Reimplement integer variable detection
This is a reimplementation of the integer variable detection procedure. The idea is to iteratively assume variables to be noninteger, and to prove that this would lead to a false or erroneous result. If the proof is successful, the variable is integer as a consequence.
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05F3611E97A70ABF
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@ -1,3 +1,6 @@
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#show p/2.
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#external integer(n(0)).
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{p(1..n, 1..n)}.
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:- p(X, Y1), p(X, Y2), Y1 != Y2.
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@ -8,5 +11,3 @@ q2(Y) :- p(_, Y).
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:- not q1(X), X = 1..n.
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:- not q2(Y), Y = 1..n.
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#show p/2.
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@ -1,4 +1,5 @@
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#show prime/1.
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#external integer(n(0)).
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composite(I * J) :- I = 2..n, J = 2..n.
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prime(N) :- N = 2..n, not composite(N).
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@ -1,7 +1,9 @@
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#show in/2.
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#external integer(n(0)).
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#external integer(r(0)).
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{in(1..n, 1..r)}.
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covered(I) :- in(I, S).
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:- I = 1..n, not covered(I).
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:- in(I, S), in(J, S), in(I + J, S).
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#show in/2.
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@ -16,7 +16,30 @@ namespace anthem
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//
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////////////////////////////////////////////////////////////////////////////////////////////////////
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ast::Domain domain(ast::Term &term);
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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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@ -28,371 +51,538 @@ enum class OperationResult
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////////////////////////////////////////////////////////////////////////////////////////////////////
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struct TermDomainVisitor
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enum class EvaluationResult
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{
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static ast::Domain visit(ast::BinaryOperation &binaryOperation)
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True,
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False,
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Unknown,
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Error,
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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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struct IsTermArithmeticVisitor
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{
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static EvaluationResult visit(const ast::BinaryOperation &binaryOperation, VariableDomainMap &variableDomainMap)
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{
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const auto leftDomain = domain(binaryOperation.left);
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const auto rightDomain = domain(binaryOperation.right);
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const auto isLeftArithemtic = isArithmetic(binaryOperation.left, variableDomainMap);
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const auto isRightArithmetic = isArithmetic(binaryOperation.right, variableDomainMap);
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if (leftDomain == ast::Domain::General || rightDomain == ast::Domain::General)
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return ast::Domain::General;
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if (isLeftArithemtic == EvaluationResult::Error || isRightArithmetic == EvaluationResult::Error)
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return EvaluationResult::Error;
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if (leftDomain == ast::Domain::Integer || rightDomain == ast::Domain::Integer)
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return ast::Domain::Integer;
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if (isLeftArithemtic == EvaluationResult::False || isRightArithmetic == EvaluationResult::False)
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return EvaluationResult::Error;
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return ast::Domain::Unknown;
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if (isLeftArithemtic == EvaluationResult::Unknown || isRightArithmetic == EvaluationResult::Unknown)
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return EvaluationResult::Unknown;
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return EvaluationResult::True;
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}
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static ast::Domain visit(ast::Boolean &)
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static EvaluationResult visit(const ast::Boolean &, VariableDomainMap &)
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{
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return ast::Domain::General;
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return EvaluationResult::False;
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}
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static ast::Domain visit(ast::Function &function)
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static EvaluationResult visit(const ast::Function &function, VariableDomainMap &)
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{
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return function.declaration->domain;
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switch (function.declaration->domain)
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{
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case ast::Domain::General:
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return EvaluationResult::False;
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case ast::Domain::Integer:
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return EvaluationResult::True;
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case ast::Domain::Unknown:
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return EvaluationResult::Unknown;
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}
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return EvaluationResult::Unknown;
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}
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static ast::Domain visit(ast::Integer &)
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static EvaluationResult visit(const ast::Integer &, VariableDomainMap &)
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{
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return ast::Domain::Integer;
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return EvaluationResult::True;
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}
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static ast::Domain visit(ast::Interval &interval)
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static EvaluationResult visit(const ast::Interval &interval, VariableDomainMap &variableDomainMap)
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{
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const auto fromDomain = domain(interval.from);
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const auto toDomain = domain(interval.to);
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const auto isFromArithmetic = isArithmetic(interval.from, variableDomainMap);
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const auto isToArithmetic = isArithmetic(interval.to, variableDomainMap);
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if (fromDomain == ast::Domain::General || toDomain == ast::Domain::General)
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return ast::Domain::General;
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if (isFromArithmetic == EvaluationResult::Error || isToArithmetic == EvaluationResult::Error)
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return EvaluationResult::Error;
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if (fromDomain == ast::Domain::Integer || toDomain == ast::Domain::Integer)
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return ast::Domain::Integer;
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if (isFromArithmetic == EvaluationResult::False || isToArithmetic == EvaluationResult::False)
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return EvaluationResult::Error;
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return ast::Domain::Unknown;
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if (isFromArithmetic == EvaluationResult::Unknown || isToArithmetic == EvaluationResult::Unknown)
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return EvaluationResult::Unknown;
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return EvaluationResult::True;
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}
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static ast::Domain visit(ast::SpecialInteger &)
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static EvaluationResult visit(const ast::SpecialInteger &, VariableDomainMap &)
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{
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// TODO: check correctness
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return ast::Domain::Integer;
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return EvaluationResult::False;
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}
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static ast::Domain visit(ast::String &)
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static EvaluationResult visit(const ast::String &, VariableDomainMap &)
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{
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return ast::Domain::General;
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return EvaluationResult::False;
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}
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static ast::Domain visit(ast::UnaryOperation &unaryOperation)
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static EvaluationResult visit(const ast::UnaryOperation &unaryOperation, VariableDomainMap &variableDomainMap)
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{
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return domain(unaryOperation.argument);
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const auto isArgumentArithmetic = isArithmetic(unaryOperation.argument, variableDomainMap);
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switch (unaryOperation.operator_)
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{
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case ast::UnaryOperation::Operator::Absolute:
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return (isArgumentArithmetic == EvaluationResult::False ? EvaluationResult::Error : isArgumentArithmetic);
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}
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return EvaluationResult::Unknown;
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}
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static ast::Domain visit(ast::Variable &variable)
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static EvaluationResult visit(const ast::Variable &variable, VariableDomainMap &variableDomainMap)
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{
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return variable.declaration->domain;
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switch (domain(variable, variableDomainMap))
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{
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case ast::Domain::General:
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return EvaluationResult::False;
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case ast::Domain::Integer:
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return EvaluationResult::True;
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case ast::Domain::Unknown:
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return EvaluationResult::Unknown;
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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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ast::Domain domain(ast::Term &term)
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EvaluationResult isArithmetic(const ast::Term &term, VariableDomainMap &variableDomainMap)
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{
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return term.accept(TermDomainVisitor());
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return term.accept(IsTermArithmeticVisitor(), variableDomainMap);
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}
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////////////////////////////////////////////////////////////////////////////////////////////////////
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bool isVariable(const ast::Term &term, const ast::VariableDeclaration &variableDeclaration)
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{
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if (!term.is<ast::Variable>())
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return false;
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auto &variable = term.get<ast::Variable>();
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return (variable.declaration == &variableDeclaration);
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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 VariableDomainInFormulaVisitor
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struct EvaluateFormulaVisitor
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{
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static ast::Domain visit(ast::And &and_, ast::VariableDeclaration &variableDeclaration)
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static EvaluationResult visit(const ast::And &and_, VariableDomainMap &variableDomainMap)
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{
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bool integer = false;
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bool someFalse = false;
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bool someUnknown = false;
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for (auto &argument : and_.arguments)
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for (const auto &argument : and_.arguments)
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{
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const auto domain = argument.accept(VariableDomainInFormulaVisitor(), variableDeclaration);
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const auto result = evaluate(argument, variableDomainMap);
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if (domain == ast::Domain::General)
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return ast::Domain::General;
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if (domain == ast::Domain::Integer)
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integer = true;
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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 (integer)
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return ast::Domain::Integer;
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if (someFalse)
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return EvaluationResult::False;
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return ast::Domain::Unknown;
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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 ast::Domain visit(ast::Biconditional &biconditional, ast::VariableDeclaration &variableDeclaration)
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static EvaluationResult visit(const ast::Biconditional &biconditional, VariableDomainMap &variableDomainMap)
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{
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const auto leftDomain = biconditional.left.accept(VariableDomainInFormulaVisitor(), variableDeclaration);
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const auto rightDomain = biconditional.right.accept(VariableDomainInFormulaVisitor(), variableDeclaration);
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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 (leftDomain == ast::Domain::General || rightDomain == ast::Domain::General)
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return ast::Domain::General;
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if (leftResult == EvaluationResult::Error || rightResult == EvaluationResult::Error)
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return EvaluationResult::Error;
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if (leftDomain == ast::Domain::Integer || rightDomain == ast::Domain::Integer)
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return ast::Domain::Integer;
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if (leftResult == EvaluationResult::Unknown || rightResult == EvaluationResult::Unknown)
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return EvaluationResult::Unknown;
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return ast::Domain::Unknown;
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return (leftResult == rightResult ? EvaluationResult::True : EvaluationResult::False);
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}
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static ast::Domain visit(ast::Boolean &, ast::VariableDeclaration &)
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static EvaluationResult visit(const ast::Boolean &boolean, VariableDomainMap &)
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{
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// Variable doesn’t occur in Booleans, hence it’s still considered integer until the contrary is found
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return ast::Domain::Unknown;
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return (boolean.value == true ? EvaluationResult::True : EvaluationResult::False);
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}
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static ast::Domain visit(ast::Comparison &comparison, ast::VariableDeclaration &variableDeclaration)
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static EvaluationResult visit(const ast::Comparison &comparison, VariableDomainMap &variableDomainMap)
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{
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const auto leftIsVariable = isVariable(comparison.left, variableDeclaration);
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const auto rightIsVariable = isVariable(comparison.right, variableDeclaration);
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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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// TODO: implement more cases
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if (!leftIsVariable && !rightIsVariable)
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return ast::Domain::Unknown;
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if (isLeftArithmetic == EvaluationResult::Error || isRightArithmetic == EvaluationResult::Error)
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return EvaluationResult::Error;
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auto &otherSide = (leftIsVariable ? comparison.right : comparison.left);
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if (isLeftArithmetic == EvaluationResult::Unknown || isRightArithmetic == EvaluationResult::Unknown)
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return EvaluationResult::Unknown;
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return domain(otherSide);
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}
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if (isLeftArithmetic == isRightArithmetic)
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return EvaluationResult::Unknown;
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static ast::Domain visit(ast::Exists &exists, ast::VariableDeclaration &variableDeclaration)
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{
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return exists.argument.accept(VariableDomainInFormulaVisitor(), variableDeclaration);
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}
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static ast::Domain visit(ast::ForAll &forAll, ast::VariableDeclaration &variableDeclaration)
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{
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return forAll.argument.accept(VariableDomainInFormulaVisitor(), variableDeclaration);
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}
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static ast::Domain visit(ast::Implies &implies, ast::VariableDeclaration &variableDeclaration)
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{
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const auto antecedentDomain = implies.antecedent.accept(VariableDomainInFormulaVisitor(), variableDeclaration);
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const auto consequentDomain = implies.antecedent.accept(VariableDomainInFormulaVisitor(), variableDeclaration);
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if (antecedentDomain == ast::Domain::General || consequentDomain == ast::Domain::General)
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return ast::Domain::General;
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if (antecedentDomain == ast::Domain::Integer || consequentDomain == ast::Domain::Integer)
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return ast::Domain::Integer;
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return ast::Domain::Unknown;
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}
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static ast::Domain visit(ast::In &in, ast::VariableDeclaration &variableDeclaration)
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{
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const auto elementIsVariable = isVariable(in.element, variableDeclaration);
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const auto setIsVariable = isVariable(in.set, variableDeclaration);
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// TODO: implement more cases
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if (!elementIsVariable && !setIsVariable)
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return ast::Domain::Unknown;
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auto &otherSide = (elementIsVariable ? in.set : in.element);
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return domain(otherSide);
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}
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static ast::Domain visit(ast::Not ¬_, ast::VariableDeclaration &variableDeclaration)
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{
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return not_.argument.accept(VariableDomainInFormulaVisitor(), variableDeclaration);
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}
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static ast::Domain visit(ast::Or &or_, ast::VariableDeclaration &variableDeclaration)
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{
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bool integer = false;
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for (auto &argument : or_.arguments)
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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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const auto domain = argument.accept(VariableDomainInFormulaVisitor(), variableDeclaration);
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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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if (domain == ast::Domain::General)
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return ast::Domain::General;
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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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if (domain == ast::Domain::Integer)
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integer = true;
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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 (integer)
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return ast::Domain::Integer;
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if (someTrue)
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return EvaluationResult::True;
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return ast::Domain::Unknown;
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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 ast::Domain visit(ast::Predicate &predicate, ast::VariableDeclaration &variableDeclaration)
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static EvaluationResult visit(const ast::Predicate &predicate, VariableDomainMap &variableDomainMap)
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{
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// TODO: check implementation for nested arguments
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assert(predicate.arguments.size() == predicate.declaration->arity());
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|
||||
// Inherit the domain of the predicate’s parameters
|
||||
for (size_t i = 0; i < predicate.arguments.size(); i++)
|
||||
{
|
||||
auto &argument = predicate.arguments[i];
|
||||
const auto &argument = predicate.arguments[i];
|
||||
const auto ¶meter = predicate.declaration->parameters[i];
|
||||
|
||||
if (!argument.is<ast::Variable>())
|
||||
if (parameter.domain != ast::Domain::Integer)
|
||||
continue;
|
||||
|
||||
auto &variable = argument.get<ast::Variable>();
|
||||
const auto isArgumentArithmetic = isArithmetic(argument, variableDomainMap);
|
||||
|
||||
if (variable.declaration != &variableDeclaration)
|
||||
continue;
|
||||
|
||||
auto ¶meter = predicate.declaration->parameters[i];
|
||||
|
||||
return parameter.domain;
|
||||
if (isArgumentArithmetic == EvaluationResult::Error || isArgumentArithmetic == EvaluationResult::False)
|
||||
return isArgumentArithmetic;
|
||||
}
|
||||
|
||||
return ast::Domain::Unknown;
|
||||
return EvaluationResult::Unknown;
|
||||
}
|
||||
};
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
// Recursively finds every variable declaration and executes functor to the formula in the scope of the declaration
|
||||
EvaluationResult evaluate(const ast::Formula &formula, VariableDomainMap &variableDomainMap)
|
||||
{
|
||||
return formula.accept(EvaluateFormulaVisitor(), variableDomainMap);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
OperationResult detectIntegerVariables(ast::Formula &formula, ast::Formula &definition, VariableDomainMap &variableDomainMap);
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
struct DetectIntegerVariablesVisitor
|
||||
{
|
||||
static OperationResult visit(ast::And &and_)
|
||||
static OperationResult visit(ast::And &and_, ast::Formula &definition, VariableDomainMap &variableDomainMap)
|
||||
{
|
||||
auto operationResult = OperationResult::Unchanged;
|
||||
|
||||
for (auto &argument : and_.arguments)
|
||||
if (argument.accept(DetectIntegerVariablesVisitor()) == OperationResult::Changed)
|
||||
if (detectIntegerVariables(argument, definition, variableDomainMap) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
return operationResult;
|
||||
}
|
||||
|
||||
static OperationResult visit(ast::Biconditional &biconditional)
|
||||
static OperationResult visit(ast::Biconditional &biconditional, ast::Formula &definition, VariableDomainMap &variableDomainMap)
|
||||
{
|
||||
auto operationResult = OperationResult::Unchanged;
|
||||
|
||||
if (biconditional.left.accept(DetectIntegerVariablesVisitor()) == OperationResult::Changed)
|
||||
if (detectIntegerVariables(biconditional.left, definition, variableDomainMap) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
if (biconditional.right.accept(DetectIntegerVariablesVisitor()) == OperationResult::Changed)
|
||||
if (detectIntegerVariables(biconditional.right, definition, variableDomainMap) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
return operationResult;
|
||||
}
|
||||
|
||||
static OperationResult visit(ast::Boolean &)
|
||||
static OperationResult visit(ast::Boolean &, ast::Formula &, VariableDomainMap &)
|
||||
{
|
||||
return OperationResult::Unchanged;
|
||||
}
|
||||
|
||||
static OperationResult visit(ast::Comparison &)
|
||||
static OperationResult visit(ast::Comparison &, ast::Formula &, VariableDomainMap &)
|
||||
{
|
||||
return OperationResult::Unchanged;
|
||||
}
|
||||
|
||||
static OperationResult visit(ast::Exists &exists)
|
||||
static OperationResult visit(ast::Exists &exists, ast::Formula &definition, VariableDomainMap &variableDomainMap)
|
||||
{
|
||||
auto operationResult = OperationResult::Unchanged;
|
||||
|
||||
if (exists.argument.accept(DetectIntegerVariablesVisitor()) == OperationResult::Changed)
|
||||
if (detectIntegerVariables(exists.argument, definition, variableDomainMap) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
for (auto &variableDeclaration : exists.variables)
|
||||
if (variableDeclaration->domain != ast::Domain::General)
|
||||
{
|
||||
if (variableDeclaration->domain != ast::Domain::Unknown)
|
||||
continue;
|
||||
|
||||
clearVariableDomainMap(variableDomainMap);
|
||||
|
||||
auto argumentResult = evaluate(exists.argument, variableDomainMap);
|
||||
auto definitionResult = evaluate(definition, variableDomainMap);
|
||||
|
||||
if (argumentResult == EvaluationResult::Error || argumentResult == EvaluationResult::False
|
||||
|| definitionResult == EvaluationResult::Error || definitionResult == EvaluationResult::False)
|
||||
{
|
||||
auto newDomain = exists.argument.accept(VariableDomainInFormulaVisitor(), *variableDeclaration);
|
||||
|
||||
if (variableDeclaration->domain == newDomain)
|
||||
continue;
|
||||
|
||||
operationResult = OperationResult::Changed;
|
||||
variableDeclaration->domain = newDomain;
|
||||
continue;
|
||||
}
|
||||
|
||||
// As a hypothesis, make the parameter’s domain noninteger
|
||||
variableDomainMap[variableDeclaration.get()] = ast::Domain::General;
|
||||
|
||||
argumentResult = evaluate(exists.argument, variableDomainMap);
|
||||
definitionResult = evaluate(definition, variableDomainMap);
|
||||
|
||||
if (argumentResult == EvaluationResult::Error || argumentResult == EvaluationResult::False
|
||||
|| definitionResult == EvaluationResult::Error || definitionResult == EvaluationResult::False)
|
||||
{
|
||||
// If making the variable noninteger leads to a false or erroneous result, it’s proven to be integer
|
||||
operationResult = OperationResult::Changed;
|
||||
variableDeclaration->domain = ast::Domain::Integer;
|
||||
}
|
||||
}
|
||||
|
||||
return operationResult;
|
||||
}
|
||||
|
||||
static OperationResult visit(ast::ForAll &forAll)
|
||||
static OperationResult visit(ast::ForAll &forAll, ast::Formula &definition, VariableDomainMap &variableDomainMap)
|
||||
{
|
||||
auto operationResult = OperationResult::Unchanged;
|
||||
|
||||
if (forAll.argument.accept(DetectIntegerVariablesVisitor()) == OperationResult::Changed)
|
||||
if (detectIntegerVariables(forAll.argument, definition, variableDomainMap) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
for (auto &variableDeclaration : forAll.variables)
|
||||
if (variableDeclaration->domain != ast::Domain::General)
|
||||
{
|
||||
if (variableDeclaration->domain != ast::Domain::Unknown)
|
||||
continue;
|
||||
|
||||
clearVariableDomainMap(variableDomainMap);
|
||||
|
||||
auto argumentResult = evaluate(forAll.argument, variableDomainMap);
|
||||
auto definitionResult = evaluate(definition, variableDomainMap);
|
||||
|
||||
if (argumentResult == EvaluationResult::Error || argumentResult == EvaluationResult::False
|
||||
|| definitionResult == EvaluationResult::Error || definitionResult == EvaluationResult::False)
|
||||
{
|
||||
auto newDomain = forAll.argument.accept(VariableDomainInFormulaVisitor(), *variableDeclaration);
|
||||
|
||||
if (variableDeclaration->domain == newDomain)
|
||||
continue;
|
||||
|
||||
operationResult = OperationResult::Changed;
|
||||
variableDeclaration->domain = newDomain;
|
||||
continue;
|
||||
}
|
||||
|
||||
// As a hypothesis, make the parameter’s domain noninteger
|
||||
variableDomainMap[variableDeclaration.get()] = ast::Domain::General;
|
||||
|
||||
argumentResult = evaluate(forAll.argument, variableDomainMap);
|
||||
definitionResult = evaluate(definition, variableDomainMap);
|
||||
|
||||
if (argumentResult == EvaluationResult::Error || argumentResult == EvaluationResult::False
|
||||
|| definitionResult == EvaluationResult::Error || definitionResult == EvaluationResult::False)
|
||||
{
|
||||
// If making the variable noninteger leads to a false or erroneous result, it’s proven to be integer
|
||||
operationResult = OperationResult::Changed;
|
||||
variableDeclaration->domain = ast::Domain::Integer;
|
||||
}
|
||||
}
|
||||
|
||||
return operationResult;
|
||||
}
|
||||
|
||||
static OperationResult visit(ast::Implies &implies)
|
||||
static OperationResult visit(ast::Implies &implies, ast::Formula &definition, VariableDomainMap &variableDomainMap)
|
||||
{
|
||||
auto operationResult = OperationResult::Unchanged;
|
||||
|
||||
if (implies.antecedent.accept(DetectIntegerVariablesVisitor()) == OperationResult::Changed)
|
||||
if (detectIntegerVariables(implies.antecedent, definition, variableDomainMap) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
if (implies.consequent.accept(DetectIntegerVariablesVisitor()) == OperationResult::Changed)
|
||||
if (detectIntegerVariables(implies.consequent, definition, variableDomainMap) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
return operationResult;
|
||||
}
|
||||
|
||||
static OperationResult visit(ast::In &)
|
||||
static OperationResult visit(ast::In &, ast::Formula &, VariableDomainMap &)
|
||||
{
|
||||
return OperationResult::Unchanged;
|
||||
}
|
||||
|
||||
static OperationResult visit(ast::Not ¬_)
|
||||
static OperationResult visit(ast::Not ¬_, ast::Formula &definition, VariableDomainMap &variableDomainMap)
|
||||
{
|
||||
return not_.argument.accept(DetectIntegerVariablesVisitor());
|
||||
return detectIntegerVariables(not_.argument, definition, variableDomainMap);
|
||||
}
|
||||
|
||||
static OperationResult visit(ast::Or &or_)
|
||||
static OperationResult visit(ast::Or &or_, ast::Formula &definition, VariableDomainMap &variableDomainMap)
|
||||
{
|
||||
auto operationResult = OperationResult::Unchanged;
|
||||
|
||||
for (auto &argument : or_.arguments)
|
||||
if (argument.accept(DetectIntegerVariablesVisitor()) == OperationResult::Changed)
|
||||
if (detectIntegerVariables(argument, definition, variableDomainMap) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
return operationResult;
|
||||
}
|
||||
|
||||
static OperationResult visit(ast::Predicate &)
|
||||
static OperationResult visit(ast::Predicate &predicate, ast::Formula &, VariableDomainMap &)
|
||||
{
|
||||
return OperationResult::Unchanged;
|
||||
auto operationResult = OperationResult::Unchanged;
|
||||
|
||||
assert(predicate.arguments.size() == predicate.declaration->arity());
|
||||
|
||||
// Propagate integer domains from predicates to variables
|
||||
for (size_t i = 0; i < predicate.arguments.size(); i++)
|
||||
{
|
||||
auto &variableArgument = predicate.arguments[i];
|
||||
auto ¶meter = predicate.declaration->parameters[i];
|
||||
|
||||
if (parameter.domain != ast::Domain::Integer)
|
||||
continue;
|
||||
|
||||
if (!variableArgument.is<ast::Variable>())
|
||||
continue;
|
||||
|
||||
auto &variable = variableArgument.get<ast::Variable>();
|
||||
|
||||
if (variable.declaration->domain == ast::Domain::Integer)
|
||||
continue;
|
||||
|
||||
operationResult = OperationResult::Changed;
|
||||
variable.declaration->domain = ast::Domain::Integer;
|
||||
}
|
||||
|
||||
return operationResult;
|
||||
}
|
||||
};
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
OperationResult detectIntegerVariables(ast::Formula &formula, ast::Formula &definition, VariableDomainMap &variableDomainMap)
|
||||
{
|
||||
return formula.accept(DetectIntegerVariablesVisitor(), definition, variableDomainMap);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
// Assumes the completed formulas to be in translated but not simplified form.
|
||||
// That is, completed formulas are either variable-free or universally quantified
|
||||
void detectIntegerVariables(std::vector<ast::Formula> &completedFormulas)
|
||||
{
|
||||
auto operationResult{OperationResult::Changed};
|
||||
VariableDomainMap variableDomainMap;
|
||||
auto operationResult = OperationResult::Changed;
|
||||
|
||||
while (operationResult == OperationResult::Changed)
|
||||
{
|
||||
|
|
@ -400,12 +590,14 @@ void detectIntegerVariables(std::vector<ast::Formula> &completedFormulas)
|
|||
|
||||
for (auto &completedFormula : completedFormulas)
|
||||
{
|
||||
if (detectIntegerVariables(completedFormula, completedFormula, variableDomainMap) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
if (!completedFormula.is<ast::ForAll>())
|
||||
continue;
|
||||
|
||||
auto &forAll = completedFormula.get<ast::ForAll>();
|
||||
|
||||
// TODO: check that integrity constraints are also handled
|
||||
if (!forAll.argument.is<ast::Biconditional>())
|
||||
continue;
|
||||
|
||||
|
|
@ -417,38 +609,42 @@ void detectIntegerVariables(std::vector<ast::Formula> &completedFormulas)
|
|||
auto &predicate = biconditional.left.get<ast::Predicate>();
|
||||
auto &definition = biconditional.right;
|
||||
|
||||
if (definition.accept(DetectIntegerVariablesVisitor()) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
for (auto &variableDeclaration : forAll.variables)
|
||||
if (variableDeclaration->domain != ast::Domain::General)
|
||||
{
|
||||
auto newDomain = forAll.argument.accept(VariableDomainInFormulaVisitor(), *variableDeclaration);
|
||||
|
||||
if (variableDeclaration->domain == newDomain)
|
||||
continue;
|
||||
|
||||
operationResult = OperationResult::Changed;
|
||||
variableDeclaration->domain = newDomain;
|
||||
}
|
||||
|
||||
assert(predicate.arguments.size() == predicate.declaration->arity());
|
||||
|
||||
// Update parameter domains
|
||||
if (detectIntegerVariables(definition, definition, variableDomainMap) == OperationResult::Changed)
|
||||
operationResult = OperationResult::Changed;
|
||||
|
||||
for (size_t i = 0; i < predicate.arguments.size(); i++)
|
||||
{
|
||||
auto &variableArgument = predicate.arguments[i];
|
||||
auto ¶meter = predicate.declaration->parameters[i];
|
||||
|
||||
assert(variableArgument.is<ast::Variable>());
|
||||
|
||||
auto &variable = variableArgument.get<ast::Variable>();
|
||||
auto ¶meter = predicate.declaration->parameters[i];
|
||||
|
||||
if (parameter.domain == variable.declaration->domain)
|
||||
if (parameter.domain != ast::Domain::Unknown)
|
||||
continue;
|
||||
|
||||
operationResult = OperationResult::Changed;
|
||||
parameter.domain = variable.declaration->domain;
|
||||
clearVariableDomainMap(variableDomainMap);
|
||||
|
||||
auto result = evaluate(definition, variableDomainMap);
|
||||
|
||||
if (result == EvaluationResult::Error || result == EvaluationResult::False)
|
||||
continue;
|
||||
|
||||
// As a hypothesis, make the parameter’s domain noninteger
|
||||
variableDomainMap[variable.declaration] = ast::Domain::General;
|
||||
|
||||
result = evaluate(definition, variableDomainMap);
|
||||
|
||||
if (result == EvaluationResult::Error || result == EvaluationResult::False)
|
||||
{
|
||||
// If making the variable noninteger leads to a false or erroneous result, it’s proven to be integer
|
||||
operationResult = OperationResult::Changed;
|
||||
variable.declaration->domain = ast::Domain::Integer;
|
||||
parameter.domain = ast::Domain::Integer;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue