Split predicates from their declarations

This refactoring separates predicates from their declarations. The
purpose of this is to avoid duplicating properties specific to the
predicate declaration and not its occurrences in the program.

include/anthem/AST.h

@@ -187,13 +187,13 @@ struct Interval
 
 struct Predicate
 {
-	explicit Predicate(std::string &&name)
+	explicit Predicate(PredicateDeclaration *declaration)
-	:	name{std::move(name)}
+	:	declaration{declaration}
 	{
 	}
 
-	explicit Predicate(std::string &&name, std::vector<Term> &&arguments)
+	explicit Predicate(PredicateDeclaration *declaration, std::vector<Term> &&arguments)
-	:	name{std::move(name)},
+	:	declaration{declaration},
 		arguments{std::move(arguments)}
 	{
 	}
@@ -203,35 +203,37 @@ struct Predicate
 	Predicate(Predicate &&other) noexcept = default;
 	Predicate &operator=(Predicate &&other) noexcept = default;
 
-	std::size_t arity() const
+	PredicateDeclaration *declaration{nullptr};
-	{
-		return arguments.size();
-	}
-
-	std::string name;
 	std::vector<Term> arguments;
 };
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
-// TODO: make more use of this class
+struct PredicateDeclaration
-struct PredicateSignature
 {
-	explicit PredicateSignature(std::string &&name, size_t arity)
+	enum class Visibility
+	{
+		Default,
+		Visible,
+		Hidden
+	};
+
+	explicit PredicateDeclaration(std::string &&name, size_t arity)
 	:	name{std::move(name)},
 		arity{arity}
 	{
 	}
 
-	PredicateSignature(const PredicateSignature &other) = delete;
+	PredicateDeclaration(const PredicateDeclaration &other) = delete;
-	PredicateSignature &operator=(const PredicateSignature &other) = delete;
+	PredicateDeclaration &operator=(const PredicateDeclaration &other) = delete;
-	// TODO: make noexcept again
+	PredicateDeclaration(PredicateDeclaration &&other) noexcept = default;
-	// GCC versions before 7 don’t declare moving std::string noexcept and would complain here
+	PredicateDeclaration &operator=(PredicateDeclaration &&other) noexcept = default;
-	PredicateSignature(PredicateSignature &&other) = default;
-	PredicateSignature &operator=(PredicateSignature &&other) = default;
 
 	std::string name;
 	size_t arity;
+	bool isUsed{false};
+	bool isExternal{false};
+	Visibility visibility{Visibility::Default};
 };
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////

include/anthem/ASTForward.h

@@ -34,6 +34,7 @@ struct Interval;
 struct Not;
 struct Or;
 struct Predicate;
+struct PredicateDeclaration;
 struct SpecialInteger;
 struct String;
 struct UnaryOperation;

include/anthem/ASTUtils.h

@@ -36,12 +36,6 @@ class VariableStack
 		std::vector<Layer> m_layers;
 };
 
-////////////////////////////////////////////////////////////////////////////////////////////////////
-
-bool matches(const Predicate &lhs, const Predicate &rhs);
-bool matches(const Predicate &predicate, const PredicateSignature &signature);
-bool matches(const PredicateSignature &lhs, const PredicateSignature &rhs);
-void collectPredicateSignatures(const Formula &formula, std::vector<PredicateSignature> &predicateSignatures, Context &context);
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 // Replacing Variables

include/anthem/Body.h

@@ -43,19 +43,22 @@ ast::Comparison::Operator translate(Clingo::AST::ComparisonOperator comparisonOp
 struct BodyTermTranslateVisitor
 {
 	// TODO: refactor
-	std::optional<ast::Formula> visit(const Clingo::AST::Function &function, const Clingo::AST::Literal &literal, const Clingo::AST::Term &, RuleContext &ruleContext, ast::VariableStack &variableStack)
+	std::optional<ast::Formula> visit(const Clingo::AST::Function &function,
+		const Clingo::AST::Literal &literal, const Clingo::AST::Term &, RuleContext &ruleContext,
+		Context &context, ast::VariableStack &variableStack)
 	{
 		if (literal.sign == Clingo::AST::Sign::DoubleNegation)
 			throw TranslationException(literal.location, "double-negated literals currently unsupported");
 
+		auto predicateDeclaration = context.findOrCreatePredicateDeclaration(function.name, function.arguments.size());
+		predicateDeclaration->isUsed = true;
+
 		if (function.arguments.empty())
 		{
-			auto predicate = ast::Formula::make<ast::Predicate>(std::string(function.name));
-
 			if (literal.sign == Clingo::AST::Sign::None)
-				return std::move(predicate);
+				return ast::Predicate(predicateDeclaration);
 			else if (literal.sign == Clingo::AST::Sign::Negation)
-				return ast::Formula::make<ast::Not>(std::move(predicate));
+				return ast::Formula::make<ast::Not>(ast::Predicate(predicateDeclaration));
 		}
 
 		// Create new body variable declarations
@@ -78,7 +81,7 @@ struct BodyTermTranslateVisitor
 
 		variableStack.pop();
 
-		ast::Predicate predicate(std::string(function.name));
+		ast::Predicate predicate(predicateDeclaration);
 		predicate.arguments.reserve(function.arguments.size());
 
 		for (size_t i = 0; i < function.arguments.size(); i++)
@@ -93,7 +96,8 @@ struct BodyTermTranslateVisitor
 	}
 
 	template<class T>
-	std::optional<ast::Formula> visit(const T &, const Clingo::AST::Literal &, const Clingo::AST::Term &term, RuleContext &, ast::VariableStack &)
+	std::optional<ast::Formula> visit(const T &, const Clingo::AST::Literal &,
+		const Clingo::AST::Term &term, RuleContext &, Context &, ast::VariableStack &)
 	{
 		assert(!term.data.is<Clingo::AST::Function>());
 
@@ -106,18 +110,18 @@ struct BodyTermTranslateVisitor
 
 struct BodyLiteralTranslateVisitor
 {
-	std::optional<ast::Formula> visit(const Clingo::AST::Boolean &boolean, const Clingo::AST::Literal &, RuleContext &, ast::VariableStack &)
+	std::optional<ast::Formula> visit(const Clingo::AST::Boolean &boolean, const Clingo::AST::Literal &, RuleContext &, Context &, ast::VariableStack &)
 	{
 		return ast::Formula::make<ast::Boolean>(boolean.value);
 	}
 
-	std::optional<ast::Formula> visit(const Clingo::AST::Term &term, const Clingo::AST::Literal &literal, RuleContext &ruleContext, ast::VariableStack &variableStack)
+	std::optional<ast::Formula> visit(const Clingo::AST::Term &term, const Clingo::AST::Literal &literal, RuleContext &ruleContext, Context &context, ast::VariableStack &variableStack)
 	{
-		return term.data.accept(BodyTermTranslateVisitor(), literal, term, ruleContext, variableStack);
+		return term.data.accept(BodyTermTranslateVisitor(), literal, term, ruleContext, context, variableStack);
 	}
 
 	// TODO: refactor
-	std::optional<ast::Formula> visit(const Clingo::AST::Comparison &comparison, const Clingo::AST::Literal &literal, RuleContext &ruleContext, ast::VariableStack &variableStack)
+	std::optional<ast::Formula> visit(const Clingo::AST::Comparison &comparison, const Clingo::AST::Literal &literal, RuleContext &ruleContext, Context &, ast::VariableStack &variableStack)
 	{
 		// Comparisons should never have a sign, because these are converted to positive comparisons by clingo
 		if (literal.sign != Clingo::AST::Sign::None)
@@ -140,7 +144,7 @@ struct BodyLiteralTranslateVisitor
 	}
 
 	template<class T>
-	std::optional<ast::Formula> visit(const T &, const Clingo::AST::Literal &literal, RuleContext &, ast::VariableStack &)
+	std::optional<ast::Formula> visit(const T &, const Clingo::AST::Literal &literal, RuleContext &, Context &, ast::VariableStack &)
 	{
 		throw TranslationException(literal.location, "literal currently unsupported in this context, expected function or term");
 		return std::nullopt;
@@ -151,16 +155,16 @@ struct BodyLiteralTranslateVisitor
 
 struct BodyBodyLiteralTranslateVisitor
 {
-	std::optional<ast::Formula> visit(const Clingo::AST::Literal &literal, const Clingo::AST::BodyLiteral &bodyLiteral, RuleContext &ruleContext, ast::VariableStack &variableStack)
+	std::optional<ast::Formula> visit(const Clingo::AST::Literal &literal, const Clingo::AST::BodyLiteral &bodyLiteral, RuleContext &ruleContext, Context &context, ast::VariableStack &variableStack)
 	{
 		if (bodyLiteral.sign != Clingo::AST::Sign::None)
 			throw TranslationException(bodyLiteral.location, "only positive body literals supported currently");
 
-		return literal.data.accept(BodyLiteralTranslateVisitor(), literal, ruleContext, variableStack);
+		return literal.data.accept(BodyLiteralTranslateVisitor(), literal, ruleContext, context, variableStack);
 	}
 
 	template<class T>
-	std::optional<ast::Formula> visit(const T &, const Clingo::AST::BodyLiteral &bodyLiteral, RuleContext &, ast::VariableStack &)
+	std::optional<ast::Formula> visit(const T &, const Clingo::AST::BodyLiteral &bodyLiteral, RuleContext &, Context &, ast::VariableStack &)
 	{
 		throw TranslationException(bodyLiteral.location, "body literal currently unsupported in this context, expected literal");
 		return std::nullopt;

include/anthem/Context.h

@@ -16,9 +16,9 @@ namespace anthem
 //
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
-struct PredicateSignatureMeta
+struct PredicateDeclarationMeta
 {
-	ast::PredicateSignature predicateSignature;
+	ast::PredicateDeclaration *declaration;
 	bool used{false};
 };
 
@@ -33,13 +33,36 @@ struct Context
 	{
 	}
 
+	ast::PredicateDeclaration *findOrCreatePredicateDeclaration(const char *name, size_t arity)
+	{
+		const auto matchesExistingPredicateDeclaration =
+			[&](const auto &predicateDeclaration)
+			{
+				return (predicateDeclaration->arity == arity
+					&& strcmp(predicateDeclaration->name.c_str(), name) == 0);
+			};
+
+		auto matchingPredicateDeclaration = std::find_if(predicateDeclarations.begin(),
+			predicateDeclarations.end(), matchesExistingPredicateDeclaration);
+
+		if (matchingPredicateDeclaration != predicateDeclarations.end())
+			return matchingPredicateDeclaration->get();
+
+		predicateDeclarations.emplace_back(std::make_unique<ast::PredicateDeclaration>(name, arity));
+
+		return predicateDeclarations.back().get();
+	}
+
 	output::Logger logger;
 
 	bool performSimplification{false};
 	bool performCompletion{false};
 
-	std::optional<std::vector<PredicateSignatureMeta>> visiblePredicateSignatures;
+	std::vector<std::unique_ptr<ast::PredicateDeclaration>> predicateDeclarations;
-	std::optional<std::vector<PredicateSignatureMeta>> externalPredicateSignatures;
+	ast::PredicateDeclaration::Visibility defaultPredicateVisibility{ast::PredicateDeclaration::Visibility::Visible};
+
+	bool externalStatementsUsed{false};
+	bool showStatementsUsed{false};
 
 	ast::ParenthesisStyle parenthesisStyle = ast::ParenthesisStyle::Normal;
 };

include/anthem/Equality.h

@@ -237,7 +237,7 @@ struct FormulaEqualityVisitor
 
 		const auto &otherPredicate = otherFormula.get<Predicate>();
 
-		if (!matches(predicate, otherPredicate))
+		if (predicate.declaration != otherPredicate.declaration)
 			return Tristate::False;
 
 		assert(predicate.arguments.size() == otherPredicate.arguments.size());

include/anthem/Head.h

@@ -118,8 +118,7 @@ struct HeadLiteralCollectFunctionTermsVisitor
 
 struct FunctionTermTranslateVisitor
 {
-	// TODO: check correctness
+	std::optional<ast::Formula> visit(const Clingo::AST::Function &function, const Clingo::AST::Term &term, RuleContext &ruleContext, Context &context, size_t &headVariableIndex)
-	std::optional<ast::Formula> visit(const Clingo::AST::Function &function, const Clingo::AST::Term &term, RuleContext &ruleContext, size_t &headVariableIndex)
 	{
 		if (function.external)
 			throw TranslationException(term.location, "external functions currently unsupported");
@@ -130,11 +129,14 @@ struct FunctionTermTranslateVisitor
 		for (size_t i = 0; i < function.arguments.size(); i++)
 			arguments.emplace_back(ast::Variable(ruleContext.freeVariables[headVariableIndex++].get()));
 
-		return ast::Formula::make<ast::Predicate>(function.name, std::move(arguments));
+		auto predicateDeclaration = context.findOrCreatePredicateDeclaration(function.name, function.arguments.size());
+		predicateDeclaration->isUsed = true;
+
+		return ast::Predicate(predicateDeclaration, std::move(arguments));
 	}
 
 	template<class T>
-	std::optional<ast::Formula> visit(const T &, const Clingo::AST::Term &term, RuleContext &, size_t &)
+	std::optional<ast::Formula> visit(const T &, const Clingo::AST::Term &term, RuleContext &, Context &, size_t &)
 	{
 		throw TranslationException(term.location, "term currently unsupported in this context, function expected");
 		return std::nullopt;
@@ -145,18 +147,18 @@ struct FunctionTermTranslateVisitor
 
 struct LiteralTranslateVisitor
 {
-	std::optional<ast::Formula> visit(const Clingo::AST::Boolean &boolean, const Clingo::AST::Literal &, RuleContext &, size_t &)
+	std::optional<ast::Formula> visit(const Clingo::AST::Boolean &boolean, const Clingo::AST::Literal &, RuleContext &, Context &, size_t &)
 	{
 		return ast::Formula::make<ast::Boolean>(boolean.value);
 	}
 
-	std::optional<ast::Formula> visit(const Clingo::AST::Term &term, const Clingo::AST::Literal &, RuleContext &ruleContext, size_t &headVariableIndex)
+	std::optional<ast::Formula> visit(const Clingo::AST::Term &term, const Clingo::AST::Literal &, RuleContext &ruleContext, Context &context, size_t &headVariableIndex)
 	{
-		return term.data.accept(FunctionTermTranslateVisitor(), term, ruleContext, headVariableIndex);
+		return term.data.accept(FunctionTermTranslateVisitor(), term, ruleContext, context, headVariableIndex);
 	}
 
 	template<class T>
-	std::optional<ast::Formula> visit(const T &, const Clingo::AST::Literal &literal, RuleContext &, size_t &)
+	std::optional<ast::Formula> visit(const T &, const Clingo::AST::Literal &literal, RuleContext &, Context &, size_t &)
 	{
 		throw TranslationException(literal.location, "only disjunctions of literals allowed as head literals");
 		return std::nullopt;
@@ -167,12 +169,12 @@ struct LiteralTranslateVisitor
 
 struct HeadLiteralTranslateToConsequentVisitor
 {
-	std::optional<ast::Formula> visit(const Clingo::AST::Literal &literal, const Clingo::AST::HeadLiteral &, RuleContext &ruleContext, size_t &headVariableIndex)
+	std::optional<ast::Formula> visit(const Clingo::AST::Literal &literal, const Clingo::AST::HeadLiteral &, RuleContext &ruleContext, Context &context, size_t &headVariableIndex)
 	{
 		if (literal.sign == Clingo::AST::Sign::DoubleNegation)
 			throw TranslationException(literal.location, "double-negated head literals currently unsupported");
 
-		auto translatedLiteral = literal.data.accept(LiteralTranslateVisitor(), literal, ruleContext, headVariableIndex);
+		auto translatedLiteral = literal.data.accept(LiteralTranslateVisitor(), literal, ruleContext, context, headVariableIndex);
 
 		if (literal.sign == Clingo::AST::Sign::None)
 			return translatedLiteral;
@@ -183,7 +185,7 @@ struct HeadLiteralTranslateToConsequentVisitor
 		return ast::Formula::make<ast::Not>(std::move(translatedLiteral.value()));
 	}
 
-	std::optional<ast::Formula> visit(const Clingo::AST::Disjunction &disjunction, const Clingo::AST::HeadLiteral &headLiteral, RuleContext &ruleContext, size_t &headVariableIndex)
+	std::optional<ast::Formula> visit(const Clingo::AST::Disjunction &disjunction, const Clingo::AST::HeadLiteral &headLiteral, RuleContext &ruleContext, Context &context, size_t &headVariableIndex)
 	{
 		std::vector<ast::Formula> arguments;
 		arguments.reserve(disjunction.elements.size());
@@ -193,7 +195,7 @@ struct HeadLiteralTranslateToConsequentVisitor
 			if (!conditionalLiteral.condition.empty())
 				throw TranslationException(headLiteral.location, "conditional head literals currently unsupported");
 
-			auto argument = visit(conditionalLiteral.literal, headLiteral, ruleContext, headVariableIndex);
+			auto argument = visit(conditionalLiteral.literal, headLiteral, ruleContext, context, headVariableIndex);
 
 			if (!argument)
 				throw TranslationException(headLiteral.location, "could not parse argument");
@@ -204,7 +206,7 @@ struct HeadLiteralTranslateToConsequentVisitor
 		return ast::Formula::make<ast::Or>(std::move(arguments));
 	}
 
-	std::optional<ast::Formula> visit(const Clingo::AST::Aggregate &aggregate, const Clingo::AST::HeadLiteral &headLiteral, RuleContext &ruleContext, size_t &headVariableIndex)
+	std::optional<ast::Formula> visit(const Clingo::AST::Aggregate &aggregate, const Clingo::AST::HeadLiteral &headLiteral, RuleContext &ruleContext, Context &context, size_t &headVariableIndex)
 	{
 		if (aggregate.left_guard || aggregate.right_guard)
 			throw TranslationException(headLiteral.location, "aggregates with left or right guards currently unsupported");
@@ -215,7 +217,7 @@ struct HeadLiteralTranslateToConsequentVisitor
 				if (!conditionalLiteral.condition.empty())
 					throw TranslationException(headLiteral.location, "conditional head literals currently unsupported");
 
-				return this->visit(conditionalLiteral.literal, headLiteral, ruleContext, headVariableIndex);
+				return this->visit(conditionalLiteral.literal, headLiteral, ruleContext, context, headVariableIndex);
 			};
 
 		if (aggregate.elements.size() == 1)
@@ -238,7 +240,7 @@ struct HeadLiteralTranslateToConsequentVisitor
 	}
 
 	template<class T>
-	std::optional<ast::Formula> visit(const T &, const Clingo::AST::HeadLiteral &headLiteral, RuleContext &, size_t &)
+	std::optional<ast::Formula> visit(const T &, const Clingo::AST::HeadLiteral &headLiteral, RuleContext &, Context &, size_t &)
 	{
 		throw TranslationException(headLiteral.location, "head literal currently unsupported in this context, expected literal, disjunction, or aggregate");
 		return std::nullopt;

include/anthem/HiddenPredicateElimination.h

@@ -13,7 +13,7 @@ namespace anthem
 //
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
-void eliminateHiddenPredicates(const std::vector<ast::PredicateSignature> &predicateSignatures, std::vector<ast::Formula> &completedFormulas, Context &context);
+void eliminateHiddenPredicates(std::vector<ast::Formula> &completedFormulas, Context &context);
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 

include/anthem/StatementVisitor.h

@@ -73,7 +73,7 @@ struct StatementVisitor
 
 		// Compute consequent
 		auto headVariableIndex = ruleContext.headVariablesStartIndex;
-		auto consequent = rule.head.data.accept(HeadLiteralTranslateToConsequentVisitor(), rule.head, ruleContext, headVariableIndex);
+		auto consequent = rule.head.data.accept(HeadLiteralTranslateToConsequentVisitor(), rule.head, ruleContext, context, headVariableIndex);
 
 		assert(ruleContext.headTerms.size() == headVariableIndex - ruleContext.headVariablesStartIndex);
 
@@ -98,7 +98,7 @@ struct StatementVisitor
 		{
 			const auto &bodyLiteral = *i;
 
-			auto argument = bodyLiteral.data.accept(BodyBodyLiteralTranslateVisitor(), bodyLiteral, ruleContext, variableStack);
+			auto argument = bodyLiteral.data.accept(BodyBodyLiteralTranslateVisitor(), bodyLiteral, ruleContext, context, variableStack);
 
 			if (!argument)
 				throw TranslationException(bodyLiteral.location, "could not translate body literal");
@@ -165,8 +165,8 @@ struct StatementVisitor
 		if (signature.negative())
 			throw LogicException(statement.location, "negative #show atom signatures are currently unsupported");
 
-		if (!context.visiblePredicateSignatures)
+		context.showStatementsUsed = true;
-			context.visiblePredicateSignatures.emplace();
+		context.defaultPredicateVisibility = ast::PredicateDeclaration::Visibility::Hidden;
 
 		if (std::strlen(signature.name()) == 0)
 		{
@@ -176,8 +176,8 @@ struct StatementVisitor
 
 		context.logger.log(output::Priority::Debug, statement.location) << "showing “" << signature.name() << "/" << signature.arity() << "”";
 
-		auto predicateSignature = ast::PredicateSignature{std::string(signature.name()), signature.arity()};
+		auto predicateDeclaration = context.findOrCreatePredicateDeclaration(signature.name(), signature.arity());
-		context.visiblePredicateSignatures.value().emplace_back(PredicateSignatureMeta{std::move(predicateSignature)});
+		predicateDeclaration->visibility = ast::PredicateDeclaration::Visibility::Visible;
 	}
 
 	void visit(const Clingo::AST::ShowTerm &, const Clingo::AST::Statement &statement, std::vector<ast::ScopedFormula> &, Context &)
@@ -214,13 +214,12 @@ struct StatementVisitor
 		if (aritySymbol.type() != Clingo::SymbolType::Number)
 			fail();
 
+		context.externalStatementsUsed = true;
+
 		const size_t arity = aritySymbol.number();
 
-		if (!context.externalPredicateSignatures)
+		auto predicateDeclaration = context.findOrCreatePredicateDeclaration(predicate.name, arity);
-			context.externalPredicateSignatures.emplace();
+		predicateDeclaration->isExternal = true;
-
-		auto predicateSignature = ast::PredicateSignature{std::string(predicate.name), arity};
-		context.externalPredicateSignatures->emplace_back(PredicateSignatureMeta{std::move(predicateSignature)});
 	}
 
 	template<class T>

include/anthem/output/AST.h

@@ -51,6 +51,7 @@ output::ColorStream &print(output::ColorStream &stream, const In &in, PrintConte
 output::ColorStream &print(output::ColorStream &stream, const Integer &integer, PrintContext &printContext, bool omitParentheses = false);
 output::ColorStream &print(output::ColorStream &stream, const Interval &interval, PrintContext &printContext, bool omitParentheses = false);
 output::ColorStream &print(output::ColorStream &stream, const Predicate &predicate, PrintContext &printContext, bool omitParentheses = false);
+output::ColorStream &print(output::ColorStream &stream, const PredicateDeclaration &predicateDeclaration, PrintContext &printContext, bool omitParentheses = false);
 output::ColorStream &print(output::ColorStream &stream, const SpecialInteger &specialInteger, PrintContext &printContext, bool omitParentheses = false);
 output::ColorStream &print(output::ColorStream &stream, const String &string, PrintContext &printContext, bool omitParentheses = false);
 output::ColorStream &print(output::ColorStream &stream, const UnaryOperation &unaryOperation, PrintContext &printContext, bool omitParentheses = false);
@@ -236,7 +237,7 @@ inline output::ColorStream &print(output::ColorStream &stream, const Interval &i
 
 inline output::ColorStream &print(output::ColorStream &stream, const Predicate &predicate, PrintContext &printContext, bool)
 {
-	stream << predicate.name;
+	stream << predicate.declaration->name;
 
 	if (predicate.arguments.empty())
 		return stream;
@@ -258,6 +259,13 @@ inline output::ColorStream &print(output::ColorStream &stream, const Predicate &
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
+inline output::ColorStream &print(output::ColorStream &stream, const PredicateDeclaration &predicateDeclaration, PrintContext &, bool)
+{
+	return (stream << predicateDeclaration.name << "/" << predicateDeclaration.arity);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
 inline output::ColorStream &print(output::ColorStream &stream, const SpecialInteger &specialInteger, PrintContext &, bool)
 {
 	switch (specialInteger.type)

src/anthem/ASTCopy.cpp

@@ -133,7 +133,7 @@ Interval prepareCopy(const Interval &other)
 
 Predicate prepareCopy(const Predicate &other)
 {
-	return Predicate(std::string(other.name), prepareCopy(other.arguments));
+	return Predicate(other.declaration, prepareCopy(other.arguments));
 }
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////

src/anthem/ASTUtils.cpp

@@ -193,84 +193,5 @@ struct CollectFreeVariablesVisitor
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
-struct CollectPredicateSignaturesVisitor : public RecursiveFormulaVisitor<CollectPredicateSignaturesVisitor>
-{
-	static void accept(const Predicate &predicate, const Formula &, std::vector<PredicateSignature> &predicateSignatures, Context &context)
-	{
-		const auto predicateSignatureMatches =
-			[&predicate](const auto &predicateSignature)
-			{
-				return matches(predicate, predicateSignature);
-			};
-
-		if (std::find_if(predicateSignatures.cbegin(), predicateSignatures.cend(), predicateSignatureMatches) != predicateSignatures.cend())
-			return;
-
-		// TODO: avoid copies
-		auto predicateSignature = PredicateSignature(std::string(predicate.name), predicate.arity());
-
-		// Ignore predicates that are declared #external
-		if (context.externalPredicateSignatures)
-		{
-			const auto matchesPredicateSignature =
-				[&](const auto &otherPredicateSignature)
-				{
-					return ast::matches(predicateSignature, otherPredicateSignature.predicateSignature);
-				};
-
-			auto &externalPredicateSignatures = context.externalPredicateSignatures.value();
-
-			const auto matchingExternalPredicateSignature =
-				std::find_if(externalPredicateSignatures.begin(), externalPredicateSignatures.end(), matchesPredicateSignature);
-
-			if (matchingExternalPredicateSignature != externalPredicateSignatures.end())
-			{
-				matchingExternalPredicateSignature->used = true;
-				return;
-			}
-		}
-
-		predicateSignatures.emplace_back(std::move(predicateSignature));
-	}
-
-	// Ignore all other types of expressions
-	template<class T>
-	static void accept(const T &, const Formula &, std::vector<PredicateSignature> &, const Context &)
-	{
-	}
-};
-
-////////////////////////////////////////////////////////////////////////////////////////////////////
-
-bool matches(const Predicate &lhs, const Predicate &rhs)
-{
-	return (lhs.name == rhs.name && lhs.arity() == rhs.arity());
-}
-
-////////////////////////////////////////////////////////////////////////////////////////////////////
-
-bool matches(const Predicate &predicate, const PredicateSignature &signature)
-{
-	return (predicate.name == signature.name && predicate.arity() == signature.arity);
-}
-
-////////////////////////////////////////////////////////////////////////////////////////////////////
-
-bool matches(const PredicateSignature &lhs, const PredicateSignature &rhs)
-{
-	return (lhs.name == rhs.name && lhs.arity == rhs.arity);
-}
-
-////////////////////////////////////////////////////////////////////////////////////////////////////
-
-// TODO: remove const_cast
-void collectPredicateSignatures(const Formula &formula, std::vector<PredicateSignature> &predicateSignatures, Context &context)
-{
-	auto &formulaMutable = const_cast<Formula &>(formula);
-	formulaMutable.accept(CollectPredicateSignaturesVisitor(), formulaMutable, predicateSignatures, context);
-}
-
-////////////////////////////////////////////////////////////////////////////////////////////////////
-
 }
 }

src/anthem/Completion.cpp

@@ -35,7 +35,7 @@ ast::Formula buildCompletedFormulaDisjunction(const ast::Predicate &predicate, c
 
 		auto &otherPredicate = implies.consequent.get<ast::Predicate>();
 
-		if (!ast::matches(predicate, otherPredicate))
+		if (predicate.declaration != otherPredicate.declaration)
 			continue;
 
 		assert(otherPredicate.arguments.size() == parameters.size());
@@ -100,22 +100,22 @@ ast::Formula buildCompletedFormulaQuantified(ast::Predicate &&predicate, ast::Fo
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
-ast::Formula completePredicate(const ast::PredicateSignature &predicateSignature, std::vector<ast::ScopedFormula> &scopedFormulas)
+ast::Formula completePredicate(ast::PredicateDeclaration &predicateDeclaration, std::vector<ast::ScopedFormula> &scopedFormulas)
 {
 	// Create new set of parameters for the completed definition for the predicate
 	ast::VariableDeclarationPointers parameters;
-	parameters.reserve(predicateSignature.arity);
+	parameters.reserve(predicateDeclaration.arity);
 
 	std::vector<ast::Term> arguments;
-	arguments.reserve(predicateSignature.arity);
+	arguments.reserve(predicateDeclaration.arity);
 
-	for (size_t i = 0; i < predicateSignature.arity; i++)
+	for (size_t i = 0; i < predicateDeclaration.arity; i++)
 	{
 		parameters.emplace_back(std::make_unique<ast::VariableDeclaration>(ast::VariableDeclaration::Type::Head));
 		arguments.emplace_back(ast::Term::make<ast::Variable>(parameters.back().get()));
 	}
 
-	ast::Predicate predicateCopy(std::string(predicateSignature.name), std::move(arguments));
+	ast::Predicate predicateCopy(&predicateDeclaration, std::move(arguments));
 
 	auto completedFormulaDisjunction = buildCompletedFormulaDisjunction(predicateCopy, parameters, scopedFormulas);
 	auto completedFormulaQuantified = buildCompletedFormulaQuantified(std::move(predicateCopy), std::move(completedFormulaDisjunction));
@@ -161,28 +161,27 @@ std::vector<ast::Formula> complete(std::vector<ast::ScopedFormula> &&scopedFormu
 			throw CompletionException("cannot perform completion, only single predicates and Booleans supported as formula consequent currently");
 	}
 
-	std::vector<ast::PredicateSignature> predicateSignatures;
+	std::sort(context.predicateDeclarations.begin(), context.predicateDeclarations.end(),
-
-	// Get a list of all predicates
-	for (const auto &scopedFormula : scopedFormulas)
-		ast::collectPredicateSignatures(scopedFormula.formula, predicateSignatures, context);
-
-	std::sort(predicateSignatures.begin(), predicateSignatures.end(),
 		[](const auto &lhs, const auto &rhs)
 		{
-			const auto order = std::strcmp(lhs.name.c_str(), rhs.name.c_str());
+			const auto order = std::strcmp(lhs->name.c_str(), rhs->name.c_str());
 
 			if (order != 0)
 				return (order < 0);
 
-			return lhs.arity < rhs.arity;
+			return lhs->arity < rhs->arity;
 		});
 
 	std::vector<ast::Formula> completedFormulas;
 
 	// Complete predicates
-	for (const auto &predicateSignature : predicateSignatures)
+	for (auto &predicateDeclaration : context.predicateDeclarations)
-		completedFormulas.emplace_back(completePredicate(predicateSignature, scopedFormulas));
+	{
+		if (!predicateDeclaration->isUsed || predicateDeclaration->isExternal)
+			continue;
+
+		completedFormulas.emplace_back(completePredicate(*predicateDeclaration, scopedFormulas));
+	}
 
 	// Complete integrity constraints
 	for (auto &scopedFormula : scopedFormulas)
@@ -202,7 +201,7 @@ std::vector<ast::Formula> complete(std::vector<ast::ScopedFormula> &&scopedFormu
 	}
 
 	// Eliminate all predicates that should not be visible in the output
-	eliminateHiddenPredicates(predicateSignatures, completedFormulas, context);
+	eliminateHiddenPredicates(completedFormulas, context);
 
 	return completedFormulas;
 }

src/anthem/HiddenPredicateElimination.cpp

@@ -78,7 +78,7 @@ struct ReplacePredicateInFormulaVisitor : public ast::RecursiveFormulaVisitor<Re
 {
 	static void accept(ast::Predicate &predicate, ast::Formula &formula, const PredicateReplacement &predicateReplacement)
 	{
-		if (!ast::matches(predicate, predicateReplacement.predicate))
+		if (predicate.declaration != predicateReplacement.predicate.declaration)
 			return;
 
 		auto formulaReplacement = ast::prepareCopy(predicateReplacement.replacement);
@@ -109,15 +109,15 @@ struct ReplacePredicateInFormulaVisitor : public ast::RecursiveFormulaVisitor<Re
 // Detect whether a formula contains a circular dependency on a given predicate
 struct DetectCircularDependcyVisitor : public ast::RecursiveFormulaVisitor<DetectCircularDependcyVisitor>
 {
-	static void accept(ast::Predicate &predicate, ast::Formula &, const ast::PredicateSignature &predicateSignature, bool &hasCircularDependency)
+	static void accept(ast::Predicate &predicate, ast::Formula &, const ast::PredicateDeclaration &predicateDeclaration, bool &hasCircularDependency)
 	{
-		if (ast::matches(predicate, predicateSignature))
+		if (predicate.declaration == &predicateDeclaration)
 			hasCircularDependency = true;
 	}
 
 	// Ignore all other types of expressions
 	template<class T>
-	static void accept(T &, ast::Formula &, const ast::PredicateSignature &, bool &)
+	static void accept(T &, ast::Formula &, const ast::PredicateDeclaration &, bool &)
 	{
 	}
 };
@@ -125,12 +125,12 @@ struct DetectCircularDependcyVisitor : public ast::RecursiveFormulaVisitor<Detec
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
 // Finds the replacement for predicates of the form “p(X1, ..., Xn) <-> q(X1, ..., Xn)”
-PredicateReplacement findReplacement(const ast::PredicateSignature &predicateSignature, const ast::Predicate &predicate)
+PredicateReplacement findReplacement(const ast::PredicateDeclaration &predicateDeclaration, const ast::Predicate &predicate)
 {
 	// Declare variable used, only used in debug mode
-	(void)(predicateSignature);
+	(void)(predicateDeclaration);
 
-	assert(ast::matches(predicate, predicateSignature));
+	assert(predicate.declaration == &predicateDeclaration);
 
 	// Replace with “#true”
 	return {predicate, ast::Formula::make<ast::Boolean>(true)};
@@ -139,13 +139,13 @@ PredicateReplacement findReplacement(const ast::PredicateSignature &predicateSig
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
 // Finds the replacement for predicates of the form “p(X1, ..., Xn) <-> not q(X1, ..., Xn)”
-PredicateReplacement findReplacement(const ast::PredicateSignature &predicateSignature, const ast::Not &not_)
+PredicateReplacement findReplacement(const ast::PredicateDeclaration &predicateDeclaration, const ast::Not &not_)
 {
 	// Declare variable used, only used in debug mode
-	(void)(predicateSignature);
+	(void)(predicateDeclaration);
 
 	assert(not_.argument.is<ast::Predicate>());
-	assert(ast::matches(not_.argument.get<ast::Predicate>(), predicateSignature));
+	assert(not_.argument.get<ast::Predicate>().declaration == &predicateDeclaration);
 
 	// Replace with “#false”
 	return {not_.argument.get<ast::Predicate>(), ast::Formula::make<ast::Boolean>(false)};
@@ -154,13 +154,13 @@ PredicateReplacement findReplacement(const ast::PredicateSignature &predicateSig
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
 // Finds the replacement for predicates of the form “forall X1, ..., Xn (p(X1, ..., Xn) <-> ...)”
-PredicateReplacement findReplacement(const ast::PredicateSignature &predicateSignature, const ast::Biconditional &biconditional)
+PredicateReplacement findReplacement(const ast::PredicateDeclaration &predicateDeclaration, const ast::Biconditional &biconditional)
 {
 	// Declare variable used, only used in debug mode
-	(void)(predicateSignature);
+	(void)(predicateDeclaration);
 
 	assert(biconditional.left.is<ast::Predicate>());
-	assert(ast::matches(biconditional.left.get<ast::Predicate>(), predicateSignature));
+	assert(biconditional.left.get<ast::Predicate>().declaration == &predicateDeclaration);
 
 	// TODO: avoid copy
 	return {biconditional.left.get<ast::Predicate>(), ast::prepareCopy(biconditional.right)};
@@ -169,77 +169,65 @@ PredicateReplacement findReplacement(const ast::PredicateSignature &predicateSig
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
 // Finds a replacement for a predicate that should be hidden
-PredicateReplacement findReplacement(const ast::PredicateSignature &predicateSignature, const ast::Formula &completedPredicateDefinition)
+PredicateReplacement findReplacement(const ast::PredicateDeclaration &predicateDeclaration, const ast::Formula &completedPredicateDefinition)
 {
 	// TODO: refactor
 	if (completedPredicateDefinition.is<ast::ForAll>())
-		return findReplacement(predicateSignature, completedPredicateDefinition.get<ast::ForAll>().argument);
+		return findReplacement(predicateDeclaration, completedPredicateDefinition.get<ast::ForAll>().argument);
 	else if (completedPredicateDefinition.is<ast::Biconditional>())
-		return findReplacement(predicateSignature, completedPredicateDefinition.get<ast::Biconditional>());
+		return findReplacement(predicateDeclaration, completedPredicateDefinition.get<ast::Biconditional>());
 	else if (completedPredicateDefinition.is<ast::Predicate>())
-		return findReplacement(predicateSignature, completedPredicateDefinition.get<ast::Predicate>());
+		return findReplacement(predicateDeclaration, completedPredicateDefinition.get<ast::Predicate>());
 	else if (completedPredicateDefinition.is<ast::Not>())
-		return findReplacement(predicateSignature, completedPredicateDefinition.get<ast::Not>());
+		return findReplacement(predicateDeclaration, completedPredicateDefinition.get<ast::Not>());
 
-	throw CompletionException("unsupported completed definition for predicate “" + predicateSignature.name + "/" +  std::to_string(predicateSignature.arity) + "” for hiding predicates");
+	throw CompletionException("unsupported completed definition for predicate “" + predicateDeclaration.name + "/" +  std::to_string(predicateDeclaration.arity) + "” for hiding predicates");
 }
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
-void eliminateHiddenPredicates(const std::vector<ast::PredicateSignature> &predicateSignatures, std::vector<ast::Formula> &completedFormulas, Context &context)
+void eliminateHiddenPredicates(std::vector<ast::Formula> &completedFormulas, Context &context)
 {
-	if (!context.visiblePredicateSignatures)
+	if (context.defaultPredicateVisibility == ast::PredicateDeclaration::Visibility::Visible)
 	{
 		context.logger.log(output::Priority::Debug) << "no predicates to be eliminated";
 		return;
 	}
 
-	auto &visiblePredicateSignatures = context.visiblePredicateSignatures.value();
+	assert(context.defaultPredicateVisibility == ast::PredicateDeclaration::Visibility::Hidden);
+
+	// TODO: get rid of index-wise matching of completed formulas and predicate declarations
+	size_t i = -1;
 
 	// Replace all occurrences of hidden predicates
-	for (size_t i = 0; i < predicateSignatures.size(); i++)
+	for (auto &predicateDeclaration : context.predicateDeclarations)
 	{
-		auto &predicateSignature = predicateSignatures[i];
+		// Check that the predicate is used and not declared #external
+		if (!predicateDeclaration->isUsed || predicateDeclaration->isExternal)
+			continue;
 
-		const auto matchesPredicateSignature =
+		i++;
-			[&](const auto &otherPredicateSignature)
-			{
-				return ast::matches(predicateSignature, otherPredicateSignature.predicateSignature);
-			};
 
-		const auto matchingVisiblePredicateSignature =
+		const auto isPredicateVisible =
-			std::find_if(visiblePredicateSignatures.begin(), visiblePredicateSignatures.end(), matchesPredicateSignature);
+			(predicateDeclaration->visibility == ast::PredicateDeclaration::Visibility::Visible)
+			|| (predicateDeclaration->visibility == ast::PredicateDeclaration::Visibility::Default
+				&& context.defaultPredicateVisibility == ast::PredicateDeclaration::Visibility::Visible);
 
 		// If the predicate ought to be visible, don’t eliminate it
-		if (matchingVisiblePredicateSignature != visiblePredicateSignatures.end())
+		if (isPredicateVisible)
-		{
-			matchingVisiblePredicateSignature->used = true;
 			continue;
-		}
 
-		// Check that the predicate is not declared #external
+		context.logger.log(output::Priority::Debug) << "eliminating “" << predicateDeclaration->name << "/" << predicateDeclaration->arity << "”";
-		if (context.externalPredicateSignatures)
-		{
-			const auto &externalPredicateSignatures = context.externalPredicateSignatures.value();
-
-			const auto matchingExternalPredicateSignature =
-				std::find_if(externalPredicateSignatures.cbegin(), externalPredicateSignatures.cend(), matchesPredicateSignature);
-
-			if (matchingExternalPredicateSignature != externalPredicateSignatures.cend())
-				continue;
-		}
-
-		context.logger.log(output::Priority::Debug) << "eliminating “" << predicateSignature.name << "/" << predicateSignature.arity << "”";
 
 		const auto &completedPredicateDefinition = completedFormulas[i];
-		auto replacement = findReplacement(predicateSignature, completedPredicateDefinition);
+		auto replacement = findReplacement(*predicateDeclaration, completedPredicateDefinition);
 
 		bool hasCircularDependency = false;
-		replacement.replacement.accept(DetectCircularDependcyVisitor(), replacement.replacement, predicateSignature, hasCircularDependency);
+		replacement.replacement.accept(DetectCircularDependcyVisitor(), replacement.replacement, *predicateDeclaration, hasCircularDependency);
 
 		if (hasCircularDependency)
 		{
-			context.logger.log(output::Priority::Warning) << "cannot hide predicate “" << predicateSignature.name << "/" << predicateSignature.arity << "” due to circular dependency";
+			context.logger.log(output::Priority::Warning) << "cannot hide predicate “" << predicateDeclaration->name << "/" << predicateDeclaration->arity << "” due to circular dependency";
 			continue;
 		}
 

src/anthem/Translation.cpp

@@ -67,10 +67,10 @@ void translate(const char *fileName, std::istream &stream, Context &context)
 			for (auto &scopedFormula : scopedFormulas)
 				simplify(scopedFormula.formula);
 
-		if (context.visiblePredicateSignatures)
+		if (context.showStatementsUsed)
 			context.logger.log(output::Priority::Warning) << "#show statements are ignored because completion is not enabled";
 
-		if (context.externalPredicateSignatures)
+		if (context.externalStatementsUsed)
 			context.logger.log(output::Priority::Warning) << "#external statements are ignored because completion is not enabled";
 
 		for (const auto &scopedFormula : scopedFormulas)
@@ -85,25 +85,29 @@ void translate(const char *fileName, std::istream &stream, Context &context)
 	// Perform completion
 	auto completedFormulas = complete(std::move(scopedFormulas), context);
 
+	for (const auto &predicateDeclaration : context.predicateDeclarations)
+	{
+		if (predicateDeclaration->isUsed)
+			continue;
+
 		// Check for #show statements with undeclared predicates
-	if (context.visiblePredicateSignatures)
+		if (predicateDeclaration->visibility != ast::PredicateDeclaration::Visibility::Default)
-		for (const auto &predicateSignature : context.visiblePredicateSignatures.value())
-			if (!predicateSignature.used)
 			context.logger.log(output::Priority::Warning)
 				<< "#show declaration of “"
-					<< predicateSignature.predicateSignature.name
+				<< predicateDeclaration->name
-					<< "/" << predicateSignature.predicateSignature.arity
+				<< "/"
-					<< "” does not match any eligible predicate";
+				<< predicateDeclaration->arity
+				<< "” does not match any declared predicate";
 
 		// Check for #external statements with undeclared predicates
-	if (context.externalPredicateSignatures)
+		if (predicateDeclaration->isExternal && !predicateDeclaration->isUsed)
-		for (const auto &predicateSignature : context.externalPredicateSignatures.value())
-			if (!predicateSignature.used)
 			context.logger.log(output::Priority::Warning)
 				<< "#external declaration of “"
-					<< predicateSignature.predicateSignature.name
+				<< predicateDeclaration->name
-					<< "/" << predicateSignature.predicateSignature.arity
+				<< "/"
-					<< "” does not match any eligible predicate";
+				<< predicateDeclaration->arity
+				<< "” does not match any declared predicate";
+	}
 
 	// Simplify output if specified
 	if (context.performSimplification)