Iteratively apply simplification tableau rules
With this change, the tableau rules for simplifying formula are applied iteratively until a fixpoint is reached.
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@ -3,3 +3,5 @@ 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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@ -12,6 +12,14 @@ namespace anthem
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//
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////////////////////////////////////////////////////////////////////////////////////////////////////
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enum class SimplificationResult
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{
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Simplified,
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Unchanged,
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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void simplify(ast::Formula &formula);
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////////////////////////////////////////////////////////////////////////////////////////////////////
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198
include/anthem/SimplificationVisitors.h
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198
include/anthem/SimplificationVisitors.h
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@ -0,0 +1,198 @@
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#ifndef __ANTHEM__SIMPLIFICATION_VISITORS_H
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#define __ANTHEM__SIMPLIFICATION_VISITORS_H
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#include <anthem/AST.h>
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#include <anthem/Simplification.h>
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namespace anthem
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{
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namespace ast
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{
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////////////////////////////////////////////////////////////////////////////////////////////////////
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//
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// Simplification Visitor
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//
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////////////////////////////////////////////////////////////////////////////////////////////////////
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template<class T>
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struct FormulaSimplificationVisitor
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{
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template <class... Arguments>
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SimplificationResult visit(And &and_, Formula &formula, Arguments &&... arguments)
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{
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for (auto &argument : and_.arguments)
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if (argument.accept(*this, argument, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Biconditional &biconditional, Formula &formula, Arguments &&... arguments)
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{
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if (biconditional.left.accept(*this, biconditional.left, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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if (biconditional.right.accept(*this, biconditional.right, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Boolean &, Formula &formula, Arguments &&... arguments)
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{
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Comparison &, Formula &formula, Arguments &&... arguments)
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{
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Exists &exists, Formula &formula, Arguments &&... arguments)
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{
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if (exists.argument.accept(*this, exists.argument, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(ForAll &forAll, Formula &formula, Arguments &&... arguments)
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{
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if (forAll.argument.accept(*this, forAll.argument, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Implies &implies, Formula &formula, Arguments &&... arguments)
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{
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if (implies.antecedent.accept(*this, implies.antecedent, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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if (implies.consequent.accept(*this, implies.consequent, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(In &, Formula &formula, Arguments &&... arguments)
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{
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Not ¬_, Formula &formula, Arguments &&... arguments)
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{
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if (not_.argument.accept(*this, not_.argument, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Or &or_, Formula &formula, Arguments &&... arguments)
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{
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for (auto &argument : or_.arguments)
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if (argument.accept(*this, argument, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Predicate &, Formula &formula, Arguments &&... arguments)
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{
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return T::accept(formula, std::forward<Arguments>(arguments)...);
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}
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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template<class T, class SimplificationResult = void>
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struct TermSimplificationVisitor
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{
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template <class... Arguments>
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SimplificationResult visit(BinaryOperation &binaryOperation, Term &term, Arguments &&... arguments)
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{
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if (binaryOperation.left.accept(*this, binaryOperation.left, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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if (binaryOperation.right.accept(*this, binaryOperation.right, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return T::accept(term, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Boolean &, Term &term, Arguments &&... arguments)
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{
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return T::accept(term, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Constant &, Term &term, Arguments &&... arguments)
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{
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return T::accept(term, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Function &function, Term &term, Arguments &&... arguments)
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{
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for (auto &argument : function.arguments)
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if (argument.accept(*this, argument, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return T::accept(term, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Integer &, Term &term, Arguments &&... arguments)
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{
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return T::accept(term, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Interval &interval, Term &term, Arguments &&... arguments)
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{
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if (interval.from.accept(*this, interval.from, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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if (interval.to.accept(*this, interval.to, std::forward<Arguments>(arguments)...) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return T::accept(term, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(SpecialInteger &, Term &term, Arguments &&... arguments)
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{
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return T::accept(term, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(String &, Term &term, Arguments &&... arguments)
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{
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return T::accept(term, std::forward<Arguments>(arguments)...);
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}
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template <class... Arguments>
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SimplificationResult visit(Variable &, Term &term, Arguments &&... arguments)
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{
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return T::accept(term, std::forward<Arguments>(arguments)...);
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}
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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}
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}
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#endif
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@ -3,7 +3,7 @@
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#include <optional>
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#include <anthem/ASTCopy.h>
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#include <anthem/ASTVisitors.h>
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#include <anthem/SimplificationVisitors.h>
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namespace anthem
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{
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@ -97,14 +97,6 @@ struct ReplaceVariableInFormulaVisitor : public ast::RecursiveFormulaVisitor<Rep
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////////////////////////////////////////////////////////////////////////////////////////////////////
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enum class SimplificationResult
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{
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Simplified,
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Unchanged,
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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template<class SimplificationRule>
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SimplificationResult simplify(ast::Formula &formula)
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{
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@ -113,13 +105,13 @@ SimplificationResult simplify(ast::Formula &formula)
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////////////////////////////////////////////////////////////////////////////////////////////////////
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template<class SimplificationRule, class... OtherSimplificationRules>
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template<class FirstSimplificationRule, class SecondSimplificationRule, class... OtherSimplificationRules>
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SimplificationResult simplify(ast::Formula &formula)
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{
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if (SimplificationRule::apply(formula) == SimplificationResult::Simplified)
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if (simplify<FirstSimplificationRule>(formula) == SimplificationResult::Simplified)
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return SimplificationResult::Simplified;
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return simplify<OtherSimplificationRules...>(formula);
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return simplify<SecondSimplificationRule, OtherSimplificationRules...>(formula);
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}
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////////////////////////////////////////////////////////////////////////////////////////////////////
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@ -341,39 +333,27 @@ struct SimplificationRuleInWithPrimitiveArguments
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////////////////////////////////////////////////////////////////////////////////////////////////////
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void simplify(ast::Exists &exists, ast::Formula &formula)
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{
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SimplificationRuleTrivialAssignmentInExists::apply(formula);
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SimplificationRuleAssignmentInExists::apply(formula);
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SimplificationRuleEmptyConjunction::apply(exists.argument);
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SimplificationRuleTrivialExists::apply(formula);
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SimplificationRuleOneElementConjunction::apply(exists.argument);
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SimplificationRuleExistsWithoutQuantifiedVariables::apply(formula);
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}
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const auto simplifyWithDefaultRules =
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simplify
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<
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SimplificationRuleTrivialAssignmentInExists,
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SimplificationRuleAssignmentInExists,
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SimplificationRuleEmptyConjunction,
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SimplificationRuleTrivialExists,
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SimplificationRuleOneElementConjunction,
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SimplificationRuleExistsWithoutQuantifiedVariables,
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SimplificationRuleInWithPrimitiveArguments
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>;
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////////////////////////////////////////////////////////////////////////////////////////////////////
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// Performs the different simplification techniques
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struct SimplifyFormulaVisitor : public ast::RecursiveFormulaVisitor<SimplifyFormulaVisitor>
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struct SimplifyFormulaVisitor : public ast::FormulaSimplificationVisitor<SimplifyFormulaVisitor>
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{
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// Forward exists statements to the dedicated simplification function
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static void accept(ast::Exists &exists, ast::Formula &formula)
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{
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simplify(exists, formula);
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}
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// Simplify formulas of type “A in B” to “A = B” if A and B are primitive
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static void accept(ast::In &, ast::Formula &formula)
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{
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SimplificationRuleInWithPrimitiveArguments::apply(formula);
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}
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// Do nothing for all other types of expressions
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template<class T>
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static void accept(T &, ast::Formula &)
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static SimplificationResult accept(ast::Formula &formula)
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{
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return simplifyWithDefaultRules(formula);
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}
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};
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@ -381,7 +361,7 @@ struct SimplifyFormulaVisitor : public ast::RecursiveFormulaVisitor<SimplifyForm
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void simplify(ast::Formula &formula)
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{
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formula.accept(SimplifyFormulaVisitor(), formula);
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while (formula.accept(SimplifyFormulaVisitor(), formula) == SimplificationResult::Simplified);
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}
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////////////////////////////////////////////////////////////////////////////////////////////////////
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