547 lines
18 KiB
C++
547 lines
18 KiB
C++
#include <anthem/IntegerVariableDetection.h>
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#include <anthem/Arithmetics.h>
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#include <anthem/ASTCopy.h>
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#include <anthem/ASTUtils.h>
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#include <anthem/ASTVisitors.h>
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#include <anthem/Exception.h>
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#include <anthem/Simplification.h>
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#include <anthem/Utils.h>
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#include <anthem/output/AST.h>
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namespace anthem
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{
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////////////////////////////////////////////////////////////////////////////////////////////////////
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//
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// IntegerVariableDetection
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//
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////////////////////////////////////////////////////////////////////////////////////////////////////
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using VariableDomainMap = std::map<const ast::VariableDeclaration *, ast::Domain>;
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////////////////////////////////////////////////////////////////////////////////////////////////////
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ast::Domain domain(const ast::Variable &variable, VariableDomainMap &variableDomainMap)
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{
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if (variable.declaration->domain != ast::Domain::Unknown)
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return variable.declaration->domain;
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const auto match = variableDomainMap.find(variable.declaration);
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if (match == variableDomainMap.end())
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return ast::Domain::Unknown;
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return match->second;
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}
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////////////////////////////////////////////////////////////////////////////////////////////////////
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void clearVariableDomainMap(VariableDomainMap &variableDomainMap)
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{
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for (auto &variableDeclaration : variableDomainMap)
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variableDeclaration.second = ast::Domain::Unknown;
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}
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////////////////////////////////////////////////////////////////////////////////////////////////////
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struct VariableDomainMapAccessor
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{
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ast::Domain operator()(const ast::Variable &variable, VariableDomainMap &variableDomainMap)
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{
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return domain(variable, variableDomainMap);
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}
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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EvaluationResult isArithmetic(const ast::Term &term, VariableDomainMap &variableDomainMap)
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{
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return isArithmetic<VariableDomainMapAccessor>(term, variableDomainMap);
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}
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////////////////////////////////////////////////////////////////////////////////////////////////////
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EvaluationResult evaluate(const ast::Formula &formula, VariableDomainMap &variableDomainMap);
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////////////////////////////////////////////////////////////////////////////////////////////////////
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struct EvaluateFormulaVisitor
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{
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static EvaluationResult visit(const ast::And &and_, VariableDomainMap &variableDomainMap)
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{
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bool someFalse = false;
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bool someUnknown = false;
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for (const auto &argument : and_.arguments)
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{
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const auto result = evaluate(argument, variableDomainMap);
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switch (result)
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{
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case EvaluationResult::Error:
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return EvaluationResult::Error;
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case EvaluationResult::True:
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break;
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case EvaluationResult::False:
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someFalse = true;
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break;
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case EvaluationResult::Unknown:
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someUnknown = true;
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break;
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}
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}
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if (someFalse)
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return EvaluationResult::False;
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if (someUnknown)
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return EvaluationResult::Unknown;
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return EvaluationResult::True;
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}
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static EvaluationResult visit(const ast::Biconditional &biconditional, VariableDomainMap &variableDomainMap)
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{
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const auto leftResult = evaluate(biconditional.left, variableDomainMap);
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const auto rightResult = evaluate(biconditional.right, variableDomainMap);
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if (leftResult == EvaluationResult::Error || rightResult == EvaluationResult::Error)
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return EvaluationResult::Error;
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if (leftResult == EvaluationResult::Unknown || rightResult == EvaluationResult::Unknown)
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return EvaluationResult::Unknown;
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return (leftResult == rightResult ? EvaluationResult::True : EvaluationResult::False);
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}
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static EvaluationResult visit(const ast::Boolean &boolean, VariableDomainMap &)
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{
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return (boolean.value == true ? EvaluationResult::True : EvaluationResult::False);
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}
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static EvaluationResult visit(const ast::Comparison &comparison, VariableDomainMap &variableDomainMap)
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{
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const auto isLeftArithmetic = isArithmetic(comparison.left, variableDomainMap);
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const auto isRightArithmetic = isArithmetic(comparison.right, variableDomainMap);
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if (isLeftArithmetic == EvaluationResult::Error || isRightArithmetic == EvaluationResult::Error)
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return EvaluationResult::Error;
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if (isLeftArithmetic == EvaluationResult::Unknown || isRightArithmetic == EvaluationResult::Unknown)
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return EvaluationResult::Unknown;
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if (isLeftArithmetic == isRightArithmetic)
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return EvaluationResult::Unknown;
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// Handle the case where one side is arithmetic but the other one isn’t
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switch (comparison.operator_)
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{
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case ast::Comparison::Operator::Equal:
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return EvaluationResult::False;
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case ast::Comparison::Operator::NotEqual:
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return EvaluationResult::True;
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default:
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// TODO: implement more cases
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return EvaluationResult::Unknown;
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}
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}
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static EvaluationResult visit(const ast::Exists &exists, VariableDomainMap &variableDomainMap)
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{
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return evaluate(exists.argument, variableDomainMap);
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}
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static EvaluationResult visit(const ast::ForAll &forAll, VariableDomainMap &variableDomainMap)
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{
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return evaluate(forAll.argument, variableDomainMap);
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}
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static EvaluationResult visit(const ast::Implies &implies, VariableDomainMap &variableDomainMap)
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{
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const auto antecedentResult = evaluate(implies.antecedent, variableDomainMap);
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const auto consequentResult = evaluate(implies.consequent, variableDomainMap);
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if (antecedentResult == EvaluationResult::Error || consequentResult == EvaluationResult::Error)
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return EvaluationResult::Error;
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if (antecedentResult == EvaluationResult::False)
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return EvaluationResult::True;
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if (consequentResult == EvaluationResult::True)
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return EvaluationResult::True;
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if (antecedentResult == EvaluationResult::True && consequentResult == EvaluationResult::False)
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return EvaluationResult::False;
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return EvaluationResult::Unknown;
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}
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static EvaluationResult visit(const ast::In &in, VariableDomainMap &variableDomainMap)
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{
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const auto isElementArithmetic = isArithmetic(in.element, variableDomainMap);
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const auto isSetArithmetic = isArithmetic(in.set, variableDomainMap);
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if (isElementArithmetic == EvaluationResult::Error || isSetArithmetic == EvaluationResult::Error)
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return EvaluationResult::Error;
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if (isElementArithmetic == EvaluationResult::Unknown || isSetArithmetic == EvaluationResult::Unknown)
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return EvaluationResult::Unknown;
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if (isElementArithmetic == isSetArithmetic)
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return EvaluationResult::Unknown;
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// If one side is arithmetic, but the other one isn’t, set inclusion is never satisfied
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return EvaluationResult::False;
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}
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static EvaluationResult visit(const ast::Not ¬_, VariableDomainMap &variableDomainMap)
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{
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const auto result = evaluate(not_.argument, variableDomainMap);
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if (result == EvaluationResult::Error || result == EvaluationResult::Unknown)
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return result;
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return (result == EvaluationResult::True ? EvaluationResult::False : EvaluationResult::True);
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}
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static EvaluationResult visit(const ast::Or &or_, VariableDomainMap &variableDomainMap)
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{
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bool someTrue = false;
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bool someUnknown = false;
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for (const auto &argument : or_.arguments)
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{
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const auto result = evaluate(argument, variableDomainMap);
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switch (result)
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{
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case EvaluationResult::Error:
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return EvaluationResult::Error;
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case EvaluationResult::True:
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someTrue = true;
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break;
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case EvaluationResult::False:
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break;
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case EvaluationResult::Unknown:
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someUnknown = true;
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break;
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}
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}
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if (someTrue)
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return EvaluationResult::True;
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if (someUnknown)
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return EvaluationResult::Unknown;
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return EvaluationResult::False;
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}
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static EvaluationResult visit(const ast::Predicate &predicate, VariableDomainMap &variableDomainMap)
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{
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assert(predicate.arguments.size() == predicate.declaration->arity());
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for (size_t i = 0; i < predicate.arguments.size(); i++)
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{
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const auto &argument = predicate.arguments[i];
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const auto ¶meter = predicate.declaration->parameters[i];
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if (parameter.domain != ast::Domain::Integer)
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continue;
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const auto isArgumentArithmetic = isArithmetic(argument, variableDomainMap);
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if (isArgumentArithmetic == EvaluationResult::Error || isArgumentArithmetic == EvaluationResult::False)
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return isArgumentArithmetic;
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}
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return EvaluationResult::Unknown;
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}
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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EvaluationResult evaluate(const ast::Formula &formula, VariableDomainMap &variableDomainMap)
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{
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return formula.accept(EvaluateFormulaVisitor(), variableDomainMap);
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}
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////////////////////////////////////////////////////////////////////////////////////////////////////
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template <class Functor>
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struct ForEachVariableDeclarationVisitor
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{
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template <class... Arguments>
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static OperationResult visit(ast::And &and_, Arguments &&... arguments)
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{
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auto operationResult = OperationResult::Unchanged;
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for (auto &argument : and_.arguments)
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if (argument.accept(ForEachVariableDeclarationVisitor(), std::forward<Arguments>(arguments)...) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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return operationResult;
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}
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template <class... Arguments>
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static OperationResult visit(ast::Biconditional &biconditional, Arguments &&... arguments)
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{
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auto operationResult = OperationResult::Unchanged;
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if (biconditional.left.accept(ForEachVariableDeclarationVisitor(), std::forward<Arguments>(arguments)...) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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if (biconditional.right.accept(ForEachVariableDeclarationVisitor(), std::forward<Arguments>(arguments)...) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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return operationResult;
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}
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template <class... Arguments>
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static OperationResult visit(ast::Boolean &, Arguments &&...)
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{
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return OperationResult::Unchanged;
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}
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template <class... Arguments>
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static OperationResult visit(ast::Comparison &, Arguments &&...)
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{
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return OperationResult::Unchanged;
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}
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template <class... Arguments>
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static OperationResult visit(ast::Exists &exists, Arguments &&... arguments)
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{
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auto operationResult = OperationResult::Unchanged;
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if (exists.argument.accept(ForEachVariableDeclarationVisitor(), std::forward<Arguments>(arguments)...) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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for (auto &variableDeclaration : exists.variables)
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if (Functor()(*variableDeclaration, exists.argument, std::forward<Arguments>(arguments)...) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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return operationResult;
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}
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template <class... Arguments>
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static OperationResult visit(ast::ForAll &forAll, Arguments &&... arguments)
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{
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auto operationResult = OperationResult::Unchanged;
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if (forAll.argument.accept(ForEachVariableDeclarationVisitor(), std::forward<Arguments>(arguments)...) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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for (auto &variableDeclaration : forAll.variables)
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if (Functor()(*variableDeclaration, forAll.argument, std::forward<Arguments>(arguments)...) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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return operationResult;
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}
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template <class... Arguments>
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static OperationResult visit(ast::Implies &implies, Arguments &&... arguments)
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{
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auto operationResult = OperationResult::Unchanged;
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if (implies.antecedent.accept(ForEachVariableDeclarationVisitor(), std::forward<Arguments>(arguments)...) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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if (implies.consequent.accept(ForEachVariableDeclarationVisitor(), std::forward<Arguments>(arguments)...) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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return operationResult;
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}
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template <class... Arguments>
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static OperationResult visit(ast::In &, Arguments &&...)
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{
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return OperationResult::Unchanged;
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}
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template <class... Arguments>
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static OperationResult visit(ast::Not ¬_, Arguments &&... arguments)
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{
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return not_.argument.accept(ForEachVariableDeclarationVisitor(), std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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static OperationResult visit(ast::Or &or_, Arguments &&... arguments)
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{
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auto operationResult = OperationResult::Unchanged;
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for (auto &argument : or_.arguments)
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if (argument.accept(ForEachVariableDeclarationVisitor(), std::forward<Arguments>(arguments)...) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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return operationResult;
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}
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template <class... Arguments>
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static OperationResult visit(ast::Predicate &, Arguments &&...)
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{
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return OperationResult::Unchanged;
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}
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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struct CheckIfDefinitionFalseFunctor
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{
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OperationResult operator()(ast::VariableDeclaration &variableDeclaration,
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ast::Formula &, ast::Formula &definition, VariableDomainMap &variableDomainMap)
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{
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if (variableDeclaration.domain != ast::Domain::Unknown)
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return OperationResult::Unchanged;
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clearVariableDomainMap(variableDomainMap);
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auto result = evaluate(definition, variableDomainMap);
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if (result == EvaluationResult::Error || result == EvaluationResult::False)
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return OperationResult::Unchanged;
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// As a hypothesis, make the parameter’s domain noninteger
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variableDomainMap[&variableDeclaration] = ast::Domain::General;
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result = evaluate(definition, variableDomainMap);
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if (result == EvaluationResult::Error || result == EvaluationResult::False)
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{
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// If making the variable noninteger leads to a false or erroneous result, it’s proven to be integer
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variableDeclaration.domain = ast::Domain::Integer;
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return OperationResult::Changed;
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}
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return OperationResult::Unchanged;
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}
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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struct CheckIfQuantifiedFormulaFalseFunctor
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{
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OperationResult operator()(ast::VariableDeclaration &variableDeclaration,
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ast::Formula &quantifiedFormula, VariableDomainMap &variableDomainMap)
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{
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if (variableDeclaration.domain != ast::Domain::Unknown)
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return OperationResult::Unchanged;
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clearVariableDomainMap(variableDomainMap);
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auto result = evaluate(quantifiedFormula, variableDomainMap);
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if (result == EvaluationResult::Error || result == EvaluationResult::False)
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return OperationResult::Unchanged;
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// As a hypothesis, make the parameter’s domain noninteger
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variableDomainMap[&variableDeclaration] = ast::Domain::General;
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result = evaluate(quantifiedFormula, variableDomainMap);
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if (result == EvaluationResult::Error || result == EvaluationResult::False)
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{
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// If making the variable noninteger leads to a false or erroneous result, it’s proven to be integer
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variableDeclaration.domain = ast::Domain::Integer;
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return OperationResult::Changed;
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}
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return OperationResult::Unchanged;
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}
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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struct CheckIfCompletedFormulaTrueFunctor
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{
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OperationResult operator()(ast::VariableDeclaration &variableDeclaration,
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ast::Formula &, ast::Formula &completedFormula, VariableDomainMap &variableDomainMap)
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{
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if (variableDeclaration.domain != ast::Domain::Unknown)
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return OperationResult::Unchanged;
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clearVariableDomainMap(variableDomainMap);
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auto result = evaluate(completedFormula, variableDomainMap);
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if (result == EvaluationResult::Error || result == EvaluationResult::True)
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return OperationResult::Unchanged;
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// As a hypothesis, make the parameter’s domain noninteger
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variableDomainMap[&variableDeclaration] = ast::Domain::General;
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result = evaluate(completedFormula, variableDomainMap);
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if (result == EvaluationResult::Error || result == EvaluationResult::True)
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{
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// If making the variable noninteger leads to a false or erroneous result, it’s proven to be integer
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variableDeclaration.domain = ast::Domain::Integer;
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return OperationResult::Changed;
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}
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return OperationResult::Unchanged;
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}
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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// Assumes the completed formulas to be in translated but not simplified form.
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// That is, completed formulas are either variable-free or universally quantified
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void detectIntegerVariables(std::vector<ast::Formula> &completedFormulas)
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{
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VariableDomainMap variableDomainMap;
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auto operationResult = OperationResult::Changed;
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while (operationResult == OperationResult::Changed)
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{
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operationResult = OperationResult::Unchanged;
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for (auto &completedFormula : completedFormulas)
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{
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if (completedFormula.accept(ForEachVariableDeclarationVisitor<CheckIfQuantifiedFormulaFalseFunctor>(), variableDomainMap) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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if (completedFormula.accept(ForEachVariableDeclarationVisitor<CheckIfCompletedFormulaTrueFunctor>(), completedFormula, variableDomainMap) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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if (!completedFormula.is<ast::ForAll>())
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continue;
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auto &forAll = completedFormula.get<ast::ForAll>();
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if (!forAll.argument.is<ast::Biconditional>())
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continue;
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auto &biconditional = forAll.argument.get<ast::Biconditional>();
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if (!biconditional.left.is<ast::Predicate>())
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continue;
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auto &predicate = biconditional.left.get<ast::Predicate>();
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auto &definition = biconditional.right;
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if (completedFormula.accept(ForEachVariableDeclarationVisitor<CheckIfDefinitionFalseFunctor>(), definition, variableDomainMap) == OperationResult::Changed)
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operationResult = OperationResult::Changed;
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assert(predicate.arguments.size() == predicate.declaration->arity());
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for (size_t i = 0; i < predicate.arguments.size(); i++)
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{
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auto &variableArgument = predicate.arguments[i];
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auto ¶meter = predicate.declaration->parameters[i];
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assert(variableArgument.is<ast::Variable>());
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auto &variable = variableArgument.get<ast::Variable>();
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parameter.domain = variable.declaration->domain;
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}
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}
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}
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}
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////////////////////////////////////////////////////////////////////////////////////////////////////
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}
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