#include "FormulaParserGrammar.h"
#include "storm/storage/expressions/ExpressionManager.h"

#include <memory>

namespace storm {
    namespace parser {

        FormulaParserGrammar::FormulaParserGrammar(std::shared_ptr<storm::expressions::ExpressionManager const> const& manager) : FormulaParserGrammar::base_type(start), constManager(manager), manager(nullptr), expressionParser(*manager, keywords_, true, true), propertyCount(0) {
            initialize();
        }

        FormulaParserGrammar::FormulaParserGrammar(std::shared_ptr<storm::expressions::ExpressionManager> const& manager) : FormulaParserGrammar::base_type(start), constManager(manager), manager(manager), expressionParser(*manager, keywords_, true, true), propertyCount(0) {
            initialize();
        }

        void FormulaParserGrammar::initialize() {
            // Register all variables so we can parse them in the expressions.
            for (auto variableTypePair : *constManager) {
                addIdentifierExpression(variableTypePair.first.getName(), variableTypePair.first);
            }
            // Set the identifier mapping to actually generate expressions.
            expressionParser.setIdentifierMapping(&identifiers_);

            keywords_.name("keyword");
            nonStandardKeywords_.name("non-standard Storm-specific keyword");
            relationalOperator_.name("relational operator");
            optimalityOperator_.name("optimality operator");
            rewardMeasureType_.name("reward measure");
            operatorKeyword_.name("Operator keyword");
            filterType_.name("filter type");

            // Auxiliary helpers
            isPathFormula = qi::eps(qi::_r1 == FormulaKind::Path);
            noAmbiguousNonAssociativeOperator = !(qi::lit(qi::_r2)[qi::_pass = phoenix::bind(&FormulaParserGrammar::raiseAmbiguousNonAssociativeOperatorError, phoenix::ref(*this), qi::_r1, qi::_r2)]);
            noAmbiguousNonAssociativeOperator.name("no ambiguous non-associative operator");
            identifier %= qi::as_string[qi::raw[qi::lexeme[((qi::alpha | qi::char_('_') | qi::char_('.')) >> *(qi::alnum | qi::char_('_')))]]];
            identifier.name("identifier");
            label %= qi::as_string[qi::raw[qi::lexeme[((qi::alpha | qi::char_('_')) >> *(qi::alnum | qi::char_('_')))]]];
            label.name("label");
            quotedString %= qi::as_string[qi::lexeme[qi::omit[qi::char_('"')] > qi::raw[*(!qi::char_('"') >> qi::char_)] > qi::omit[qi::lit('"')]]];
            quotedString.name("quoted string");

            // PCTL-like Operator Formulas
            operatorInformation = (-optimalityOperator_)[qi::_a = qi::_1] >>
                                  ((qi::lit("=") > qi::lit("?"))[qi::_val = phoenix::bind(&FormulaParserGrammar::createOperatorInformation, phoenix::ref(*this), qi::_a, boost::none, boost::none)]
                                     | (relationalOperator_ > expressionParser)[qi::_val = phoenix::bind(&FormulaParserGrammar::createOperatorInformation, phoenix::ref(*this), qi::_a, qi::_1, qi::_2)]
                                  );
            operatorInformation.name("operator information");
            operatorSubFormula = ((   (qi::eps(qi::_r1 == storm::logic::FormulaContext::Probability) > formula(FormulaKind::Path, qi::_r1))
                                    | (qi::eps(qi::_r1 == storm::logic::FormulaContext::Reward) > (longRunAverageRewardFormula | eventuallyFormula( qi::_r1) | cumulativeRewardFormula | instantaneousRewardFormula | totalRewardFormula))
                                    | (qi::eps(qi::_r1 == storm::logic::FormulaContext::Time) > eventuallyFormula(qi::_r1))
                                    | (qi::eps(qi::_r1 == storm::logic::FormulaContext::LongRunAverage) > formula(FormulaKind::State, storm::logic::FormulaContext::LongRunAverage))
                                  ) >> -(qi::lit("||") > formula(FormulaKind::Path, storm::logic::FormulaContext::Probability))
                                 )[qi::_val = phoenix::bind(&FormulaParserGrammar::createConditionalFormula, phoenix::ref(*this), qi::_1, qi::_2, qi::_r1)];
            operatorSubFormula.name("operator subformula");
            rewardModelName = qi::eps(qi::_r1 == storm::logic::FormulaContext::Reward) >> (qi::lit("{\"") > label > qi::lit("\"}"));
            rewardModelName.name("reward model name");
            rewardMeasureType = qi::eps(qi::_r1 == storm::logic::FormulaContext::Reward || qi::_r1 == storm::logic::FormulaContext::Time) >> qi::lit("[") >> rewardMeasureType_ >> qi::lit("]");
            rewardMeasureType.name("reward measure type");
            operatorFormula = (operatorKeyword_[qi::_a = qi::_1] > -rewardMeasureType(qi::_a) > -rewardModelName(qi::_a) > operatorInformation > qi::lit("[") > operatorSubFormula(qi::_a) > qi::lit("]"))
                                      [qi::_val = phoenix::bind(&FormulaParserGrammar::createOperatorFormula, phoenix::ref(*this), qi::_a, qi::_2, qi::_3, qi::_4, qi::_5)];
            operatorFormula.name("operator formula");


            // Atomic propositions
            labelFormula = (qi::lit("\"") >> label >> qi::lit("\""))[qi::_val = phoenix::bind(&FormulaParserGrammar::createAtomicLabelFormula, phoenix::ref(*this), qi::_1)];
            labelFormula.name("label formula");
            booleanLiteralFormula = (qi::lit("true")[qi::_a = true] | qi::lit("false")[qi::_a = false])[qi::_val = phoenix::bind(&FormulaParserGrammar::createBooleanLiteralFormula, phoenix::ref(*this), qi::_a)];
            booleanLiteralFormula.name("boolean literal formula");
            expressionFormula = expressionParser[qi::_val = phoenix::bind(&FormulaParserGrammar::createAtomicExpressionFormula, phoenix::ref(*this), qi::_1)];
            expressionFormula.name("expression formula");
            atomicPropositionFormula = (booleanLiteralFormula | labelFormula | expressionFormula);
            atomicPropositionFormula.name("atomic proposition");

            // Propositional Logic operators
            // To correctly parse the operator precedences (! binds stronger than & binds stronger than |), we run through different "precedence levels" starting with the weakest binding operator.
            basicPropositionalFormula = (qi::lit("(") >> (formula(qi::_r1, qi::_r2) > qi::lit(")")))
                                | atomicPropositionFormula // Should be checked before operator formulas and others. Otherwise, e.g. variable "Random" would be parsed as reward operator 'R' (followed by andom)
                                | negationPropositionalFormula(qi::_r1, qi::_r2)
                                | operatorFormula
                                | (isPathFormula(qi::_r1) >> prefixOperatorPathFormula(qi::_r2)) // Needed for e.g. F "a" & X "a" = F ("a" & (X "a"))
                                | multiOperatorFormula // Has to come after prefixOperatorPathFormula to avoid confusion with multiBoundedPathFormula
                                | quantileFormula
                                | gameFormula;
            negationPropositionalFormula = (qi::lit("!") > basicPropositionalFormula(qi::_r1, qi::_r2))[qi::_val = phoenix::bind(&FormulaParserGrammar::createUnaryBooleanStateOrPathFormula, phoenix::ref(*this), qi::_1, storm::logic::UnaryBooleanOperatorType::Not)];
            basicPropositionalFormula.name("basic propositional formula");
            andLevelPropositionalFormula = basicPropositionalFormula(qi::_r1, qi::_r2)[qi::_val = qi::_1]
                                           >> *( qi::lit("&")
                                                > basicPropositionalFormula(qi::_r1, qi::_r2)[qi::_val = phoenix::bind(&FormulaParserGrammar::createBinaryBooleanStateOrPathFormula, phoenix::ref(*this), qi::_val, qi::_1, storm::logic::BinaryBooleanStateFormula::OperatorType::And)]);
            andLevelPropositionalFormula.name("and precedence level propositional formula");
            orLevelPropositionalFormula = andLevelPropositionalFormula(qi::_r1, qi::_r2)[qi::_val = qi::_1]
                                          >> *( (!qi::lit("||") >> qi::lit("|")) // Make sure to not confuse with conditional operator "||"
                                               > andLevelPropositionalFormula(qi::_r1, qi::_r2)[qi::_val = phoenix::bind(&FormulaParserGrammar::createBinaryBooleanStateOrPathFormula, phoenix::ref(*this), qi::_val, qi::_1, storm::logic::BinaryBooleanStateFormula::OperatorType::Or)]);
            orLevelPropositionalFormula.name("or precedence level propositional formula");
            propositionalFormula = orLevelPropositionalFormula(qi::_r1, qi::_r2);

            // Path operators
            // Again need to parse precedences correctly. Propositional formulae bind stronger than temporal operators.
            basicPathFormula = propositionalFormula(FormulaKind::Path, qi::_r1) // Bracketed case is handled here as well
                               | prefixOperatorPathFormula(qi::_r1); // Needs to be checked *after* atomic expression formulas. Otherwise e.g. variable Fail would be parsed as "F (ail)"
            prefixOperatorPathFormula = eventuallyFormula(qi::_r1)
                                   | nextFormula(qi::_r1)
                                   | globallyFormula(qi::_r1)
                                   | hoaPathFormula(qi::_r1)
                                   | multiBoundedPathFormula(qi::_r1);
            basicPathFormula.name("basic path formula");
            timeBoundReference = (-qi::lit("rew") >> rewardModelName(storm::logic::FormulaContext::Reward))[qi::_val = phoenix::bind(&FormulaParserGrammar::createTimeBoundReference, phoenix::ref(*this), storm::logic::TimeBoundType::Reward, qi::_1)]
                                 | (qi::lit("steps"))[qi::_val = phoenix::bind(&FormulaParserGrammar::createTimeBoundReference, phoenix::ref(*this), storm::logic::TimeBoundType::Steps, boost::none)]
                                 | (-qi::lit("time"))[qi::_val = phoenix::bind(&FormulaParserGrammar::createTimeBoundReference, phoenix::ref(*this), storm::logic::TimeBoundType::Time, boost::none)];
            timeBoundReference.name("time bound reference");
            timeBound = ((timeBoundReference >> qi::lit("[")) > expressionParser > qi::lit(",") > expressionParser > qi::lit("]"))
                            [qi::_val = phoenix::bind(&FormulaParserGrammar::createTimeBoundFromInterval, phoenix::ref(*this), qi::_2, qi::_3, qi::_1)]
                        | ( timeBoundReference >> (qi::lit("<=")[qi::_a = true, qi::_b = false] | qi::lit("<")[qi::_a = true, qi::_b = true] | qi::lit(">=")[qi::_a = false, qi::_b = false] | qi::lit(">")[qi::_a = false, qi::_b = true]) >> expressionParser)
                            [qi::_val = phoenix::bind(&FormulaParserGrammar::createTimeBoundFromSingleBound, phoenix::ref(*this), qi::_2, qi::_a, qi::_b, qi::_1)]
                        | ( timeBoundReference >> qi::lit("=") >> expressionParser)
                            [qi::_val = phoenix::bind(&FormulaParserGrammar::createTimeBoundFromInterval, phoenix::ref(*this), qi::_2, qi::_2, qi::_1)];
            timeBound.name("time bound");
            timeBounds = (timeBound % qi::lit(",")) | (((-qi::lit("^") >> qi::lit("{")) >> (timeBound % qi::lit(","))) >> qi::lit("}"));
            timeBounds.name("time bounds");
            eventuallyFormula = (qi::lit("F") > (-timeBounds) > basicPathFormula(qi::_r1))[qi::_val = phoenix::bind(&FormulaParserGrammar::createEventuallyFormula, phoenix::ref(*this), qi::_1, qi::_r1, qi::_2)];
            eventuallyFormula.name("eventually formula");
            nextFormula = (qi::lit("X") > basicPathFormula(qi::_r1))[qi::_val = phoenix::bind(&FormulaParserGrammar::createNextFormula, phoenix::ref(*this), qi::_1)];
            nextFormula.name("next formula");
            globallyFormula = (qi::lit("G") > basicPathFormula(qi::_r1))[qi::_val = phoenix::bind(&FormulaParserGrammar::createGloballyFormula, phoenix::ref(*this), qi::_1)];
            globallyFormula.name("globally formula");
            hoaPathFormula = qi::lit("HOA:") > qi::lit("{")
                > quotedString[qi::_val = phoenix::bind(&FormulaParserGrammar::createHOAPathFormula, phoenix::ref(*this), qi::_1)]
                >> *(qi::lit(",") > quotedString > qi::lit("->") > formula(FormulaKind::State, qi::_r1) )[phoenix::bind(&FormulaParserGrammar::addHoaAPMapping, phoenix::ref(*this), *qi::_val, qi::_1, qi::_2)]
                > qi::lit("}");
            multiBoundedPathFormulaOperand = pathFormula(qi::_r1)[qi::_pass = phoenix::bind(&FormulaParserGrammar::isValidMultiBoundedPathFormulaOperand, phoenix::ref(*this), qi::_1)][qi::_val = qi::_1];
            multiBoundedPathFormulaOperand.name("multi bounded path formula operand");
            multiBoundedPathFormula = ((qi::lit("multi") > qi::lit("(")) >> (multiBoundedPathFormulaOperand(qi::_r1) % qi::lit(",")) >> qi::lit(")"))[qi::_val = phoenix::bind(&FormulaParserGrammar::createMultiBoundedPathFormula, phoenix::ref(*this), qi::_1)];
            multiBoundedPathFormula.name("multi bounded path formula");
            untilLevelPathFormula = basicPathFormula(qi::_r1)[qi::_val = qi::_1]
                                               >> -( (qi::lit("U")
                                                     > (-timeBounds) > basicPathFormula(qi::_r1))[qi::_val = phoenix::bind(&FormulaParserGrammar::createUntilFormula, phoenix::ref(*this), qi::_val, qi::_1, qi::_2)])
                                               >> (qi::eps > noAmbiguousNonAssociativeOperator(qi::_val,std::string("U"))); // Do not parse a U b U c
            untilLevelPathFormula.name("until precedence level path formula");
            pathFormula = untilLevelPathFormula(qi::_r1);
            pathFormula.name("path formula");

            // Quantitative path formulae (reward)
            longRunAverageRewardFormula = (qi::lit("LRA") | qi::lit("S") | qi::lit("MP"))[qi::_val = phoenix::bind(&FormulaParserGrammar::createLongRunAverageRewardFormula, phoenix::ref(*this))];
            longRunAverageRewardFormula.name("long run average reward formula");
            instantaneousRewardFormula = (qi::lit("I=") > expressionParser)[qi::_val = phoenix::bind(&FormulaParserGrammar::createInstantaneousRewardFormula, phoenix::ref(*this), qi::_1)];
            instantaneousRewardFormula.name("instantaneous reward formula");
            cumulativeRewardFormula = (qi::lit("C") >> timeBounds)[qi::_val = phoenix::bind(&FormulaParserGrammar::createCumulativeRewardFormula, phoenix::ref(*this), qi::_1)];
            cumulativeRewardFormula.name("cumulative reward formula");
            totalRewardFormula = (qi::lit("C"))[qi::_val = phoenix::bind(&FormulaParserGrammar::createTotalRewardFormula, phoenix::ref(*this))];
            totalRewardFormula.name("total reward formula");

            // Game Formulae
            playerCoalition = (-((identifier[phoenix::push_back(qi::_a, qi::_1)] | qi::uint_[phoenix::push_back(qi::_a, qi::_1)]) % ','))[qi::_val = phoenix::bind(&FormulaParserGrammar::createPlayerCoalition, phoenix::ref(*this), qi::_a)];
            playerCoalition.name("player coalition");
            gameFormula = (qi::lit("<<") > playerCoalition > qi::lit(">>") > operatorFormula)[qi::_val = phoenix::bind(&FormulaParserGrammar::createGameFormula, phoenix::ref(*this), qi::_1, qi::_2)];
            gameFormula.name("game formula");

            // Multi-objective, quantiles
            multiOperatorFormula = (qi::lit("multi") > qi::lit("(")
                                    > (operatorFormula % qi::lit(","))
                                    > qi::lit(")"))[qi::_val = phoenix::bind(&FormulaParserGrammar::createMultiOperatorFormula, phoenix::ref(*this), qi::_1)];
            multiOperatorFormula.name("multi-objective operator formula");
            quantileBoundVariable = (-optimalityOperator_ >> identifier >> qi::lit(","))[qi::_val = phoenix::bind(&FormulaParserGrammar::createQuantileBoundVariables, phoenix::ref(*this), qi::_1,  qi::_2)];
            quantileBoundVariable.name("quantile bound variable");
            quantileFormula = (qi::lit("quantile") > qi::lit("(") > *(quantileBoundVariable) > operatorFormula[qi::_pass = phoenix::bind(&FormulaParserGrammar::isBooleanReturnType, phoenix::ref(*this), qi::_1, true)] > qi::lit(")"))[qi::_val = phoenix::bind(&FormulaParserGrammar::createQuantileFormula, phoenix::ref(*this), qi::_1, qi::_2)];
            quantileFormula.name("Quantile formula");

            // General formulae
            formula = (isPathFormula(qi::_r1) >> pathFormula(qi::_r2) | propositionalFormula(qi::_r1, qi::_r2));
            formula.name("formula");

            topLevelFormula = formula(FormulaKind::State, storm::logic::FormulaContext::Undefined);
            topLevelFormula.name("top-level formula");

            formulaName = qi::lit("\"") >> identifier >> qi::lit("\"") >> qi::lit(":");
            formulaName.name("formula name");

            constantDefinition = (qi::lit("const") > -(qi::lit("int")[qi::_a = ConstantDataType::Integer] | qi::lit("bool")[qi::_a = ConstantDataType::Bool] | qi::lit("double")[qi::_a = ConstantDataType::Rational]) >> identifier >> -(qi::lit("=") > expressionParser))[phoenix::bind(&FormulaParserGrammar::addConstant, phoenix::ref(*this), qi::_1, qi::_a, qi::_2)];
            constantDefinition.name("constant definition");

            // Shielding properties
            shieldExpression = (qi::lit("<") > label > qi::lit(",") > shieldingType > -(qi::lit(",") > shieldComparison) > qi::lit(">"))[qi::_val = phoenix::bind(&FormulaParserGrammar::createShieldExpression, phoenix::ref(*this), qi::_2, qi::_1, qi::_3)];

            shieldExpression.name("shield expression");

            shieldingType = (qi::lit("PreSafety")[qi::_val = storm::logic::ShieldingType::PreSafety]   |
                             qi::lit("PostSafety")[qi::_val = storm::logic::ShieldingType::PostSafety] |
                             qi::lit("Optimal")[qi::_val = storm::logic::ShieldingType::Optimal]) > -qi::lit("Shield");
            shieldingType.name("shielding type");

            probability = qi::double_[qi::_pass = (qi::_1 >= 0) & (qi::_1 <= 1.0), qi::_val = qi::_1 ];
            probability.name("double between 0 and 1");

            shieldComparison = ((qi::lit("lambda")[qi::_a = storm::logic::ShieldComparison::Relative] |
                                 qi::lit("gamma")[qi::_a = storm::logic::ShieldComparison::Absolute]) > qi::lit("=") > probability)[qi::_val = phoenix::bind(&FormulaParserGrammar::createShieldComparisonStruct, phoenix::ref(*this), qi::_a, qi::_1)];
            shieldComparison.name("shield comparison type");

#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Woverloaded-shift-op-parentheses"

            filterProperty = (-formulaName >> qi::lit("filter") > qi::lit("(") > filterType_ > qi::lit(",") > topLevelFormula > qi::lit(",") > formula(FormulaKind::State, storm::logic::FormulaContext::Undefined)> qi::lit(")"))[qi::_val = phoenix::bind(&FormulaParserGrammar::createProperty, phoenix::ref(*this), qi::_1, qi::_2, qi::_3, qi::_4)] |
                             (-formulaName >> topLevelFormula)[qi::_val = phoenix::bind(&FormulaParserGrammar::createPropertyWithDefaultFilterTypeAndStates, phoenix::ref(*this), qi::_1, qi::_2)]  |
                             (-formulaName >> shieldExpression >> topLevelFormula)[qi::_val = phoenix::bind(&FormulaParserGrammar::createShieldingProperty, phoenix::ref(*this), qi::_1, qi::_3, qi::_2)];
            filterProperty.name("filter property");

#pragma clang diagnostic pop

            start = (qi::eps >> filterProperty[phoenix::push_back(qi::_val, qi::_1)]
                     | qi::eps(phoenix::bind(&FormulaParserGrammar::areConstantDefinitionsAllowed, phoenix::ref(*this))) >> constantDefinition
                     | qi::eps)
                     % +(qi::char_("\n;")) >> qi::skip(storm::spirit_encoding::space_type() | qi::lit("//") >> *(qi::char_ - (qi::eol | qi::eoi)))[qi::eps] >> qi::eoi;
            start.name("start");

            // Enable the following lines to print debug output for most the rules.
            //debug(rewardModelName);
            //debug(rewardMeasureType);
            //debug(operatorFormula);
            //debug(labelFormula);
            //debug(expressionFormula);
            //debug(booleanLiteralFormula);
            //debug(atomicPropositionFormula);
            //debug(basicPropositionalFormula);
            //debug(negationPropositionalFormula);
            //debug(andLevelPropositionalFormula);
            //debug(orLevelPropositionalFormula);
            //debug(propositionalFormula);
            //debug(timeBoundReference);
            //debug(timeBound);
            //debug(timeBounds);
            //debug(eventuallyFormula);
            //debug(nextFormula);
            //debug(globallyFormula);
            //debug(hoaPathFormula);
            //debug(multiBoundedPathFormula);
            //debug(prefixOperatorPathFormula);
            //debug(basicPathFormula);
            //debug(untilLevelPathFormula);
            //debug(pathFormula);
            //debug(longRunAverageRewardFormula);
            //debug(instantaneousRewardFormula);
            //debug(cumulativeRewardFormula);
            //debug(totalRewardFormula);
            ////debug(playerCoalition);
            //debug(gameFormula);
            //debug(multiOperatorFormula);
            //debug(quantileBoundVariable);
            //debug(quantileFormula);
            //debug(formula);
            //debug(topLevelFormula);
            //debug(formulaName);
            //debug(filterProperty);
            ////debug(constantDefinition);
            //debug(start);

            // Enable error reporting.
            qi::on_error<qi::fail>(rewardModelName, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(rewardMeasureType, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(operatorFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(labelFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(expressionFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(booleanLiteralFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(atomicPropositionFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(basicPropositionalFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(negationPropositionalFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(andLevelPropositionalFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(orLevelPropositionalFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(propositionalFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(timeBoundReference, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(timeBound, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(timeBounds, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(eventuallyFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(nextFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(globallyFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(hoaPathFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(multiBoundedPathFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(prefixOperatorPathFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(basicPathFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(untilLevelPathFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(pathFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(longRunAverageRewardFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(instantaneousRewardFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(cumulativeRewardFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(totalRewardFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(playerCoalition, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(gameFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(multiOperatorFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(quantileBoundVariable, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(quantileFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(formula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(topLevelFormula, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(formulaName, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(filterProperty, handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(constantDefinition , handler(qi::_1, qi::_2, qi::_3, qi::_4));
            qi::on_error<qi::fail>(start, handler(qi::_1, qi::_2, qi::_3, qi::_4));
        }

        void FormulaParserGrammar::addIdentifierExpression(std::string const& identifier, storm::expressions::Expression const& expression) {
            STORM_LOG_WARN_COND(keywords_.find(identifier) == nullptr, "Identifier `" << identifier << "' coincides with a reserved keyword or operator. Property expressions using the variable or constant '" << identifier << "' will not be parsed correctly.");
            STORM_LOG_WARN_COND(nonStandardKeywords_.find(identifier) == nullptr, "Identifier `" << identifier << "' coincides with a reserved keyword or operator. Property expressions using the variable or constant '" << identifier << "' might not be parsed correctly.");
            this->identifiers_.add(identifier, expression);
        }

        void FormulaParserGrammar::addConstant(std::string const& name, ConstantDataType type, boost::optional<storm::expressions::Expression> const& expression) {
            STORM_LOG_ASSERT(manager, "Mutable expression manager required to define new constants.");
            storm::expressions::Variable newVariable;
            STORM_LOG_THROW(!manager->hasVariable(name), storm::exceptions::WrongFormatException, "Invalid constant definition '" << name << "' in property: variable already exists.");

            if (type == ConstantDataType::Bool) {
                newVariable = manager->declareBooleanVariable(name);
            } else if (type == ConstantDataType::Integer)  {
                newVariable = manager->declareIntegerVariable(name);
            } else {
                newVariable = manager->declareRationalVariable(name);
            }

            if (expression) {
                addIdentifierExpression(name, expression.get());
            } else {
                undefinedConstants.insert(newVariable);
                addIdentifierExpression(name, newVariable);
            }
        }

        bool FormulaParserGrammar::areConstantDefinitionsAllowed() const {
            return static_cast<bool>(manager);
        }

        std::shared_ptr<storm::logic::TimeBoundReference> FormulaParserGrammar::createTimeBoundReference(storm::logic::TimeBoundType const& type, boost::optional<std::string> const& rewardModelName) const {
            if (type == storm::logic::TimeBoundType::Reward) {
                STORM_LOG_THROW(rewardModelName, storm::exceptions::WrongFormatException, "Reward bound does not specify a reward model name.");
                return std::make_shared<storm::logic::TimeBoundReference>(rewardModelName.get());
            } else {
                return std::make_shared<storm::logic::TimeBoundReference>(type);
            }
        }

        std::tuple<boost::optional<storm::logic::TimeBound>, boost::optional<storm::logic::TimeBound>, std::shared_ptr<storm::logic::TimeBoundReference>> FormulaParserGrammar::createTimeBoundFromInterval(storm::expressions::Expression const& lowerBound, storm::expressions::Expression const& upperBound, std::shared_ptr<storm::logic::TimeBoundReference> const& timeBoundReference) const {
            // As soon as it somehow does not break everything anymore, I will change return types here.

            storm::logic::TimeBound lower(false, lowerBound);
            storm::logic::TimeBound upper(false, upperBound);
            return std::make_tuple(lower, upper, timeBoundReference);
        }

        std::tuple<boost::optional<storm::logic::TimeBound>, boost::optional<storm::logic::TimeBound>, std::shared_ptr<storm::logic::TimeBoundReference>> FormulaParserGrammar::createTimeBoundFromSingleBound(storm::expressions::Expression const& bound, bool upperBound, bool strict, std::shared_ptr<storm::logic::TimeBoundReference> const& timeBoundReference) const {
            // As soon as it somehow does not break everything anymore, I will change return types here.
            if (upperBound) {
                return std::make_tuple(boost::none, storm::logic::TimeBound(strict, bound), timeBoundReference);
            } else {
                return std::make_tuple(storm::logic::TimeBound(strict, bound), boost::none, timeBoundReference);
            }
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createInstantaneousRewardFormula(storm::expressions::Expression const& timeBound) const {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::InstantaneousRewardFormula(timeBound));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createCumulativeRewardFormula(std::vector<std::tuple<boost::optional<storm::logic::TimeBound>, boost::optional<storm::logic::TimeBound>, std::shared_ptr<storm::logic::TimeBoundReference>>> const& timeBounds) const {
            std::vector<storm::logic::TimeBound> bounds;
            std::vector<storm::logic::TimeBoundReference> timeBoundReferences;
            for (auto const& timeBound : timeBounds) {
                STORM_LOG_THROW(!std::get<0>(timeBound), storm::exceptions::WrongFormatException, "Cumulative reward formulas with lower time bound are not allowed.");
                STORM_LOG_THROW(std::get<1>(timeBound), storm::exceptions::WrongFormatException, "Cumulative reward formulas require an upper bound.");
                bounds.push_back(std::get<1>(timeBound).get());
                timeBoundReferences.emplace_back(*std::get<2>(timeBound));
            }
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::CumulativeRewardFormula(bounds, timeBoundReferences));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createTotalRewardFormula() const {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::TotalRewardFormula());
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createLongRunAverageRewardFormula() const {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::LongRunAverageRewardFormula());
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createAtomicExpressionFormula(storm::expressions::Expression const& expression) const {
            STORM_LOG_THROW(expression.hasBooleanType(), storm::exceptions::WrongFormatException, "Expected expression of boolean type.");
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::AtomicExpressionFormula(expression));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createBooleanLiteralFormula(bool literal) const {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::BooleanLiteralFormula(literal));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createAtomicLabelFormula(std::string const& label) const {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::AtomicLabelFormula(label));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createEventuallyFormula(boost::optional<std::vector<std::tuple<boost::optional<storm::logic::TimeBound>, boost::optional<storm::logic::TimeBound>, std::shared_ptr<storm::logic::TimeBoundReference>>>> const& timeBounds, storm::logic::FormulaContext context, std::shared_ptr<storm::logic::Formula const> const& subformula) const {
            if (timeBounds && !timeBounds.get().empty()) {
                std::vector<boost::optional<storm::logic::TimeBound>> lowerBounds, upperBounds;
                std::vector<storm::logic::TimeBoundReference> timeBoundReferences;
                for (auto const& timeBound : timeBounds.get()) {
                    lowerBounds.push_back(std::get<0>(timeBound));
                    upperBounds.push_back(std::get<1>(timeBound));
                    timeBoundReferences.emplace_back(*std::get<2>(timeBound));
                }
                return std::shared_ptr<storm::logic::Formula const>(new storm::logic::BoundedUntilFormula(createBooleanLiteralFormula(true), subformula, lowerBounds, upperBounds, timeBoundReferences));
            } else {
                return std::shared_ptr<storm::logic::Formula const>(new storm::logic::EventuallyFormula(subformula, context));
            }
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createGloballyFormula(std::shared_ptr<storm::logic::Formula const> const& subformula) const {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::GloballyFormula(subformula));
        }

        /*
        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createGloballyFormula(boost::optional<std::vector<std::tuple<boost::optional<storm::logic::TimeBound>, boost::optional<storm::logic::TimeBound>, std::shared_ptr<storm::logic::TimeBoundReference>>>> const& timeBounds, std::shared_ptr<storm::logic::Formula const> const& subformula) const {
            if (timeBounds && !timeBounds.get().empty()) {
                std::vector<boost::optional<storm::logic::TimeBound>> lowerBounds, upperBounds;
                std::vector<storm::logic::TimeBoundReference> timeBoundReferences;
                for (auto const& timeBound : timeBounds.get()) {
                    STORM_LOG_ASSERT(!std::get<0>(timeBound), "Cannot use lower time bounds (or intervals) in globally formulas.");
                    lowerBounds.push_back(std::get<0>(timeBound));
                    upperBounds.push_back(std::get<1>(timeBound));
                    timeBoundReferences.emplace_back(*std::get<2>(timeBound));
                }
                return std::shared_ptr<storm::logic::Formula const>(new storm::logic::BoundedGloballyFormula(subformula, lowerBounds, upperBounds, timeBoundReferences));
            } else {
                return std::shared_ptr<storm::logic::Formula const>(new storm::logic::GloballyFormula(subformula));
            }
        }
        */

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createNextFormula(std::shared_ptr<storm::logic::Formula const> const& subformula) const {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::NextFormula(subformula));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createUntilFormula(std::shared_ptr<storm::logic::Formula const> const& leftSubformula, boost::optional<std::vector<std::tuple<boost::optional<storm::logic::TimeBound>, boost::optional<storm::logic::TimeBound>, std::shared_ptr<storm::logic::TimeBoundReference>>>> const& timeBounds, std::shared_ptr<storm::logic::Formula const> const& rightSubformula) {
            if (timeBounds && !timeBounds.get().empty()) {
                std::vector<boost::optional<storm::logic::TimeBound>> lowerBounds, upperBounds;
                std::vector<storm::logic::TimeBoundReference> timeBoundReferences;
                for (auto const& timeBound : timeBounds.get()) {
                    lowerBounds.push_back(std::get<0>(timeBound));
                    upperBounds.push_back(std::get<1>(timeBound));
                    timeBoundReferences.emplace_back(*std::get<2>(timeBound));
                }
                return std::shared_ptr<storm::logic::Formula const>(new storm::logic::BoundedUntilFormula(leftSubformula, rightSubformula, lowerBounds, upperBounds, timeBoundReferences));
            } else {
                return std::shared_ptr<storm::logic::Formula const>(new storm::logic::UntilFormula(leftSubformula, rightSubformula));
            }
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createHOAPathFormula(std::string const& automatonFile) const {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::HOAPathFormula(automatonFile));
        }

        void FormulaParserGrammar::addHoaAPMapping(storm::logic::Formula const& hoaFormula, const std::string& ap, std::shared_ptr<storm::logic::Formula const>& expression) const {
            // taking a const Formula reference and doing static_ and const_cast from Formula to allow non-const access to
            // qi::_val of the hoaPathFormula rule
            storm::logic::HOAPathFormula& hoaFormula_ = static_cast<storm::logic::HOAPathFormula&>(const_cast<storm::logic::Formula&>(hoaFormula));
            hoaFormula_.addAPMapping(ap, expression);
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createConditionalFormula(std::shared_ptr<storm::logic::Formula const> const& leftSubformula, boost::optional<std::shared_ptr<storm::logic::Formula const>> const& rightSubformula, storm::logic::FormulaContext context) const {
            if (rightSubformula) {
                return std::shared_ptr<storm::logic::Formula const>(new storm::logic::ConditionalFormula(leftSubformula, rightSubformula.get(), context));
            } else {
                // If there is no rhs, just return the lhs
                return leftSubformula;
            }
        }

        storm::logic::OperatorInformation FormulaParserGrammar::createOperatorInformation(boost::optional<storm::OptimizationDirection> const& optimizationDirection, boost::optional<storm::logic::ComparisonType> const& comparisonType, boost::optional<storm::expressions::Expression> const& threshold) const {
            if (comparisonType && threshold) {
                storm::expressions::ExpressionEvaluator<storm::RationalNumber> evaluator(*constManager);
                return storm::logic::OperatorInformation(optimizationDirection, storm::logic::Bound(comparisonType.get(), threshold.get()));
            } else {
                return storm::logic::OperatorInformation(optimizationDirection, boost::none);
            }
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createOperatorFormula(storm::logic::FormulaContext const& context, boost::optional<storm::logic::RewardMeasureType> const& rewardMeasureType, boost::optional<std::string> const& rewardModelName, storm::logic::OperatorInformation const& operatorInformation, std::shared_ptr<storm::logic::Formula const> const& subformula) {
            switch(context) {
                case storm::logic::FormulaContext::Probability:
                    STORM_LOG_ASSERT(!rewardMeasureType && !rewardModelName, "Probability operator with reward information parsed");
                    return createProbabilityOperatorFormula(operatorInformation, subformula);
                case storm::logic::FormulaContext::Reward:
                    return createRewardOperatorFormula(rewardMeasureType, rewardModelName, operatorInformation, subformula);
                case storm::logic::FormulaContext::LongRunAverage:
                    STORM_LOG_ASSERT(!rewardMeasureType && !rewardModelName, "LRA operator with reward information parsed");
                    return createLongRunAverageOperatorFormula(operatorInformation, subformula);
                case storm::logic::FormulaContext::Time:
                    STORM_LOG_ASSERT(!rewardModelName, "Time operator with reward model name parsed");
                    return createTimeOperatorFormula(rewardMeasureType, operatorInformation, subformula);
                default:
                    STORM_LOG_THROW(false, storm::exceptions::WrongFormatException, "Unexpected formula context.");
            }
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createLongRunAverageOperatorFormula(storm::logic::OperatorInformation const& operatorInformation, std::shared_ptr<storm::logic::Formula const> const& subformula) const {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::LongRunAverageOperatorFormula(subformula, operatorInformation));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createRewardOperatorFormula(boost::optional<storm::logic::RewardMeasureType> const& rewardMeasureType, boost::optional<std::string> const& rewardModelName, storm::logic::OperatorInformation const& operatorInformation, std::shared_ptr<storm::logic::Formula const> const& subformula) const {
            storm::logic::RewardMeasureType measureType = storm::logic::RewardMeasureType::Expectation;
            if (rewardMeasureType) {
                measureType = rewardMeasureType.get();
            }
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::RewardOperatorFormula(subformula, rewardModelName, operatorInformation, measureType));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createTimeOperatorFormula(boost::optional<storm::logic::RewardMeasureType> const& rewardMeasureType, storm::logic::OperatorInformation const& operatorInformation, std::shared_ptr<storm::logic::Formula const> const& subformula) const {
            storm::logic::RewardMeasureType measureType = storm::logic::RewardMeasureType::Expectation;
            if (rewardMeasureType) {
                measureType = rewardMeasureType.get();
            }
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::TimeOperatorFormula(subformula, operatorInformation, measureType));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createProbabilityOperatorFormula(storm::logic::OperatorInformation const& operatorInformation, std::shared_ptr<storm::logic::Formula const> const& subformula) {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::ProbabilityOperatorFormula(subformula, operatorInformation));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createBinaryBooleanStateFormula(std::shared_ptr<storm::logic::Formula const> const& leftSubformula, std::shared_ptr<storm::logic::Formula const> const& rightSubformula, storm::logic::BinaryBooleanStateFormula::OperatorType operatorType) {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::BinaryBooleanStateFormula(operatorType, leftSubformula, rightSubformula));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createUnaryBooleanStateFormula(std::shared_ptr<storm::logic::Formula const> const& subformula, boost::optional<storm::logic::UnaryBooleanStateFormula::OperatorType> const& operatorType) {
            if (operatorType) {
                return std::shared_ptr<storm::logic::Formula const>(new storm::logic::UnaryBooleanStateFormula(operatorType.get(), subformula));
            } else {
                return subformula;
            }
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createBinaryBooleanPathFormula(std::shared_ptr<storm::logic::Formula const> const& leftSubformula, std::shared_ptr<storm::logic::Formula const> const& rightSubformula, storm::logic::BinaryBooleanPathFormula::OperatorType operatorType) {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::BinaryBooleanPathFormula(operatorType, leftSubformula, rightSubformula));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createUnaryBooleanPathFormula(std::shared_ptr<storm::logic::Formula const> const& subformula, boost::optional<storm::logic::UnaryBooleanPathFormula::OperatorType> const& operatorType) {
            if (operatorType) {
                return std::shared_ptr<storm::logic::Formula const>(new storm::logic::UnaryBooleanPathFormula(operatorType.get(), subformula));
            } else {
                return subformula;
            }
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createBinaryBooleanStateOrPathFormula(std::shared_ptr<storm::logic::Formula const> const& leftSubformula, std::shared_ptr<storm::logic::Formula const> const& rightSubformula, storm::logic::BinaryBooleanOperatorType operatorType) {
            if (leftSubformula->isStateFormula() && rightSubformula->isStateFormula()) {
                return createBinaryBooleanStateFormula(leftSubformula, rightSubformula, operatorType);
            } else if (leftSubformula->isPathFormula() || rightSubformula->isPathFormula()) {
                return createBinaryBooleanPathFormula(leftSubformula, rightSubformula, operatorType);
            }
            STORM_LOG_THROW(false, storm::exceptions::WrongFormatException, "Subformulas have unexpected type.");
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createUnaryBooleanStateOrPathFormula(std::shared_ptr<storm::logic::Formula const> const& subformula, boost::optional<storm::logic::UnaryBooleanOperatorType> const& operatorType) {
            if (subformula->isStateFormula()) {
                return createUnaryBooleanStateFormula(subformula, operatorType);
            } else if (subformula->isPathFormula()) {
                return createUnaryBooleanPathFormula(subformula, operatorType);
            }
            STORM_LOG_THROW(false, storm::exceptions::WrongFormatException, "Subformulas have unexpected type.");
        }

        bool FormulaParserGrammar::isValidMultiBoundedPathFormulaOperand(std::shared_ptr<storm::logic::Formula const> const& operand) {
            if (operand->isBoundedUntilFormula()) {
                if (!operand->asBoundedUntilFormula().isMultiDimensional()) {
                    return true;
                }
                STORM_LOG_ERROR("Composition of multidimensional bounded until formula must consist of single dimension subformulas. Got '" << *operand << "' instead.");
            }
            return false;
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createMultiBoundedPathFormula(std::vector<std::shared_ptr<storm::logic::Formula const>> const& subformulas) {
            std::vector<std::shared_ptr<storm::logic::Formula const>> leftSubformulas, rightSubformulas;
            std::vector<boost::optional<storm::logic::TimeBound>> lowerBounds, upperBounds;
            std::vector<storm::logic::TimeBoundReference> timeBoundReferences;
            for (auto const& subformula : subformulas) {
                STORM_LOG_THROW(subformula->isBoundedUntilFormula(), storm::exceptions::WrongFormatException, "multi-path formulas require bounded until (or eventually) subformulae. Got '" << *subformula << "' instead.");
                auto const& f = subformula->asBoundedUntilFormula();
                STORM_LOG_THROW(!f.isMultiDimensional(), storm::exceptions::WrongFormatException, "Composition of multidimensional bounded until formula must consist of single dimension subformulas. Got '" << f << "' instead.");
                leftSubformulas.push_back(f.getLeftSubformula().asSharedPointer());
                rightSubformulas.push_back(f.getRightSubformula().asSharedPointer());
                if (f.hasLowerBound()) {
                    lowerBounds.emplace_back(storm::logic::TimeBound(f.isLowerBoundStrict(), f.getLowerBound()));
                } else {
                    lowerBounds.emplace_back();
                }
                 if (f.hasUpperBound()) {
                    upperBounds.emplace_back(storm::logic::TimeBound(f.isUpperBoundStrict(), f.getUpperBound()));
                } else {
                    upperBounds.emplace_back();
                }
                timeBoundReferences.push_back(f.getTimeBoundReference());
            }
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::BoundedUntilFormula(leftSubformulas, rightSubformulas, lowerBounds, upperBounds, timeBoundReferences));
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createMultiOperatorFormula(std::vector<std::shared_ptr<storm::logic::Formula const>> const& subformulas) {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::MultiObjectiveFormula(subformulas));
        }

        storm::expressions::Variable FormulaParserGrammar::createQuantileBoundVariables(boost::optional<storm::solver::OptimizationDirection> const& dir, std::string const& variableName) {
            STORM_LOG_ASSERT(manager, "Mutable expression manager required to define quantile bound variable.");
            storm::expressions::Variable var;
            if (manager->hasVariable(variableName)) {
                var = manager->getVariable(variableName);
                STORM_LOG_THROW(quantileFormulaVariables.count(var) > 0, storm::exceptions::WrongFormatException, "Invalid quantile variable name '" << variableName << "' in quantile formula: variable already exists.");
            } else {
                var = manager->declareRationalVariable(variableName);
                quantileFormulaVariables.insert(var);
            }
            STORM_LOG_WARN_COND(!dir.is_initialized(), "Optimization direction '" << dir.get() << "' for quantile variable " << variableName << " is ignored. This information will be derived from the subformula of the quantile.");
            addIdentifierExpression(variableName, var);
            return var;
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createQuantileFormula(std::vector<storm::expressions::Variable> const& boundVariables, std::shared_ptr<storm::logic::Formula const> const& subformula) {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::QuantileFormula(boundVariables, subformula));
        }

        std::set<storm::expressions::Variable> FormulaParserGrammar::getUndefinedConstants(std::shared_ptr<storm::logic::Formula const> const& formula) const {
            std::set<storm::expressions::Variable> result;
            std::set<storm::expressions::Variable> usedVariables = formula->getUsedVariables();
            std::set_intersection(usedVariables.begin(), usedVariables.end(), undefinedConstants.begin(), undefinedConstants.end(), std::inserter(result, result.begin()));
            return result;
        }

        storm::jani::Property FormulaParserGrammar::createProperty(boost::optional<std::string> const& propertyName, storm::modelchecker::FilterType const& filterType, std::shared_ptr<storm::logic::Formula const> const& formula, std::shared_ptr<storm::logic::Formula const> const& states) {
            storm::jani::FilterExpression filterExpression(formula, filterType, states);

            ++propertyCount;
            if (propertyName) {
                return storm::jani::Property(propertyName.get(), filterExpression, this->getUndefinedConstants(formula));
            } else {
                return storm::jani::Property(std::to_string(propertyCount - 1), filterExpression, this->getUndefinedConstants(formula));
            }
        }

        storm::jani::Property FormulaParserGrammar::createPropertyWithDefaultFilterTypeAndStates(boost::optional<std::string> const& propertyName, std::shared_ptr<storm::logic::Formula const> const& formula) {
            ++propertyCount;
            if (propertyName) {
                return storm::jani::Property(propertyName.get(), formula, this->getUndefinedConstants(formula));
            } else {
                return storm::jani::Property(std::to_string(propertyCount), formula, this->getUndefinedConstants(formula));
            }
        }

        std::pair<storm::logic::ShieldComparison, double> FormulaParserGrammar::createShieldComparisonStruct(storm::logic::ShieldComparison comparisonType, double value) {
            return std::make_pair(comparisonType, value);
        }

        std::shared_ptr<storm::logic::ShieldExpression const> FormulaParserGrammar::createShieldExpression(storm::logic::ShieldingType type, std::string name, boost::optional<std::pair<storm::logic::ShieldComparison, double>> comparisonStruct) {
            if(comparisonStruct.is_initialized()) {
                STORM_LOG_WARN_COND(type != storm::logic::ShieldingType::Optimal , "Comparison for optimal shield will be ignored.");
                return std::shared_ptr<storm::logic::ShieldExpression>(new storm::logic::ShieldExpression(type, name, comparisonStruct.get().first, comparisonStruct.get().second));
            } else {
                STORM_LOG_THROW(type == storm::logic::ShieldingType::Optimal , storm::exceptions::WrongFormatException, "Construction of safety shield needs a comparison parameter (lambda or gamma)");
                return std::shared_ptr<storm::logic::ShieldExpression>(new storm::logic::ShieldExpression(type, name));
            }
        }

        storm::jani::Property FormulaParserGrammar::createShieldingProperty(boost::optional<std::string> const& propertyName, std::shared_ptr<storm::logic::Formula const> const& formula, std::shared_ptr<storm::logic::ShieldExpression const> const& shieldExpression) {
            ++propertyCount;
            if (propertyName) {
                return storm::jani::Property(propertyName.get(), formula, this->getUndefinedConstants(formula), shieldExpression);
            } else {
                return storm::jani::Property(std::to_string(propertyCount), formula, this->getUndefinedConstants(formula), shieldExpression);
            }
        }

        storm::logic::PlayerCoalition FormulaParserGrammar::createPlayerCoalition(std::vector<boost::variant<std::string, storm::storage::PlayerIndex>> const& playerIds) const {
            return storm::logic::PlayerCoalition(playerIds);
        }

        std::shared_ptr<storm::logic::Formula const> FormulaParserGrammar::createGameFormula(storm::logic::PlayerCoalition const& coalition, std::shared_ptr<storm::logic::Formula const> const& subformula) const {
            return std::shared_ptr<storm::logic::Formula const>(new storm::logic::GameFormula(coalition, subformula));
        }

        bool FormulaParserGrammar::isBooleanReturnType(std::shared_ptr<storm::logic::Formula const> const& formula, bool raiseErrorMessage) {
            if (formula->hasQualitativeResult()) {
                return true;
            }
            STORM_LOG_ERROR_COND(!raiseErrorMessage, "Formula " << *formula << " does not have a Boolean return type.");
            return false;
        }

        bool FormulaParserGrammar::raiseAmbiguousNonAssociativeOperatorError(std::shared_ptr<storm::logic::Formula const> const& formula, std::string const& op) {
            STORM_LOG_ERROR( "Ambiguous use of non-associative operator '" << op << "' in formula '" << *formula << " U ... '");
            return true;
        }

    }
}