Person", 0);
    vectorType vector1 = new vectorType();
    vector1.add(personType);

    // (Tuple Person)
    Type tupleArity1 = manager.mkTupleType(vector1);
    // (Set (Tuple Person))
    SetType relationArity1 = manager.mkSetType(tupleArity1);

    vectorType vector2 = new vectorType();
    vector2.add(personType);
    vector2.add(personType);
    // (Tuple Person Person)
    DatatypeType tupleArity2 = manager.mkTupleType(vector2);
    // (Set (Tuple Person Person))
    SetType relationArity2 = manager.mkSetType(tupleArity2);

    // empty set
    EmptySet emptySet = new EmptySet(relationArity1);
    Expr emptySetExpr = manager.mkConst(emptySet);

    // empty relation
    EmptySet emptyRelation = new EmptySet(relationArity2);
    Expr emptyRelationExpr = manager.mkConst(emptyRelation);

    // universe set
    Expr universeSet =
        manager.mkNullaryOperator(relationArity1, Kind.UNIVERSE_SET);

    // variables
    Expr people = manager.mkVar("people", relationArity1);
    Expr males = manager.mkVar("males", relationArity1);
    Expr females = manager.mkVar("females", relationArity1);
    Expr father = manager.mkVar("father", relationArity2);
    Expr mother = manager.mkVar("mother", relationArity2);
    Expr parent = manager.mkVar("parent", relationArity2);
    Expr ancestor = manager.mkVar("ancestor", relationArity2);
    Expr descendant = manager.mkVar("descendant", relationArity2);

    Expr isEmpty1 = manager.mkExpr(Kind.EQUAL, males, emptySetExpr);
    Expr isEmpty2 = manager.mkExpr(Kind.EQUAL, females, emptySetExpr);

    // (assert (= people (as univset (Set (Tuple Person)))))
    Expr peopleAreTheUniverse = manager.mkExpr(Kind.EQUAL, people, universeSet);
    // (assert (not (= males (as emptyset (Set (Tuple Person))))))
    Expr maleSetIsNotEmpty = manager.mkExpr(Kind.NOT, isEmpty1);
    // (assert (not (= females (as emptyset (Set (Tuple Person))))))
    Expr femaleSetIsNotEmpty = manager.mkExpr(Kind.NOT, isEmpty2);

    // (assert (= (intersection males females) (as emptyset (Set (Tuple
    // Person)))))
    Expr malesFemalesIntersection =
        manager.mkExpr(Kind.INTERSECTION, males, females);
    Expr malesAndFemalesAreDisjoint =
        manager.mkExpr(Kind.EQUAL, malesFemalesIntersection, emptySetExpr);

    // (assert (not (= father (as emptyset (Set (Tuple Person Person))))))
    // (assert (not (= mother (as emptyset (Set (Tuple Person Person))))))
    Expr isEmpty3 = manager.mkExpr(Kind.EQUAL, father, emptyRelationExpr);
    Expr isEmpty4 = manager.mkExpr(Kind.EQUAL, mother, emptyRelationExpr);
    Expr fatherIsNotEmpty = manager.mkExpr(Kind.NOT, isEmpty3);
    Expr motherIsNotEmpty = manager.mkExpr(Kind.NOT, isEmpty4);

    // fathers are males
    // (assert (subset (join father people) males))
    Expr fathers = manager.mkExpr(Kind.JOIN, father, people);
    Expr fathersAreMales = manager.mkExpr(Kind.SUBSET, fathers, males);

    // mothers are females
    // (assert (subset (join mother people) females))
    Expr mothers = manager.mkExpr(Kind.JOIN, mother, people);
    Expr mothersAreFemales = manager.mkExpr(Kind.SUBSET, mothers, females);

    // (assert (= parent (union father mother)))
    Expr unionFatherMother = manager.mkExpr(Kind.UNION, father, mother);
    Expr parentIsFatherOrMother =
        manager.mkExpr(Kind.EQUAL, parent, unionFatherMother);

    // (assert (= parent (union father mother)))
    Expr transitiveClosure = manager.mkExpr(Kind.TCLOSURE, parent);
    Expr descendantFormula =
        manager.mkExpr(Kind.EQUAL, descendant, transitiveClosure);

    // (assert (= parent (union father mother)))
    Expr transpose = manager.mkExpr(Kind.TRANSPOSE, descendant);
    Expr ancestorFormula = manager.mkExpr(Kind.EQUAL, ancestor, transpose);

    // (assert (forall ((x Person)) (not (member (mkTuple x x) ancestor))))
    Expr x = manager.mkBoundVar("x", personType);
    Expr constructor = tupleArity2.getDatatype().get(0).getConstructor();
    Expr xxTuple = manager.mkExpr(Kind.APPLY_CONSTRUCTOR, constructor, x, x);
    Expr member = manager.mkExpr(Kind.MEMBER, xxTuple, ancestor);
    Expr notMember = manager.mkExpr(Kind.NOT, member);
    vectorExpr vectorExpr = new vectorExpr();
    vectorExpr.add(x);
    Expr quantifiedVariables = manager.mkExpr(Kind.BOUND_VAR_LIST, x);
    Expr noSelfAncestor =
        manager.mkExpr(Kind.FORALL, quantifiedVariables, notMember);

    // formulas
    Expr formula1 = manager.mkExpr(Kind.AND,
        peopleAreTheUniverse,
        maleSetIsNotEmpty,
        femaleSetIsNotEmpty,
        malesAndFemalesAreDisjoint);

    Expr formula2 = manager.mkExpr(Kind.AND,
        formula1,
        fatherIsNotEmpty,
        motherIsNotEmpty,
        fathersAreMales,
        mothersAreFemales);

    Expr formula3 = manager.mkExpr(Kind.AND,
        formula2,
        parentIsFatherOrMother,
        descendantFormula,
        ancestorFormula,
        noSelfAncestor);

    // check sat
    Result result = smtEngine.checkSat(formula3);

    // output
    System.out.println("CVC4 reports: " + formula3 + " is " + result + ".");
    System.out.println("people     = " + smtEngine.getValue(people));
    System.out.println("males      = " + smtEngine.getValue(males));
    System.out.println("females    = " + smtEngine.getValue(females));
    System.out.println("father     = " + smtEngine.getValue(father));
    System.out.println("mother     = " + smtEngine.getValue(mother));
    System.out.println("parent     = " + smtEngine.getValue(parent));
    System.out.println("descendant = " + smtEngine.getValue(descendant));
    System.out.println("ancestor   = " + smtEngine.getValue(ancestor));
  }
}