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SolverTheoriesTest.java
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// This file is part of JavaSMT,
// an API wrapper for a collection of SMT solvers:
// https://github.com/sosy-lab/java-smt
//
// SPDX-FileCopyrightText: 2022 Dirk Beyer <https://www.sosy-lab.org>
//
// SPDX-License-Identifier: Apache-2.0
package org.sosy_lab.java_smt.test;
import static com.google.common.truth.Truth.assertThat;
import static com.google.common.truth.TruthJUnit.assume;
import static org.junit.Assert.assertThrows;
import static org.sosy_lab.java_smt.test.ProverEnvironmentSubject.assertThat;
import com.google.common.collect.ImmutableList;
import com.google.common.collect.ImmutableSet;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.List;
import java.util.Random;
import org.junit.AssumptionViolatedException;
import org.junit.Ignore;
import org.junit.Test;
import org.sosy_lab.java_smt.SolverContextFactory.Solvers;
import org.sosy_lab.java_smt.api.ArrayFormula;
import org.sosy_lab.java_smt.api.BitvectorFormula;
import org.sosy_lab.java_smt.api.BooleanFormula;
import org.sosy_lab.java_smt.api.FormulaType;
import org.sosy_lab.java_smt.api.FunctionDeclaration;
import org.sosy_lab.java_smt.api.Model;
import org.sosy_lab.java_smt.api.NumeralFormula.IntegerFormula;
import org.sosy_lab.java_smt.api.NumeralFormula.RationalFormula;
import org.sosy_lab.java_smt.api.ProverEnvironment;
import org.sosy_lab.java_smt.api.SolverContext.ProverOptions;
import org.sosy_lab.java_smt.api.SolverException;
@SuppressWarnings("LocalVariableName")
public class SolverTheoriesTest extends SolverBasedTest0.ParameterizedSolverBasedTest0 {
@Test
public void basicBoolTest() throws SolverException, InterruptedException {
BooleanFormula a = bmgr.makeVariable("a");
BooleanFormula b = bmgr.makeBoolean(false);
BooleanFormula c = bmgr.xor(a, b);
BooleanFormula d = bmgr.makeVariable("b");
BooleanFormula e = bmgr.xor(a, d);
BooleanFormula notImpl = bmgr.and(a, bmgr.not(e));
assertThatFormula(a).implies(c);
assertThatFormula(notImpl).isSatisfiable();
}
@Test
public void basicIntTest() {
requireIntegers();
IntegerFormula a = imgr.makeVariable("a");
IntegerFormula b = imgr.makeVariable("b");
assertThat(a).isNotEqualTo(b);
}
@Test
public void basisRatTest() throws SolverException, InterruptedException {
requireRationals();
RationalFormula a = rmgr.makeVariable("int_c");
RationalFormula num = rmgr.makeNumber(4);
BooleanFormula f = rmgr.equal(rmgr.add(a, a), num);
assertThatFormula(f).isSatisfiable();
}
@Test
public void intTest1() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula a = imgr.makeVariable("int_a");
IntegerFormula num = imgr.makeNumber(2);
BooleanFormula f = imgr.equal(imgr.add(a, a), num);
assertThatFormula(f).isSatisfiable();
}
@Test
public void intTest2() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula a = imgr.makeVariable("int_b");
IntegerFormula num = imgr.makeNumber(1);
BooleanFormula f = imgr.equal(imgr.add(a, a), num);
assertThatFormula(f).isUnsatisfiable();
}
private void assertDivision(
IntegerFormula numerator,
IntegerFormula denominator,
IntegerFormula expectedResult,
BooleanFormula... constraints)
throws SolverException, InterruptedException {
assertDivision(true, numerator, denominator, expectedResult, constraints);
}
private void assertDivision(
boolean includeNegation,
IntegerFormula numerator,
IntegerFormula denominator,
IntegerFormula expectedResult,
BooleanFormula... constraints)
throws SolverException, InterruptedException {
assertOperation(
includeNegation, buildDivision(numerator, denominator, expectedResult), constraints);
}
private void assertDivision(
BitvectorFormula numerator,
BitvectorFormula denominator,
boolean signed,
BitvectorFormula expectedResult,
BooleanFormula... constraints)
throws SolverException, InterruptedException {
assertDivision(true, numerator, denominator, signed, expectedResult, constraints);
}
private void assertDivision(
boolean includeNegation,
BitvectorFormula numerator,
BitvectorFormula denominator,
boolean signed,
BitvectorFormula expectedResult,
BooleanFormula... constraints)
throws SolverException, InterruptedException {
assertOperation(
includeNegation,
buildDivision(numerator, denominator, signed, expectedResult),
constraints);
}
private void assertModulo(
IntegerFormula numerator,
IntegerFormula denominator,
IntegerFormula expectedResult,
BooleanFormula... constraints)
throws SolverException, InterruptedException {
assertModulo(true, numerator, denominator, expectedResult, constraints);
}
private void assertModulo(
boolean includeNegation,
IntegerFormula numerator,
IntegerFormula denominator,
IntegerFormula expectedResult,
BooleanFormula... constraints)
throws SolverException, InterruptedException {
assertOperation(
includeNegation, buildModulo(numerator, denominator, expectedResult), constraints);
}
private void assertModulo(
BitvectorFormula numerator,
BitvectorFormula denominator,
boolean signed,
BitvectorFormula expectedResult,
BooleanFormula... constraints)
throws SolverException, InterruptedException {
assertModulo(true, numerator, denominator, signed, expectedResult, constraints);
}
private void assertModulo(
boolean includeNegation,
BitvectorFormula numerator,
BitvectorFormula denominator,
boolean signed,
BitvectorFormula expectedResult,
BooleanFormula... constraints)
throws SolverException, InterruptedException {
assertOperation(
includeNegation, buildModulo(numerator, denominator, signed, expectedResult), constraints);
}
private BooleanFormula buildDivision(
IntegerFormula numerator, IntegerFormula denominator, IntegerFormula expectedResult) {
return imgr.equal(imgr.divide(numerator, denominator), expectedResult);
}
private BooleanFormula buildDivision(
BitvectorFormula numerator,
BitvectorFormula denominator,
boolean signed,
BitvectorFormula expectedResult) {
return bvmgr.equal(bvmgr.divide(numerator, denominator, signed), expectedResult);
}
private BooleanFormula buildModulo(
IntegerFormula numerator, IntegerFormula denominator, IntegerFormula expectedResult) {
return imgr.equal(imgr.modulo(numerator, denominator), expectedResult);
}
private BooleanFormula buildModulo(
BitvectorFormula numerator,
BitvectorFormula denominator,
boolean signed,
BitvectorFormula expectedResult) {
return bvmgr.equal(bvmgr.remainder(numerator, denominator, signed), expectedResult);
}
private void assertOperation(
boolean includeNegation, BooleanFormula equation, BooleanFormula... constraints)
throws SolverException, InterruptedException {
// check positive case
assertThatFormula(bmgr.and(bmgr.and(constraints), equation)).isSatisfiable();
// check negative case
BooleanFormulaSubject negation =
assertThatFormula(bmgr.and(bmgr.and(constraints), bmgr.not(equation)));
if (includeNegation) {
negation.isUnsatisfiable();
} else {
negation.isSatisfiable();
}
}
@Test
public void intTest3_DivModLinear() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula a = imgr.makeVariable("int_a");
IntegerFormula b = imgr.makeVariable("int_b");
IntegerFormula num10 = imgr.makeNumber(10);
IntegerFormula num5 = imgr.makeNumber(5);
IntegerFormula num3 = imgr.makeNumber(3);
IntegerFormula num4 = imgr.makeNumber(4);
IntegerFormula num2 = imgr.makeNumber(2);
IntegerFormula num1 = imgr.makeNumber(1);
IntegerFormula num0 = imgr.makeNumber(0);
IntegerFormula numNeg2 = imgr.makeNumber(-2);
IntegerFormula numNeg3 = imgr.makeNumber(-3);
IntegerFormula numNeg4 = imgr.makeNumber(-4);
IntegerFormula numNeg10 = imgr.makeNumber(-10);
BooleanFormula aEq10 = imgr.equal(a, num10);
BooleanFormula bEq2 = imgr.equal(b, num2);
BooleanFormula aEqNeg10 = imgr.equal(a, numNeg10);
BooleanFormula bEqNeg2 = imgr.equal(b, numNeg2);
assertDivision(num10, num5, num2);
assertDivision(num10, num3, num3);
assertDivision(numNeg10, num5, numNeg2);
assertDivision(numNeg10, numNeg2, num5);
assertDivision(num10, num5, num2);
assertDivision(num10, num3, num3);
assertDivision(num10, numNeg3, numNeg3);
assertDivision(num0, num3, num0);
assertDivision(a, num5, b, aEq10, bEq2);
assertDivision(a, num3, num3, aEq10);
assertDivision(a, num5, b, aEqNeg10, bEqNeg2);
assertDivision(a, num3, numNeg4, aEqNeg10);
assertDivision(a, numNeg3, num4, aEqNeg10);
assertModulo(num10, num5, num0);
assertModulo(num10, num3, num1, aEq10);
assertModulo(numNeg10, num5, num0);
assertModulo(numNeg10, num3, num2);
assertModulo(numNeg10, numNeg3, num2);
assertModulo(a, num5, num0, aEq10);
assertModulo(a, num3, num1, aEq10);
assertModulo(a, num5, num0, aEqNeg10);
assertModulo(a, num3, num2, aEqNeg10);
assertModulo(a, numNeg3, num2, aEqNeg10);
}
@Test
public void intTest3_DivModLinear_zeroDenominator() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula a = imgr.makeVariable("int_a");
IntegerFormula num10 = imgr.makeNumber(10);
IntegerFormula num1 = imgr.makeNumber(1);
IntegerFormula num0 = imgr.makeNumber(0);
BooleanFormula aEq10 = imgr.equal(a, num10);
// SMTLIB allows any value for division-by-zero.
switch (solverToUse()) {
case YICES2:
assertThrows(
IllegalArgumentException.class,
() -> assertThatFormula(buildDivision(num10, num0, num10)).isSatisfiable());
break;
case OPENSMT: // INFO: OpenSMT does not allow division by zero
assertThrows(
UnsupportedOperationException.class,
() -> assertThatFormula(buildDivision(num10, num0, num10)).isSatisfiable());
break;
default:
// division-by-zero results in an arbitrary result
assertDivision(false, num0, num0, num0);
assertDivision(false, num0, num0, num1);
assertDivision(false, num0, num0, num10);
assertDivision(false, num10, num0, num0);
assertDivision(false, num10, num0, num0);
assertDivision(false, num10, num0, num10);
assertDivision(false, a, num0, num0, aEq10);
assertDivision(false, a, num0, num1, aEq10);
assertDivision(false, a, num0, num10, aEq10);
}
switch (solverToUse()) {
case YICES2:
assertThrows(
IllegalArgumentException.class,
() -> assertThatFormula(buildModulo(num10, num0, num10)).isSatisfiable());
break;
case OPENSMT: // INFO: OpenSMT does not allow division by zero
assertThrows(UnsupportedOperationException.class, () -> buildModulo(num10, num0, num10));
break;
default:
// modulo-by-zero results in an arbitrary result
assertModulo(false, num0, num0, num0);
assertModulo(false, num0, num0, num1);
assertModulo(false, num0, num0, num10);
assertModulo(false, num10, num0, num0);
assertModulo(false, num10, num0, num0);
assertModulo(false, num10, num0, num10);
assertModulo(false, a, num0, num0, aEq10);
assertModulo(false, a, num0, num1, aEq10);
assertModulo(false, a, num0, num10, aEq10);
}
}
@Test
public void intTest3_DivModNonLinear() throws SolverException, InterruptedException {
// not all solvers support division-by-variable,
// we guarantee soundness by allowing any value that yields SAT.
requireIntegers();
IntegerFormula a = imgr.makeVariable("int_a");
IntegerFormula b = imgr.makeVariable("int_b");
IntegerFormula num10 = imgr.makeNumber(10);
IntegerFormula num5 = imgr.makeNumber(5);
IntegerFormula num2 = imgr.makeNumber(2);
IntegerFormula num0 = imgr.makeNumber(0);
IntegerFormula numNeg2 = imgr.makeNumber(-2);
IntegerFormula numNeg10 = imgr.makeNumber(-10);
BooleanFormula aEq10 = imgr.equal(a, num10);
BooleanFormula bEq2 = imgr.equal(b, num2);
BooleanFormula bEqNeg2 = imgr.equal(b, numNeg2);
BooleanFormula aEqNeg10 = imgr.equal(a, numNeg10);
switch (solverToUse()) {
case OPENSMT: // INFO: OpenSmt does not allow nonlinear terms
case SMTINTERPOL:
case YICES2:
assertThrows(UnsupportedOperationException.class, () -> buildDivision(a, b, num5));
assertThrows(UnsupportedOperationException.class, () -> buildModulo(a, b, num0));
break;
default:
assertDivision(a, b, num5, aEq10, bEq2);
assertDivision(a, b, num5, aEqNeg10, bEqNeg2);
assertModulo(a, b, num0, aEq10, bEq2);
assertModulo(a, b, num0, aEqNeg10, bEqNeg2);
}
// TODO negative case is disabled, because we would need the option
// solver.solver.useNonLinearIntegerArithmetic=true.
}
@Test
public void intTestBV_DivMod() throws SolverException, InterruptedException {
requireBitvectors();
final int bitsize = 8;
BitvectorFormula a = bvmgr.makeVariable(bitsize, "int_a");
BitvectorFormula b = bvmgr.makeVariable(bitsize, "int_b");
BitvectorFormula num253 = bvmgr.makeBitvector(bitsize, -3); // == 253 unsigned
BitvectorFormula num246 = bvmgr.makeBitvector(bitsize, -10); // == 246 unsigned
BitvectorFormula num82 = bvmgr.makeBitvector(bitsize, 82);
BitvectorFormula num49 = bvmgr.makeBitvector(bitsize, 49);
BitvectorFormula num10 = bvmgr.makeBitvector(bitsize, 10);
BitvectorFormula num5 = bvmgr.makeBitvector(bitsize, 5);
BitvectorFormula num3 = bvmgr.makeBitvector(bitsize, 3);
BitvectorFormula num2 = bvmgr.makeBitvector(bitsize, 2);
BitvectorFormula num1 = bvmgr.makeBitvector(bitsize, 1);
BitvectorFormula num0 = bvmgr.makeBitvector(bitsize, 0);
BitvectorFormula numNeg1 = bvmgr.makeBitvector(bitsize, -1);
BitvectorFormula numNeg2 = bvmgr.makeBitvector(bitsize, -2);
BitvectorFormula numNeg3 = bvmgr.makeBitvector(bitsize, -3);
BitvectorFormula numNeg10 = bvmgr.makeBitvector(bitsize, -10);
BooleanFormula aEq246 = bvmgr.equal(a, num246);
BooleanFormula aEq10 = bvmgr.equal(a, num10);
BooleanFormula bEq2 = bvmgr.equal(b, num2);
BooleanFormula bEq0 = bvmgr.equal(b, num0);
BooleanFormula aEqNeg10 = bvmgr.equal(a, numNeg10);
BooleanFormula bEq49 = bvmgr.equal(b, num49);
BooleanFormula bEq1 = bvmgr.equal(b, num1);
BooleanFormula bEqNeg1 = bvmgr.equal(b, numNeg1);
BooleanFormula bEqNeg2 = bvmgr.equal(b, numNeg2);
// positive numbers, signed.
assertDivision(a, num5, true, b, aEq10, bEq2);
assertDivision(a, num3, true, num3, aEq10);
assertDivision(a, numNeg3, true, numNeg3, aEq10);
assertDivision(a, b, true, num5, aEq10, bEq2);
assertModulo(a, num5, true, num0, aEq10);
assertModulo(a, num3, true, num1, aEq10);
assertModulo(a, numNeg3, true, num1, aEq10);
// positive numbers, unsigned.
assertDivision(a, num5, false, b, aEq10, bEq2);
assertDivision(a, num3, false, num3, aEq10);
assertDivision(a, num253, false, num0, aEq10);
assertDivision(a, b, false, num5, aEq10, bEq2);
assertModulo(a, num5, false, num0, aEq10);
assertModulo(a, num3, false, num1, aEq10);
assertModulo(a, num253, false, num10, aEq10);
// negative numbers, signed.
// bitvector-division for negative numbers is C99-conform!
assertDivision(a, num5, true, b, aEqNeg10, bEqNeg2);
assertDivision(a, num3, true, numNeg3, aEqNeg10);
assertDivision(a, numNeg3, true, num3, aEqNeg10);
assertDivision(a, b, true, num5, aEqNeg10, bEqNeg2);
assertModulo(a, num5, true, num0, aEqNeg10);
assertModulo(a, num3, true, numNeg1, aEqNeg10);
assertModulo(a, numNeg3, true, numNeg1, aEqNeg10);
// negative numbers, unsigned.
// bitvector-division for negative numbers is C99-conform!
assertDivision(a, num5, false, b, aEq246, bEq49);
assertDivision(a, num3, false, num82, aEq246);
assertDivision(a, num253, false, num0, aEq246);
assertDivision(a, b, false, num5, aEq246, bEq49);
assertModulo(a, num5, false, num1, aEq246);
assertModulo(a, num3, false, num0, aEq246);
assertModulo(a, num253, false, num246, aEq246);
// division by zero, signed.
assertDivision(a, num0, true, b, aEq10, bEqNeg1);
assertDivision(a, num0, true, b, aEqNeg10, bEq1);
assertDivision(a, b, true, numNeg1, aEq10, bEq0);
assertDivision(a, b, true, num1, aEqNeg10, bEq0);
assertModulo(a, num0, true, numNeg10, aEqNeg10);
// division by zero, unsigned.
assertDivision(a, num0, false, b, aEq10, bEqNeg1);
assertDivision(a, num0, false, b, aEqNeg10, bEqNeg1);
assertDivision(a, b, false, numNeg1, aEq10, bEq0);
assertDivision(a, b, false, numNeg1, aEqNeg10, bEq0);
assertModulo(a, num0, false, a, aEqNeg10);
}
@Test
public void intTest4_ModularCongruence_Simple() throws SolverException, InterruptedException {
requireIntegers();
final IntegerFormula x = imgr.makeVariable("x");
final BooleanFormula f1 = imgr.modularCongruence(x, imgr.makeNumber(0), 2);
final BooleanFormula f2 = imgr.equal(x, imgr.makeNumber(1));
assertThatFormula(bmgr.and(f1, f2)).isUnsatisfiable();
}
@Test
public void intTest4_ModularCongruence() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula a = imgr.makeVariable("int_a");
IntegerFormula b = imgr.makeVariable("int_b");
IntegerFormula c = imgr.makeVariable("int_c");
IntegerFormula d = imgr.makeVariable("int_d");
IntegerFormula num10 = imgr.makeNumber(10);
IntegerFormula num5 = imgr.makeNumber(5);
IntegerFormula num0 = imgr.makeNumber(0);
IntegerFormula numNeg5 = imgr.makeNumber(-5);
BooleanFormula fa = imgr.equal(a, num10);
BooleanFormula fb = imgr.equal(b, num5);
BooleanFormula fc = imgr.equal(c, num0);
BooleanFormula fd = imgr.equal(d, numNeg5);
// we have equal results modulo 5
BooleanFormula fConb5 = imgr.modularCongruence(a, b, 5);
BooleanFormula fConc5 = imgr.modularCongruence(a, c, 5);
BooleanFormula fCond5 = imgr.modularCongruence(a, d, 5);
// we have different results modulo 7
BooleanFormula fConb7 = imgr.modularCongruence(a, b, 7);
BooleanFormula fConc7 = imgr.modularCongruence(a, c, 7);
BooleanFormula fCond7 = imgr.modularCongruence(a, d, 7);
// check modular congruence, a=10 && b=5 && (a mod 5 = b mod 5)
assertThatFormula(bmgr.and(fa, fb, fConb5)).isSatisfiable();
assertThatFormula(bmgr.and(fa, fb, bmgr.not(fConb5))).isUnsatisfiable();
assertThatFormula(bmgr.and(fa, fc, fConc5)).isSatisfiable();
assertThatFormula(bmgr.and(fa, fc, bmgr.not(fConc5))).isUnsatisfiable();
assertThatFormula(bmgr.and(fa, fd, fCond5)).isSatisfiable();
assertThatFormula(bmgr.and(fa, fd, bmgr.not(fCond5))).isUnsatisfiable();
// check modular congruence, a=10 && b=5 && (a mod 7 != b mod 7)
assertThatFormula(bmgr.and(fa, fb, fConb7)).isUnsatisfiable();
assertThatFormula(bmgr.and(fa, fb, bmgr.not(fConb7))).isSatisfiable();
assertThatFormula(bmgr.and(fa, fc, fConc7)).isUnsatisfiable();
assertThatFormula(bmgr.and(fa, fc, bmgr.not(fConc7))).isSatisfiable();
assertThatFormula(bmgr.and(fa, fd, fCond7)).isUnsatisfiable();
assertThatFormula(bmgr.and(fa, fd, bmgr.not(fCond7))).isSatisfiable();
}
@Test
public void intTest4_ModularCongruence_NegativeNumbers()
throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula a = imgr.makeVariable("int_a");
IntegerFormula b = imgr.makeVariable("int_b");
IntegerFormula c = imgr.makeVariable("int_c");
IntegerFormula num8 = imgr.makeNumber(8);
IntegerFormula num3 = imgr.makeNumber(3);
IntegerFormula numNeg2 = imgr.makeNumber(-2);
BooleanFormula fa = imgr.equal(a, num8);
BooleanFormula fb = imgr.equal(b, num3);
BooleanFormula fc = imgr.equal(c, numNeg2);
BooleanFormula fConb = imgr.modularCongruence(a, b, 5);
BooleanFormula fConc = imgr.modularCongruence(a, c, 5);
// check modular congruence, a=10 && b=5 && (a mod 5 = b mod 5)
assertThatFormula(bmgr.and(fa, fb, fConb)).isSatisfiable();
assertThatFormula(bmgr.and(fa, fb, bmgr.not(fConb))).isUnsatisfiable();
assertThatFormula(bmgr.and(fa, fc, fConc)).isSatisfiable();
assertThatFormula(bmgr.and(fa, fc, bmgr.not(fConc))).isUnsatisfiable();
}
@Test
public void testHardCongruence() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula a = imgr.makeVariable("a");
IntegerFormula b = imgr.makeVariable("b");
IntegerFormula c = imgr.makeVariable("c");
List<BooleanFormula> constraints = new ArrayList<>();
Random r = new Random(42);
int bitSize = 7; // difficulty
BigInteger prime1 = BigInteger.probablePrime(bitSize, r);
BigInteger prime2 = BigInteger.probablePrime(bitSize + 1, r);
BigInteger prime3 = BigInteger.probablePrime(bitSize + 2, r);
constraints.add(imgr.modularCongruence(imgr.add(a, imgr.makeNumber(1)), b, prime1));
constraints.add(imgr.modularCongruence(b, c, prime2));
constraints.add(imgr.modularCongruence(a, c, prime3));
try (ProverEnvironment pe = context.newProverEnvironment(ProverOptions.GENERATE_MODELS)) {
pe.addConstraint(imgr.greaterThan(a, imgr.makeNumber(1)));
pe.addConstraint(imgr.greaterThan(b, imgr.makeNumber(1)));
pe.addConstraint(imgr.greaterThan(c, imgr.makeNumber(1)));
pe.addConstraint(bmgr.and(constraints));
assertThat(pe.isUnsat()).isFalse();
try (Model m = pe.getModel()) {
BigInteger aValue = m.evaluate(a);
BigInteger bValue = m.evaluate(b);
BigInteger cValue = m.evaluate(c);
assertThat(aValue.add(BigInteger.ONE).subtract(bValue).mod(prime1))
.isEqualTo(BigInteger.ZERO);
assertThat(bValue.subtract(cValue).mod(prime2)).isEqualTo(BigInteger.ZERO);
assertThat(aValue.subtract(cValue).mod(prime3)).isEqualTo(BigInteger.ZERO);
}
}
}
@Test
public void realTest() throws SolverException, InterruptedException {
requireRationals();
RationalFormula a = rmgr.makeVariable("int_c");
RationalFormula num = rmgr.makeNumber(1);
BooleanFormula f = rmgr.equal(rmgr.add(a, a), num);
assertThatFormula(f).isSatisfiable();
}
@Test
public void testUfWithBoolType() throws SolverException, InterruptedException {
requireIntegers();
FunctionDeclaration<BooleanFormula> uf =
fmgr.declareUF("fun_ib", FormulaType.BooleanType, FormulaType.IntegerType);
BooleanFormula uf0 = fmgr.callUF(uf, imgr.makeNumber(0));
BooleanFormula uf1 = fmgr.callUF(uf, imgr.makeNumber(1));
BooleanFormula uf2 = fmgr.callUF(uf, imgr.makeNumber(2));
BooleanFormula f01 = bmgr.xor(uf0, uf1);
BooleanFormula f02 = bmgr.xor(uf0, uf2);
BooleanFormula f12 = bmgr.xor(uf1, uf2);
assertThatFormula(f01).isSatisfiable();
assertThatFormula(f02).isSatisfiable();
assertThatFormula(f12).isSatisfiable();
BooleanFormula f = bmgr.and(f01, f02, f12);
assertThatFormula(f).isUnsatisfiable();
}
@Test
public void testUfWithBoolArg() throws SolverException, InterruptedException {
assume()
.withMessage("Solver %s does not support boolean arguments", solverToUse())
.that(solver)
.isNotEqualTo(Solvers.MATHSAT5);
requireIntegers();
FunctionDeclaration<IntegerFormula> uf =
fmgr.declareUF("fun_bi", FormulaType.IntegerType, FormulaType.BooleanType);
IntegerFormula ufTrue = fmgr.callUF(uf, bmgr.makeBoolean(true));
IntegerFormula ufFalse = fmgr.callUF(uf, bmgr.makeBoolean(false));
BooleanFormula f = bmgr.not(imgr.equal(ufTrue, ufFalse));
assertThatFormula(f).isSatisfiable();
}
@Test
public void quantifierEliminationTest1() throws SolverException, InterruptedException {
requireQuantifiers();
requireIntegers();
IntegerFormula var_B = imgr.makeVariable("b");
IntegerFormula var_C = imgr.makeVariable("c");
IntegerFormula num_2 = imgr.makeNumber(2);
IntegerFormula num_1000 = imgr.makeNumber(1000);
BooleanFormula eq_c_2 = imgr.equal(var_C, num_2);
IntegerFormula minus_b_c = imgr.subtract(var_B, var_C);
BooleanFormula gt_bMinusC_1000 = imgr.greaterThan(minus_b_c, num_1000);
BooleanFormula and_cEq2_bMinusCgt1000 = bmgr.and(eq_c_2, gt_bMinusC_1000);
BooleanFormula f = qmgr.exists(ImmutableList.of(var_C), and_cEq2_bMinusCgt1000);
BooleanFormula result = qmgr.eliminateQuantifiers(f);
assertThat(result.toString()).doesNotContain("exists");
assertThat(result.toString()).doesNotContain("c");
BooleanFormula expected = imgr.greaterOrEquals(var_B, imgr.makeNumber(1003));
assertThatFormula(result).isEquivalentTo(expected);
}
@Test
@Ignore
public void quantifierEliminationTest2() throws SolverException, InterruptedException {
requireQuantifiers();
requireIntegers();
IntegerFormula i1 = imgr.makeVariable("i@1");
IntegerFormula j1 = imgr.makeVariable("j@1");
IntegerFormula j2 = imgr.makeVariable("j@2");
IntegerFormula a1 = imgr.makeVariable("a@1");
IntegerFormula _1 = imgr.makeNumber(1);
IntegerFormula _minus1 = imgr.makeNumber(-1);
IntegerFormula _1_plus_a1 = imgr.add(_1, a1);
BooleanFormula not_j1_eq_minus1 = bmgr.not(imgr.equal(j1, _minus1));
BooleanFormula i1_eq_1_plus_a1 = imgr.equal(i1, _1_plus_a1);
IntegerFormula j2_plus_a1 = imgr.add(j2, a1);
BooleanFormula j1_eq_j2_plus_a1 = imgr.equal(j1, j2_plus_a1);
BooleanFormula fm = bmgr.and(i1_eq_1_plus_a1, not_j1_eq_minus1, j1_eq_j2_plus_a1);
BooleanFormula q = qmgr.exists(ImmutableList.of(j1), fm);
BooleanFormula result = qmgr.eliminateQuantifiers(q);
assertThat(result.toString()).doesNotContain("exists");
assertThat(result.toString()).doesNotContain("j@1");
BooleanFormula expected = bmgr.not(imgr.equal(i1, j2));
assertThatFormula(result).isEquivalentTo(expected);
}
@Test
public void testGetFormulaType() {
requireIntegers();
BooleanFormula _boolVar = bmgr.makeVariable("boolVar");
assertThat(mgr.getFormulaType(_boolVar)).isEqualTo(FormulaType.BooleanType);
IntegerFormula _intVar = imgr.makeNumber(1);
assertThat(mgr.getFormulaType(_intVar)).isEqualTo(FormulaType.IntegerType);
requireArrays();
ArrayFormula<IntegerFormula, IntegerFormula> _arrayVar =
amgr.makeArray("b", FormulaType.IntegerType, FormulaType.IntegerType);
assertThat(mgr.getFormulaType(_arrayVar)).isInstanceOf(FormulaType.ArrayFormulaType.class);
}
@Test
public void testMakeIntArray() {
requireArrays();
requireIntegers();
IntegerFormula _i = imgr.makeVariable("i");
IntegerFormula _1 = imgr.makeNumber(1);
IntegerFormula _i_plus_1 = imgr.add(_i, _1);
ArrayFormula<IntegerFormula, IntegerFormula> _b =
amgr.makeArray("b", FormulaType.IntegerType, FormulaType.IntegerType);
IntegerFormula _b_at_i_plus_1 = amgr.select(_b, _i_plus_1);
switch (solver) {
case MATHSAT5:
// Mathsat5 has a different internal representation of the formula
assertThat(_b_at_i_plus_1.toString()).isEqualTo("(`read_int_int` b (`+_int` i 1))");
break;
case PRINCESS:
assertThat(_b_at_i_plus_1.toString()).isEqualTo("select(b, (i + 1))");
break;
case OPENSMT:
// INFO: OpenSmt changes the order of the terms in the sum
assertThat(_b_at_i_plus_1.toString()).isEqualTo("(select b (+ 1 i))");
break;
default:
assertThat(_b_at_i_plus_1.toString())
.isEqualTo("(select b (+ i 1))"); // Compatibility to all solvers not guaranteed
}
}
@Test
public void testMakeBitVectorArray() {
requireArrays();
requireBitvectors();
assume()
.withMessage("Solver does not support bit-vector arrays.")
.that(solver)
.isNotEqualTo(Solvers.PRINCESS);
BitvectorFormula _i = mgr.getBitvectorFormulaManager().makeVariable(64, "i");
ArrayFormula<BitvectorFormula, BitvectorFormula> _b =
amgr.makeArray(
"b",
FormulaType.getBitvectorTypeWithSize(64),
FormulaType.getBitvectorTypeWithSize(32));
BitvectorFormula _b_at_i = amgr.select(_b, _i);
switch (solver) {
case MATHSAT5:
// Mathsat5 has a different internal representation of the formula
assertThat(_b_at_i.toString()).isEqualTo("(`read_T(19)_T(21)` b i)");
break;
case BOOLECTOR:
assume()
.withMessage("Solver %s does not printing formulae.", solverToUse())
.that(solver)
.isNotEqualTo(Solvers.BOOLECTOR);
break;
default:
assertThat(_b_at_i.toString())
.isEqualTo("(select b i)"); // Compatibility to all solvers not guaranteed
}
}
@Test
public void testNestedIntegerArray() {
requireArrays();
requireIntegers();
IntegerFormula _i = imgr.makeVariable("i");
ArrayFormula<IntegerFormula, ArrayFormula<IntegerFormula, IntegerFormula>> multi =
amgr.makeArray(
"multi",
FormulaType.IntegerType,
FormulaType.getArrayType(FormulaType.IntegerType, FormulaType.IntegerType));
IntegerFormula valueInMulti = amgr.select(amgr.select(multi, _i), _i);
switch (solver) {
case MATHSAT5:
assertThat(valueInMulti.toString())
.isEqualTo("(`read_int_int` (`read_int_T(18)` multi i) i)");
break;
case PRINCESS:
assertThat(valueInMulti.toString()).isEqualTo("select(select(multi, i), i)");
break;
default:
assertThat(valueInMulti.toString()).isEqualTo("(select (select multi i) i)");
}
}
@Test
public void testNestedRationalArray() {
requireArrays();
requireRationals();
requireIntegers();
IntegerFormula _i = imgr.makeVariable("i");
ArrayFormula<IntegerFormula, ArrayFormula<IntegerFormula, RationalFormula>> multi =
amgr.makeArray(
"multi",
FormulaType.IntegerType,
FormulaType.getArrayType(FormulaType.IntegerType, FormulaType.RationalType));
RationalFormula valueInMulti = amgr.select(amgr.select(multi, _i), _i);
switch (solver) {
case MATHSAT5:
assertThat(valueInMulti.toString())
.isEqualTo("(`read_int_rat` (`read_int_T(18)` multi i) i)");
break;
case PRINCESS:
assertThat(valueInMulti.toString()).isEqualTo("select(select(multi, i), i)");
break;
default:
assertThat(valueInMulti.toString()).isEqualTo("(select (select multi i) i)");
}
}
@Test
public void testNestedBitVectorArray() {
requireArrays();
requireBitvectors();
requireIntegers();
assume()
.withMessage("Solver does not support bit-vector arrays.")
.that(solver)
.isNotEqualTo(Solvers.PRINCESS);
IntegerFormula _i = imgr.makeVariable("i");
ArrayFormula<IntegerFormula, ArrayFormula<IntegerFormula, BitvectorFormula>> multi =
amgr.makeArray(
"multi",
FormulaType.IntegerType,
FormulaType.getArrayType(
FormulaType.IntegerType, FormulaType.getBitvectorTypeWithSize(32)));
BitvectorFormula valueInMulti = amgr.select(amgr.select(multi, _i), _i);
switch (solver) {
case MATHSAT5:
assertThat(valueInMulti.toString())
.isEqualTo("(`read_int_T(19)` (`read_int_T(20)` multi " + "i) i)");
break;
default:
assertThat(valueInMulti.toString()).isEqualTo("(select (select multi i) i)");
}
}
@Test
public void nonLinearMultiplication() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula i2 = imgr.makeNumber(2);
IntegerFormula i3 = imgr.makeNumber(3);
IntegerFormula i4 = imgr.makeNumber(4);
IntegerFormula x = imgr.makeVariable("x");
IntegerFormula y = imgr.makeVariable("y");
IntegerFormula z = imgr.makeVariable("z");
IntegerFormula x_mult_y;
try {
x_mult_y = imgr.multiply(x, y);
} catch (UnsupportedOperationException e) {
// do nothing, this exception is fine here, because solvers do not need
// to support non-linear arithmetic, we can then skip the test completely
throw new AssumptionViolatedException("Support for non-linear arithmetic is optional", e);
}
BooleanFormula x_equal_2 = imgr.equal(i2, x);
BooleanFormula y_equal_3 = imgr.equal(i3, y);
BooleanFormula z_equal_4 = imgr.equal(i4, z);
BooleanFormula z_equal_x_mult_y = imgr.equal(z, x_mult_y);
try (ProverEnvironment env = context.newProverEnvironment()) {
env.push(x_equal_2);
env.push(y_equal_3);
env.push(z_equal_4);
env.push(z_equal_x_mult_y);
assertThat(env).isUnsatisfiable();
}
}
@Test
public void composedLinearMultiplication() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula i2 = imgr.makeNumber(2);
IntegerFormula i3 = imgr.makeNumber(3);
IntegerFormula i4 = imgr.makeNumber(4);
IntegerFormula x = imgr.makeVariable("x");
// MULT should be supported by all solvers, DIV/MOD are missing in Mathsat.
IntegerFormula mult = imgr.multiply(x, imgr.add(i2, imgr.add(i3, i4)));
IntegerFormula div;
IntegerFormula mod;
try {
div = imgr.divide(x, imgr.add(i2, imgr.add(i3, i4)));
mod = imgr.modulo(x, imgr.add(i2, imgr.add(i3, i4)));
} catch (UnsupportedOperationException e) {
// do nothing, this exception is fine here, because solvers do not need
// to support non-linear arithmetic, we can then skip the test completely
throw new AssumptionViolatedException("Support for non-linear arithmetic is optional", e);
}
try (ProverEnvironment env = context.newProverEnvironment()) {
env.push(imgr.greaterThan(mult, i4));
env.push(imgr.greaterThan(div, i4));
env.push(imgr.greaterThan(mod, i2));
assertThat(env).isSatisfiable();
}
}
@Test
public void multiplicationSquares() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula i2 = imgr.makeNumber(2);
IntegerFormula i3 = imgr.makeNumber(3);
IntegerFormula i4 = imgr.makeNumber(4);
IntegerFormula i5 = imgr.makeNumber(5);
IntegerFormula x = imgr.makeVariable("x");
IntegerFormula y = imgr.makeVariable("y");
IntegerFormula z = imgr.makeVariable("z");
IntegerFormula xx;
IntegerFormula yy;
IntegerFormula zz;
try {
xx = imgr.multiply(x, x);
yy = imgr.multiply(y, y);
zz = imgr.multiply(z, z);
} catch (UnsupportedOperationException e) {
// do nothing, this exception is fine here, because solvers do not need
// to support non-linear arithmetic, we can then skip the test completely
throw new AssumptionViolatedException("Support for non-linear arithmetic is optional", e);
}
try (ProverEnvironment env = context.newProverEnvironment()) {
// check x*x + y*y = z*z
env.push(imgr.equal(zz, imgr.add(xx, yy)));
{
// SAT with x=4 and y=3
env.push(imgr.equal(x, i3));
env.push(imgr.equal(y, i4));
assertThat(env).isSatisfiable();
env.pop();
env.pop();
}
{ // SAT with z=5
env.push(imgr.equal(z, i5));
assertThat(env).isSatisfiable();
env.pop();
}
{
// UNSAT with z=5 and x=2
env.push(imgr.equal(z, i5));
env.push(imgr.equal(x, i2));
assertThat(env).isUnsatisfiable();
env.pop();
env.pop();
}
{ // UNSAT with z=5 and x>3 and y>3
env.push(imgr.equal(z, i5));
env.push(imgr.greaterThan(x, i3));
env.push(imgr.greaterThan(y, i3));
assertThat(env).isUnsatisfiable();
env.pop();
env.pop();
env.pop();
}
}
}
@Test
public void multiplicationFactors() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula i37 = imgr.makeNumber(37);
IntegerFormula i1 = imgr.makeNumber(1);
IntegerFormula x = imgr.makeVariable("x");
IntegerFormula y = imgr.makeVariable("y");
IntegerFormula x_mult_y;
try {
x_mult_y = imgr.multiply(x, y);
} catch (UnsupportedOperationException e) {
// do nothing, this exception is fine here, because solvers do not need
// to support non-linear arithmetic, we can then skip the test completely
throw new AssumptionViolatedException("Support for non-linear arithmetic is optional", e);
}
try (ProverEnvironment env = context.newProverEnvironment()) {
env.push(imgr.equal(x_mult_y, i37));
assertThat(env).isSatisfiable();
env.push(imgr.greaterThan(x, i1));
env.push(imgr.greaterThan(y, i1));
assertThat(env).isUnsatisfiable();
}
}
@Test
public void multiplicationCubic() throws SolverException, InterruptedException {
requireIntegers();
IntegerFormula i125 = imgr.makeNumber(125);
IntegerFormula i27 = imgr.makeNumber(27);
IntegerFormula i5 = imgr.makeNumber(5);
IntegerFormula x = imgr.makeVariable("x");