bool BitvectorTheory::handleITE(const FormulaT& ifterm, const types::TermType& thenterm, const types::TermType& elseterm, types::TermType& result, TheoryError& errors) {
types::BVTerm thent;
types::BVTerm elset;
if (!termConverter(thenterm, thent)) {
errors.next() << "Failed to construct ITE, the then-term \"" << thenterm << "\" is unsupported.";
return false;
}
if (!termConverter(elseterm, elset)) {
errors.next() << "Failed to construct ITE, the else-term \"" << elseterm << "\" is unsupported.";
return false;
}
if (thent.width() != elset.width()) {
errors.next() << "Failed to construct ITE, the then-term \"" << thent << "\" and the else-term \"" << elset << "\" have different widths.";
return false;
}
if (ifterm.isTrue()) { result = thent; return true; }
if (ifterm.isFalse()) { result = elset; return true; }
carl::SortManager& sm = carl::SortManager::getInstance();
carl::Variable var = carl::freshVariable(carl::VariableType::VT_BITVECTOR);
state->artificialVariables.emplace_back(var);
carl::BVVariable bvvar(var, sm.index(this->bvSort, {thent.width()}));
state->auxiliary_variables.insert(bvvar);
types::BVTerm vart = types::BVTerm(carl::BVTermType::VARIABLE, bvvar);
FormulaT consThen = FormulaT(types::BVConstraint::create(carl::BVCompareRelation::EQ, vart, thent));
FormulaT consElse = FormulaT(types::BVConstraint::create(carl::BVCompareRelation::EQ, vart, elset));
state->global_formulas.emplace_back(FormulaT(carl::FormulaType::IMPLIES, {ifterm, consThen}));
state->global_formulas.emplace_back(FormulaT(carl::FormulaType::IMPLIES, {FormulaT(carl::FormulaType::NOT,ifterm), consElse}));
result = vart;
return true;
}
FormulaT MixedSignEncoder::findSubEncoding(const ConstraintT& constraint) {
FormulaT chosenEncoding;
bool hasEncoded = false;
if (mShortFormulaEncoder.canEncode(constraint)) {
boost::optional<FormulaT> shortEncoding = mShortFormulaEncoder.encode(constraint);
if (shortEncoding) {
chosenEncoding = *shortEncoding;
hasEncoded = true;
}
} else if (mCardinalityEncoder.canEncode(constraint)) {
boost::optional<FormulaT> cardinalityEncoding = mCardinalityEncoder.encode(constraint);
if (cardinalityEncoding) {
chosenEncoding = *cardinalityEncoding;
hasEncoded = true;
}
} else if (mLongFormulaEncoder.canEncode(constraint)) {
boost::optional<FormulaT> longEncoding = mLongFormulaEncoder.encode(constraint);
if (longEncoding) {
chosenEncoding = *longEncoding;
hasEncoded = true;
}
}
if (!hasEncoded) {
chosenEncoding = FormulaT(constraint);
}
return chosenEncoding;
}
bool apply(const std::vector<FormulaT>& arguments, types::TermType& result, TheoryError& errors) const {
if (arguments.size() != 2) {
errors.next() << "Operator \"implies\" may only have a single argument.";
return false;
}
result = FormulaT(carl::FormulaType::IMPLIES, {arguments[0], arguments[1]});
return true;
}
bool apply(const std::vector<types::BVTerm>& arguments, types::TermType& result, TheoryError& errors) const {
if (arguments.size() != 2) {
errors.next() << "The operator \"" << type << "\" expects exactly two arguments.";
return false;
}
result = FormulaT(types::BVConstraint::create(type, arguments[0], arguments[1]));
return true;
}
bool CoreTheory::handleDistinct(const std::vector<types::TermType>& arguments, types::TermType& result, TheoryError& errors) {
std::vector<FormulaT> args;
if (!convertArguments(arguments, args, errors)) return false;
result = expandDistinct(args, [](const FormulaT& a, const FormulaT& b){
return FormulaT(carl::FormulaType::XOR, {a, b});
});
return true;
}
bool BitvectorTheory::handleDistinct(const std::vector<types::TermType>& arguments, types::TermType& result, TheoryError& errors) {
std::vector<carl::BVTerm> args;
if (!vectorConverter(arguments, args, errors)) return false;
result = expandDistinct(args, [](const carl::BVTerm& a, const carl::BVTerm& b){
return FormulaT(carl::BVConstraint::create(carl::BVCompareRelation::NEQ, a, b));
});
return true;
}
bool CoreTheory::functionCall(const Identifier& identifier, const std::vector<types::TermType>& arguments, types::TermType& result, TheoryError& errors) {
std::vector<FormulaT> args;
if (!convertArguments(arguments, args, errors)) return false;
if (boost::iequals(identifier.symbol, "=")) {
result = FormulaT(carl::FormulaType::IFF, FormulasT(args.begin(), args.end()));
return true;
}
return false;
}
bool BitvectorTheory::functionCall(const Identifier& identifier, const std::vector<types::TermType>& arguments, types::TermType& result, TheoryError& errors) {
if (identifier.symbol == "=") {
if (arguments.size() == 2) {
std::vector<types::BVTerm> args;
if (!vectorConverter(arguments, args, errors)) return false;
result = FormulaT(types::BVConstraint::create(carl::BVCompareRelation::EQ, args[0], args[1]));
return true;
}
errors.next() << "Operator \"" << identifier << "\" expects exactly two arguments, but got " << arguments.size() << ".";
return false;
}
errors.next() << "Invalid operator \"" << identifier << "\".";
return false;
}
bool CoreTheory::handleITE(const FormulaT& ifterm, const types::TermType& thenterm, const types::TermType& elseterm, types::TermType& result, TheoryError& errors) {
FormulaT thenf;
FormulaT elsef;
if (!convertTerm(thenterm, thenf)) {
errors.next() << "Failed to construct ITE, the then-term \"" << thenterm << "\" is unsupported.";
return false;
}
if (!convertTerm(elseterm, elsef)) {
errors.next() << "Failed to construct ITE, the else-term \"" << elseterm << "\" is unsupported.";
return false;
}
result = FormulaT(carl::FormulaType::ITE, {ifterm, thenf, elsef});
return true;
}
bool CoreTheory::convertTerm(const types::TermType& term, FormulaT& result) {
if (boost::get<FormulaT>(&term) != nullptr) {
result = boost::get<FormulaT>(term);
return true;
} else if (boost::get<carl::Variable>(&term) != nullptr) {
if (boost::get<carl::Variable>(term).getType() == carl::VariableType::VT_BOOL) {
result = FormulaT(boost::get<carl::Variable>(term));
return true;
} else {
return false;
}
} else {
return false;
}
}
FormulaT MCBModule<Settings>::applyReplacements(const FormulaT& f) {
if (mChoices.empty()) return f;
std::set<AVar> variables;
std::map<FormulaT, FormulaT> repl;
for (const auto& r: mChoices) {
variables.insert(r.first);
for (const auto& f: r.second) {
BVar v = f.second.first;
const FormulaT& form = f.second.second;
repl.emplace(form, FormulaT(v));
}
}
carl::FormulaSubstitutor<FormulaT> subs;
SMTRAT_LOG_DEBUG("smtrat.mcb", "Applying " << repl << " on \n\t" << f);
FormulaT res = subs.substitute(f, repl);
SMTRAT_LOG_DEBUG("smtrat.mcb", "Resulting in\n\t" << res);
mRemaining.clear();
res.allVars(mRemaining);
FormulasT equiv;
for (const auto& v: variables) {
if (mRemaining.count(v) > 0) {
// Variable is still in the formula
for (const auto& r: mChoices.at(v)) {
equiv.push_back(FormulaT(carl::FormulaType::IFF, {FormulaT(r.second.first), r.second.second}));
}
} else {
// Variable has been eliminated
ModelVariable var(v);
std::map<BVar,Rational> assignment;
for (const auto& c: mChoices.at(v)) {
assignment.emplace(c.second.first, c.first);
}
SMTRAT_LOG_DEBUG("smtrat.mcb", "Adding " << var << " = " << assignment);
mAssignments.emplace(var, carl::createSubstitution<Rational,Poly,MCBModelSubstitution>(assignment));
}
for (const auto& c1: mChoices.at(v)) {
for (const auto& c2: mChoices.at(v)) {
if (c1.second.first >= c2.second.first) continue;
equiv.push_back(FormulaT(carl::FormulaType::OR, {FormulaT(c1.second.first).negated(), FormulaT(c2.second.first).negated()}));
SMTRAT_LOG_DEBUG("smtrat.mcb", "Adding exclusion " << equiv.back());
}
}
}
if (equiv.empty()) return res;
SMTRAT_LOG_DEBUG("smtrat.mcb", "Adding equivalences " << equiv);
equiv.push_back(res);
return FormulaT(carl::FormulaType::AND, std::move(equiv));
}
Answer MCBModule<Settings>::checkCore()
{
mRemaining.clear();
mChoices.clear();
carl::FormulaVisitor<FormulaT> visitor;
auto receivedFormula = firstUncheckedReceivedSubformula();
while (receivedFormula != rReceivedFormula().end()) {
visitor.visit(receivedFormula->formula(), collectChoicesFunction);
receivedFormula++;
}
FormulaT newFormula = applyReplacements(FormulaT(rReceivedFormula()));
clearPassedFormula();
addSubformulaToPassedFormula(newFormula);
Answer ans = runBackends();
if (ans == UNSAT) {
generateTrivialInfeasibleSubset();
}
return ans;
}
boost::optional<FormulaT> MixedSignEncoder::doEncode(const ConstraintT& constraint) {
// first partition into positive and negative terms
std::vector<TermT> positiveTerms;
std::vector<TermT> negativeTerms;
for (const auto& term : constraint.lhs()) {
if (term.isConstant()) continue;
if (term.coeff() > 0) {
positiveTerms.push_back(term);
} else {
negativeTerms.push_back(term);
}
}
Poly lhs;
Poly rhs;
for (const auto& term : positiveTerms) {
lhs += term;
}
for (const auto& term : negativeTerms) {
rhs -= term;
}
if (constraint.relation() == carl::Relation::LEQ) { // we assume mixed signs
// x1 + x2 - x3 - x4 - 1 <= 0 iff x1 + x2 -1 <= x3 + x4
// lhsValues -1, 0, 1
// rhs Value 0, 1, 2
// x1 + x2 - 1 >= -1 impl. x3 + x4 >= - 1
// x1 + x2 - 1 >= 0 impl x3 + x4 >= 0
// x1 + x2 - 1 >= 1 impl x3 + x4 >= 1
// now we can express the constraint as sum of positive terms <= negative sum of negative terms - constantPart
// this holds iff
// take all possible subsetsums of our new lhs. For each of these sums b_i we construct
// encode(lhs + constant >= b_i) implies encode(rhs >= b_i)
std::vector<Rational> subsetsums = calculateSubsetsums(positiveTerms);
FormulasT conjunction;
for (const auto& sum : subsetsums) {
ConstraintT lhsImplication(lhs - sum, carl::Relation::GEQ); // poly lhs + constantPart >= bi
ConstraintT rhsImplication(rhs - sum - constraint.constantPart(), carl::Relation::GEQ); // rhs >= bi
FormulaT chosenLhsEncoding = findSubEncoding(mNormalizer.trim(lhsImplication));
FormulaT chosenRhsEncoding = findSubEncoding(mNormalizer.trim(rhsImplication));
conjunction.push_back(FormulaT(carl::FormulaType::IMPLIES, chosenLhsEncoding, chosenRhsEncoding));
}
return FormulaT(carl::FormulaType::AND, conjunction);
}
if (constraint.relation() == carl::Relation::EQ) {
// x1 + x2 - x3 - x4 - 1= 0 iff x1 + x2 -1 = x3 + x4
// positiveSums: -1, 0, 1
// negativeSums: 0, 1, 2
// x3 + x4 = 0 impl. x1 + x2 -1 = 0
// x3 + x4 = 1 impl. x1 + x2 -1 = 1
// x3 + x4 = 2 impl. x1 + x2 -1 = 2
// x1 + x2 -1 = -1 impl. x3 + x4 = -1
// x1 + x2 -1 = 0 impl. x3 + x4 = 0
// x1 + x2 -1 = 1 impl. x3 + x4 = 1
std::vector<Rational> subsetsumsPositive = calculateSubsetsums(positiveTerms);
std::vector<Rational> subsetsumsNegative = calculateSubsetsums(negativeTerms);
FormulasT conjunction;
for (const auto& sum : subsetsumsPositive) {
ConstraintT lhsImplication(lhs - sum, carl::Relation::EQ);
ConstraintT rhsImplication(rhs - sum - constraint.constantPart(), carl::Relation::EQ);
FormulaT chosenLhsEncoding = findSubEncoding(mNormalizer.trim(lhsImplication));
FormulaT chosenRhsEncoding = findSubEncoding(mNormalizer.trim(rhsImplication));
conjunction.push_back(FormulaT(carl::FormulaType::IMPLIES, chosenLhsEncoding, chosenRhsEncoding));
}
for (const auto& sum : subsetsumsNegative) {
ConstraintT lhsImplication(lhs - constraint.constantPart() - sum, carl::Relation::EQ);
ConstraintT rhsImplication(rhs - sum, carl::Relation::EQ);
FormulaT chosenLhsEncoding = findSubEncoding(mNormalizer.trim(lhsImplication));
FormulaT chosenRhsEncoding = findSubEncoding(mNormalizer.trim(rhsImplication));
conjunction.push_back(FormulaT(carl::FormulaType::IMPLIES, chosenRhsEncoding, chosenLhsEncoding));
}
return FormulaT(carl::FormulaType::AND, conjunction);
}
return {};
}
Answer CubeLIAModule<Settings>::checkCore()
{
#ifdef DEBUG_CUBELIAMODULE
print();
#endif
Answer ans;
if( !rReceivedFormula().isRealConstraintConjunction() )
{
#ifdef DEBUG_CUBELIAMODULE
std::cout << "Call internal LRAModule:" << std::endl;
mLRA.print();
#endif
mLRA.clearLemmas();
mLRAFormula->updateProperties();
ans = mLRA.check( false, mFullCheck, mMinimizingCheck );
switch( ans )
{
case SAT:
{
clearModel();
// Get the model of mLRA
mLRA.updateModel();
const Model& relaxedModel = mLRA.model();
auto iter = mRealToIntVarMap.begin();
for( auto& ass : relaxedModel )
{
assert( iter != mRealToIntVarMap.end() );
// Round the result to the next integer
mModel.emplace_hint( mModel.end(), iter->second, carl::round( ass.second.asRational() ) );
++iter;
}
// Check if the rounded model satisfies the received formula
bool receivedFormulaSatisfied = true;
for( const FormulaWithOrigins& fwo : rReceivedFormula() )
{
unsigned res = satisfies( mModel, fwo.formula() );
switch( res )
{
case 0:
case 2:
receivedFormulaSatisfied = false;
default:
break;
}
if( !receivedFormulaSatisfied )
break;
}
// If we found a model, we know that the formula is satisfiable, otherwise, we have to call the backends on the received formula
if( receivedFormulaSatisfied )
{
mModelUpdated = true;
return SAT;
}
clearModel();
break;
}
case UNSAT:
{
if( Settings::exclude_unsatisfiable_cube_space )
{
// Exclude the space for which mLRA has detected unsatisfiability
for( auto& infsubset : mLRA.infeasibleSubsets() )
{
FormulasT formulas;
for( auto& formula : infsubset )
formulas.push_back( formula.negated() );
addLemma( FormulaT( carl::FormulaType::OR, formulas ) );
}
}
break;
}
default:
assert( false );
}
}
#ifdef DEBUG_CUBELIAMODULE
std::cout << "Call Backends:" << std::endl;
#endif
// Run backends on received formula
ans = runBackends();
if( ans == UNSAT )
getInfeasibleSubsets();
else if( ans == SAT )
mModelUpdated = false;
return ans;
}
void CoreTheory::addConstants(qi::symbols<char, types::ConstType>& constants) {
constants.add("true", types::ConstType(FormulaT(carl::FormulaType::TRUE)));
constants.add("false", types::ConstType(FormulaT(carl::FormulaType::FALSE)));
}
virtual FormulaT representingFormula( const ModelVariable& mv ) {
assert(false);
return FormulaT();
}
bool apply(const std::vector<FormulaT>& arguments, types::TermType& result, TheoryError& ) const {
result = FormulaT(type, arguments);
return true;
}