#include "storm/adapters/Z3ExpressionAdapter.h"
#include <cstdint>
#include "storm/storage/expressions/Expressions.h"
#include "storm/storage/expressions/ExpressionManager.h"
#include "storm/utility/macros.h"
#include "storm/utility/constants.h"
#include "storm/exceptions/ExpressionEvaluationException.h"
#include "storm/exceptions/InvalidTypeException.h"
#include "storm/exceptions/NotImplementedException.h"
namespace storm {
namespace adapters {
#ifdef STORM_HAVE_Z3
#ifdef STORM_Z3_API_USES_STANDARD_INTEGERS
typedef int64_t Z3_SIGNED_INTEGER;
typedef uint64_t Z3_UNSIGNED_INTEGER;
#else
typedef long long Z3_SIGNED_INTEGER;
typedef unsigned long long Z3_UNSIGNED_INTEGER;
#endif
Z3ExpressionAdapter::Z3ExpressionAdapter(storm::expressions::ExpressionManager& manager, z3::context& context) : manager(manager), context(context), additionalAssertions(), variableToExpressionMapping() {
// Intentionally left empty.
}
z3::expr Z3ExpressionAdapter::translateExpression(storm::expressions::Expression const& expression) {
STORM_LOG_ASSERT(expression.getManager() == this->manager, "Invalid expression for solver.");
z3::expr result = boost::any_cast<z3::expr>(expression.getBaseExpression().accept(*this, boost::none));
expressionCache.clear();
for (z3::expr const& assertion : additionalAssertions) {
result = result && assertion;
}
additionalAssertions.clear();
return result.simplify();
}
z3::expr Z3ExpressionAdapter::translateExpression(storm::expressions::Variable const& variable) {
STORM_LOG_ASSERT(variable.getManager() == this->manager, "Invalid expression for solver.");
auto const& variableExpressionPair = variableToExpressionMapping.find(variable);
if (variableExpressionPair == variableToExpressionMapping.end()) {
return createVariable(variable);
}
return variableExpressionPair->second;
}
storm::expressions::Variable const& Z3ExpressionAdapter::getVariable(z3::func_decl z3Declaration) {
auto const& declarationVariablePair = declarationToVariableMapping.find(z3Declaration);
STORM_LOG_ASSERT(declarationVariablePair != declarationToVariableMapping.end(), "Unable to find declaration.");
return declarationVariablePair->second;
}
storm::expressions::Expression Z3ExpressionAdapter::translateExpression(z3::expr const& expr) {
if (expr.is_app()) {
switch (expr.decl().decl_kind()) {
case Z3_OP_TRUE:
return manager.boolean(true);
case Z3_OP_FALSE:
return manager.boolean(false);
case Z3_OP_EQ:
return this->translateExpression(expr.arg(0)) == this->translateExpression(expr.arg(1));
case Z3_OP_DISTINCT: {
unsigned args = expr.num_args();
STORM_LOG_THROW(args != 0, storm::exceptions::ExpressionEvaluationException, "Failed to convert Z3 expression. DISTINCT (mutual != ) operator with 0-arity is assumed to be an error.");
if (args == 1) {
return manager.boolean(true);
} else {
storm::expressions::Expression retVal = this->translateExpression(expr.arg(0)) != this->translateExpression(expr.arg(1));
for (unsigned arg2 = 2; arg2 < args; ++arg2) {
retVal = retVal && (this->translateExpression(expr.arg(0)) != this->translateExpression(expr.arg(arg2)));
}
for (unsigned arg1 = 1; arg1 < args; ++arg1) {
for (unsigned arg2 = arg1 + 1; arg2 < args; ++arg2) {
retVal = retVal && (this->translateExpression(expr.arg(arg1)) != this->translateExpression(expr.arg(arg2)));
}
}
return retVal;
}
}
case Z3_OP_ITE:
return storm::expressions::ite(this->translateExpression(expr.arg(0)), this->translateExpression(expr.arg(1)), this->translateExpression(expr.arg(2)));
case Z3_OP_AND: {
unsigned args = expr.num_args();
STORM_LOG_THROW(args != 0, storm::exceptions::ExpressionEvaluationException, "Failed to convert Z3 expression. 0-ary AND is assumed to be an error.");
if (args == 1) {
return this->translateExpression(expr.arg(0));
} else {
storm::expressions::Expression retVal = this->translateExpression(expr.arg(0));
for (unsigned i = 1; i < args; i++) {
retVal = retVal && this->translateExpression(expr.arg(i));
}
return retVal;
}
}
case Z3_OP_OR: {
unsigned args = expr.num_args();
STORM_LOG_THROW(args != 0, storm::exceptions::ExpressionEvaluationException, "Failed to convert Z3 expression. 0-ary OR is assumed to be an error.");
if (args == 1) {
return this->translateExpression(expr.arg(0));
} else {
storm::expressions::Expression retVal = this->translateExpression(expr.arg(0));
for (unsigned i = 1; i < args; i++) {
retVal = retVal || this->translateExpression(expr.arg(i));
}
return retVal;
}
}
case Z3_OP_IFF:
return storm::expressions::iff(this->translateExpression(expr.arg(0)), this->translateExpression(expr.arg(1)));
case Z3_OP_XOR:
return storm::expressions::xclusiveor(this->translateExpression(expr.arg(0)), this->translateExpression(expr.arg(1)));
case Z3_OP_NOT:
return !this->translateExpression(expr.arg(0));
case Z3_OP_IMPLIES:
return storm::expressions::implies(this->translateExpression(expr.arg(0)), this->translateExpression(expr.arg(1)));
case Z3_OP_LE:
return this->translateExpression(expr.arg(0)) <= this->translateExpression(expr.arg(1));
case Z3_OP_GE:
return this->translateExpression(expr.arg(0)) >= this->translateExpression(expr.arg(1));
case Z3_OP_LT:
return this->translateExpression(expr.arg(0)) < this->translateExpression(expr.arg(1));
case Z3_OP_GT:
return this->translateExpression(expr.arg(0)) > this->translateExpression(expr.arg(1));
case Z3_OP_ADD:
return this->translateExpression(expr.arg(0)) + this->translateExpression(expr.arg(1));
case Z3_OP_SUB:
return this->translateExpression(expr.arg(0)) - this->translateExpression(expr.arg(1));
case Z3_OP_UMINUS:
return -this->translateExpression(expr.arg(0));
case Z3_OP_MUL:
return this->translateExpression(expr.arg(0)) * this->translateExpression(expr.arg(1));
case Z3_OP_DIV:
return this->translateExpression(expr.arg(0)) / this->translateExpression(expr.arg(1));
case Z3_OP_IDIV:
return this->translateExpression(expr.arg(0)) / this->translateExpression(expr.arg(1));
case Z3_OP_ANUM:
// Arithmetic numeral.
if (expr.is_int() && expr.is_const()) {
Z3_SIGNED_INTEGER value;
if (Z3_get_numeral_int64(expr.ctx(), expr, &value)) {
return manager.integer(value);
} else {
STORM_LOG_THROW(false, storm::exceptions::ExpressionEvaluationException, "Failed to convert Z3 expression. Expression is constant integer and value does not fit into 64-bit integer.");
}
} else {
STORM_LOG_ASSERT(expr.is_real() && expr.is_const(), "Cannot handle numerical expression");
Z3_SIGNED_INTEGER num;
Z3_SIGNED_INTEGER den;
if (Z3_get_numeral_rational_int64(expr.ctx(), expr, &num, &den)) {
return manager.rational(storm::utility::convertNumber<storm::RationalNumber>(static_cast<int_fast64_t>(num)) / storm::utility::convertNumber<storm::RationalNumber>(static_cast<int_fast64_t>(den)));
} else {
return manager.rational(storm::utility::convertNumber<storm::RationalNumber>(std::string(Z3_get_numeral_string(expr.ctx(), expr))));
}
}
case Z3_OP_UNINTERPRETED:
// Currently, we only support uninterpreted constant functions.
STORM_LOG_THROW(expr.is_const(), storm::exceptions::ExpressionEvaluationException, "Failed to convert Z3 expression. Encountered non-constant uninterpreted function.");
return manager.getVariable(expr.decl().name().str()).getExpression();
default:
STORM_LOG_THROW(false, storm::exceptions::ExpressionEvaluationException, "Failed to convert Z3 expression. Encountered unhandled Z3_decl_kind " << expr.decl().decl_kind() <<".");
break;
}
} else {
STORM_LOG_THROW(false, storm::exceptions::ExpressionEvaluationException, "Failed to convert Z3 expression. Encountered unknown expression type.");
}
}
boost::any Z3ExpressionAdapter::visit(storm::expressions::BinaryBooleanFunctionExpression const& expression, boost::any const& data) {
auto cacheIt = expressionCache.find(&expression);
if (cacheIt != expressionCache.end()) {
return cacheIt->second;
}
z3::expr leftResult = boost::any_cast<z3::expr>(expression.getFirstOperand()->accept(*this, data));
z3::expr rightResult = boost::any_cast<z3::expr>(expression.getSecondOperand()->accept(*this, data));
z3::expr result(context);
switch(expression.getOperatorType()) {
case storm::expressions::BinaryBooleanFunctionExpression::OperatorType::And:
result = leftResult && rightResult;
break;
case storm::expressions::BinaryBooleanFunctionExpression::OperatorType::Or:
result = leftResult || rightResult;
break;
case storm::expressions::BinaryBooleanFunctionExpression::OperatorType::Xor:
result = z3::expr(context, Z3_mk_xor(context, leftResult, rightResult));
break;
case storm::expressions::BinaryBooleanFunctionExpression::OperatorType::Implies:
result = z3::expr(context, Z3_mk_implies(context, leftResult, rightResult));
break;
case storm::expressions::BinaryBooleanFunctionExpression::OperatorType::Iff:
result = z3::expr(context, Z3_mk_iff(context, leftResult, rightResult));
break;
default:
STORM_LOG_THROW(false, storm::exceptions::ExpressionEvaluationException, "Cannot evaluate expression: unknown boolean binary operator '" << static_cast<int>(expression.getOperatorType()) << "' in expression " << expression << ".");
}
expressionCache.emplace(&expression, result);
return result;
}
boost::any Z3ExpressionAdapter::visit(storm::expressions::BinaryNumericalFunctionExpression const& expression, boost::any const& data) {
auto cacheIt = expressionCache.find(&expression);
if (cacheIt != expressionCache.end()) {
return cacheIt->second;
}
z3::expr leftResult = boost::any_cast<z3::expr>(expression.getFirstOperand()->accept(*this, data));
z3::expr rightResult = boost::any_cast<z3::expr>(expression.getSecondOperand()->accept(*this, data));
z3::expr result(context);
switch(expression.getOperatorType()) {
case storm::expressions::BinaryNumericalFunctionExpression::OperatorType::Plus:
result = leftResult + rightResult;
break;
case storm::expressions::BinaryNumericalFunctionExpression::OperatorType::Minus:
result = leftResult - rightResult;
break;
case storm::expressions::BinaryNumericalFunctionExpression::OperatorType::Times:
result = leftResult * rightResult;
break;
case storm::expressions::BinaryNumericalFunctionExpression::OperatorType::Divide:
if (leftResult.is_int() && rightResult.is_int()) {
leftResult = z3::expr(context, Z3_mk_int2real(context, leftResult));
}
result = leftResult / rightResult;
break;
case storm::expressions::BinaryNumericalFunctionExpression::OperatorType::Min:
result = ite(leftResult <= rightResult, leftResult, rightResult);
break;
case storm::expressions::BinaryNumericalFunctionExpression::OperatorType::Max:
result = ite(leftResult >= rightResult, leftResult, rightResult);
break;
case storm::expressions::BinaryNumericalFunctionExpression::OperatorType::Power:
result = pw(leftResult,rightResult);
break;
default:
STORM_LOG_THROW(false, storm::exceptions::ExpressionEvaluationException, "Cannot evaluate expression: unknown numerical binary operator '" << static_cast<int>(expression.getOperatorType()) << "' in expression " << expression << ".");
}
expressionCache.emplace(&expression, result);
return result;
}
boost::any Z3ExpressionAdapter::visit(storm::expressions::BinaryRelationExpression const& expression, boost::any const& data) {
auto cacheIt = expressionCache.find(&expression);
if (cacheIt != expressionCache.end()) {
return cacheIt->second;
}
z3::expr leftResult = boost::any_cast<z3::expr>(expression.getFirstOperand()->accept(*this, data));
z3::expr rightResult = boost::any_cast<z3::expr>(expression.getSecondOperand()->accept(*this, data));
z3::expr result(context);
switch(expression.getRelationType()) {
case storm::expressions::BinaryRelationExpression::RelationType::Equal:
result = leftResult == rightResult;
break;
case storm::expressions::BinaryRelationExpression::RelationType::NotEqual:
result = leftResult != rightResult;
break;
case storm::expressions::BinaryRelationExpression::RelationType::Less:
result = leftResult < rightResult;
break;
case storm::expressions::BinaryRelationExpression::RelationType::LessOrEqual:
result = leftResult <= rightResult;
break;
case storm::expressions::BinaryRelationExpression::RelationType::Greater:
result = leftResult > rightResult;
break;
case storm::expressions::BinaryRelationExpression::RelationType::GreaterOrEqual:
result = leftResult >= rightResult;
break;
default:
STORM_LOG_THROW(false, storm::exceptions::ExpressionEvaluationException, "Cannot evaluate expression: unknown boolean binary operator '" << static_cast<int>(expression.getRelationType()) << "' in expression " << expression << ".");
}
expressionCache.emplace(&expression, result);
return result;
}
boost::any Z3ExpressionAdapter::visit(storm::expressions::BooleanLiteralExpression const& expression, boost::any const&) {
auto cacheIt = expressionCache.find(&expression);
if (cacheIt != expressionCache.end()) {
return cacheIt->second;
}
z3::expr result = context.bool_val(expression.getValue());
expressionCache.emplace(&expression, result);
return result;
}
boost::any Z3ExpressionAdapter::visit(storm::expressions::RationalLiteralExpression const& expression, boost::any const&) {
auto cacheIt = expressionCache.find(&expression);
if (cacheIt != expressionCache.end()) {
return cacheIt->second;
}
std::stringstream fractionStream;
fractionStream << expression.getValue();
z3::expr result = context.real_val(fractionStream.str().c_str());
expressionCache.emplace(&expression, result);
return result;
}
boost::any Z3ExpressionAdapter::visit(storm::expressions::IntegerLiteralExpression const& expression, boost::any const&) {
auto cacheIt = expressionCache.find(&expression);
if (cacheIt != expressionCache.end()) {
return cacheIt->second;
}
z3::expr result = context.int_val(static_cast<Z3_SIGNED_INTEGER>(expression.getValue()));
expressionCache.emplace(&expression, result);
return result;
}
boost::any Z3ExpressionAdapter::visit(storm::expressions::UnaryBooleanFunctionExpression const& expression, boost::any const& data) {
auto cacheIt = expressionCache.find(&expression);
if (cacheIt != expressionCache.end()) {
return cacheIt->second;
}
z3::expr result = boost::any_cast<z3::expr>(expression.getOperand()->accept(*this, data));
switch (expression.getOperatorType()) {
case storm::expressions::UnaryBooleanFunctionExpression::OperatorType::Not:
result = !result;
break;
default:
STORM_LOG_THROW(false, storm::exceptions::ExpressionEvaluationException, "Cannot evaluate expression: unknown boolean binary operator '" << static_cast<int>(expression.getOperatorType()) << "' in expression " << expression << ".");
}
expressionCache.emplace(&expression, result);
return result;
}
boost::any Z3ExpressionAdapter::visit(storm::expressions::UnaryNumericalFunctionExpression const& expression, boost::any const& data) {
auto cacheIt = expressionCache.find(&expression);
if (cacheIt != expressionCache.end()) {
return cacheIt->second;
}
z3::expr result = boost::any_cast<z3::expr>(expression.getOperand()->accept(*this, data));
switch(expression.getOperatorType()) {
case storm::expressions::UnaryNumericalFunctionExpression::OperatorType::Minus:
result = 0 - result;
break;
case storm::expressions::UnaryNumericalFunctionExpression::OperatorType::Floor: {
storm::expressions::Variable freshAuxiliaryVariable = manager.declareFreshVariable(manager.getIntegerType(), true);
z3::expr floorVariable = context.int_const(freshAuxiliaryVariable.getName().c_str());
additionalAssertions.push_back(z3::expr(context, Z3_mk_int2real(context, floorVariable)) <= result && result < (z3::expr(context, Z3_mk_int2real(context, floorVariable)) + 1));
result = floorVariable;
break;
}
case storm::expressions::UnaryNumericalFunctionExpression::OperatorType::Ceil:{
storm::expressions::Variable freshAuxiliaryVariable = manager.declareFreshVariable(manager.getIntegerType(), true);
z3::expr ceilVariable = context.int_const(freshAuxiliaryVariable.getName().c_str());
additionalAssertions.push_back(z3::expr(context, Z3_mk_int2real(context, ceilVariable)) - 1 < result && result <= z3::expr(context, Z3_mk_int2real(context, ceilVariable)));
result = ceilVariable;
break;
}
default: STORM_LOG_THROW(false, storm::exceptions::ExpressionEvaluationException, "Cannot evaluate expression: unknown numerical unary operator '" << static_cast<int>(expression.getOperatorType()) << "'.");
}
expressionCache.emplace(&expression, result);
return result;
}
boost::any Z3ExpressionAdapter::visit(storm::expressions::IfThenElseExpression const& expression, boost::any const& data) {
auto cacheIt = expressionCache.find(&expression);
if (cacheIt != expressionCache.end()) {
return cacheIt->second;
}
z3::expr conditionResult = boost::any_cast<z3::expr>(expression.getCondition()->accept(*this, data));
z3::expr thenResult = boost::any_cast<z3::expr>(expression.getThenExpression()->accept(*this, data));
z3::expr elseResult = boost::any_cast<z3::expr>(expression.getElseExpression()->accept(*this, data));
z3::expr result = z3::expr(context, Z3_mk_ite(context, conditionResult, thenResult, elseResult));
expressionCache.emplace(&expression, result);
return result;
}
boost::any Z3ExpressionAdapter::visit(storm::expressions::VariableExpression const& expression, boost::any const&) {
return this->translateExpression(expression.getVariable());
}
z3::expr Z3ExpressionAdapter::createVariable(storm::expressions::Variable const& variable) {
z3::expr z3Variable(context);
if (variable.getType().isBooleanType()) {
z3Variable = context.bool_const(variable.getName().c_str());
} else if (variable.getType().isIntegerType()) {
z3Variable = context.int_const(variable.getName().c_str());
} else if (variable.getType().isBitVectorType()) {
z3Variable = context.bv_const(variable.getName().c_str(), variable.getType().getWidth());
} else if (variable.getType().isRationalType()) {
z3Variable = context.real_const(variable.getName().c_str());
} else {
STORM_LOG_THROW(false, storm::exceptions::InvalidTypeException, "Encountered variable '" << variable.getName() << "' with unknown type while trying to create solver variables.");
}
variableToExpressionMapping.insert(std::make_pair(variable, z3Variable));
declarationToVariableMapping.insert(std::make_pair(z3Variable.decl(), variable));
return z3Variable;
}
#endif
} // namespace adapters
} // namespace storm