Provide function for evaluating formulas

This provides a new function that can be used to evaluate formulas under
partial knowledge about the individual variables’ assignments.

This will be useful for testing whether formulas or subformulas become
trivial under specific interpretations.

include/anthem/ASTUtils.h

@@ -90,6 +90,21 @@ struct ReplaceVariableInFormulaVisitor : public RecursiveFormulaVisitor<ReplaceV
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
 }
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Accessing Variable Domains
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+struct DefaultVariableDomainAccessor
+{
+	Domain operator()(const ast::Variable &variable)
+	{
+		return variable.declaration->domain;
+	}
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
 }
 
 #endif

include/anthem/Evaluation.h

@@ -0,0 +1,244 @@
+#ifndef __ANTHEM__EVALUATION_H
+#define __ANTHEM__EVALUATION_H
+
+#include <anthem/AST.h>
+#include <anthem/ASTUtils.h>
+#include <anthem/Utils.h>
+
+namespace anthem
+{
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+//
+// Evaluation
+//
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+template <class VariableDomainAccessor = DefaultVariableDomainAccessor>
+struct EvaluateFormulaVisitor
+{
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::And &and_, Arguments &&... arguments)
+	{
+		bool someFalse = false;
+		bool someUnknown = false;
+
+		for (const auto &argument : and_.arguments)
+		{
+			const auto result = evaluate(argument, std::forward<Arguments>(arguments)...);
+
+			switch (result)
+			{
+				case EvaluationResult::Error:
+					return EvaluationResult::Error;
+				case EvaluationResult::True:
+					break;
+				case EvaluationResult::False:
+					someFalse = true;
+					break;
+				case EvaluationResult::Unknown:
+					someUnknown = true;
+					break;
+			}
+		}
+
+		if (someFalse)
+			return EvaluationResult::False;
+
+		if (someUnknown)
+			return EvaluationResult::Unknown;
+
+		return EvaluationResult::True;
+	}
+
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::Biconditional &biconditional, Arguments &&... arguments)
+	{
+		const auto leftResult = evaluate(biconditional.left, std::forward<Arguments>(arguments)...);
+		const auto rightResult = evaluate(biconditional.right, std::forward<Arguments>(arguments)...);
+
+		if (leftResult == EvaluationResult::Error || rightResult == EvaluationResult::Error)
+			return EvaluationResult::Error;
+
+		if (leftResult == EvaluationResult::Unknown || rightResult == EvaluationResult::Unknown)
+			return EvaluationResult::Unknown;
+
+		return (leftResult == rightResult ? EvaluationResult::True : EvaluationResult::False);
+	}
+
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::Boolean &boolean, Arguments &&...)
+	{
+		return (boolean.value == true ? EvaluationResult::True : EvaluationResult::False);
+	}
+
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::Comparison &comparison, Arguments &&... arguments)
+	{
+		const auto leftType = type(comparison.left, std::forward<Arguments>(arguments)...);
+		const auto rightType = type(comparison.right, std::forward<Arguments>(arguments)...);
+
+		// Comparisons with empty sets always return false
+		if (leftType.setSize == SetSize::Empty || rightType.setSize == SetSize::Empty)
+			return EvaluationResult::False;
+
+		// If either side has an unknown domain, the result is unknown
+		if (leftType.domain == Domain::Unknown || rightType.domain == Domain::Unknown)
+			return EvaluationResult::Unknown;
+
+		// If both sides have the same domain, the result is unknown
+		if (leftType.domain == rightType.domain)
+			return EvaluationResult::Unknown;
+
+		// If one side is integer, but the other one isn’t, they are not equal
+		switch (comparison.operator_)
+		{
+			case ast::Comparison::Operator::Equal:
+				return EvaluationResult::False;
+			case ast::Comparison::Operator::NotEqual:
+				return EvaluationResult::True;
+			default:
+				// TODO: implement more cases
+				return EvaluationResult::Unknown;
+		}
+	}
+
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::Exists &exists, Arguments &&... arguments)
+	{
+		return evaluate(exists.argument, std::forward<Arguments>(arguments)...);
+	}
+
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::ForAll &forAll, Arguments &&... arguments)
+	{
+		return evaluate(forAll.argument, std::forward<Arguments>(arguments)...);
+	}
+
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::Implies &implies, Arguments &&... arguments)
+	{
+		const auto antecedentResult = evaluate(implies.antecedent, std::forward<Arguments>(arguments)...);
+		const auto consequentResult = evaluate(implies.consequent, std::forward<Arguments>(arguments)...);
+
+		if (antecedentResult == EvaluationResult::Error || consequentResult == EvaluationResult::Error)
+			return EvaluationResult::Error;
+
+		if (antecedentResult == EvaluationResult::False)
+			return EvaluationResult::True;
+
+		if (consequentResult == EvaluationResult::True)
+			return EvaluationResult::True;
+
+		if (antecedentResult == EvaluationResult::True && consequentResult == EvaluationResult::False)
+			return EvaluationResult::False;
+
+		return EvaluationResult::Unknown;
+	}
+
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::In &in, Arguments &&... arguments)
+	{
+		const auto elementType = type(in.element, std::forward<Arguments>(arguments)...);
+		const auto setType = type(in.set, std::forward<Arguments>(arguments)...);
+
+		// The element to test shouldn’t be empty or a proper set by itself
+		assert(elementType.setSize != SetSize::Empty && elementType.setSize != SetSize::Multi);
+
+		// If the set is empty, no element can be selected
+		if (setType.setSize == SetSize::Empty)
+			return EvaluationResult::False;
+
+		// If one of the sides has an unknown type, the result is unknown
+		if (elementType.domain == Domain::Unknown || setType.domain == Domain::Unknown)
+			return EvaluationResult::Unknown;
+
+		// If both sides have the same domain, the result is unknown
+		if (elementType.domain == setType.domain)
+			return EvaluationResult::Unknown;
+
+		// If one side is integer, but the other one isn’t, set inclusion is never satisfied
+		return EvaluationResult::False;
+	}
+
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::Not &not_, Arguments &&... arguments)
+	{
+		const auto result = evaluate(not_.argument, std::forward<Arguments>(arguments)...);
+
+		if (result == EvaluationResult::Error || result == EvaluationResult::Unknown)
+			return result;
+
+		return (result == EvaluationResult::True ? EvaluationResult::False : EvaluationResult::True);
+	}
+
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::Or &or_, Arguments &&... arguments)
+	{
+		bool someTrue = false;
+		bool someUnknown = false;
+
+		for (const auto &argument : or_.arguments)
+		{
+			const auto result = evaluate(argument, std::forward<Arguments>(arguments)...);
+
+			switch (result)
+			{
+				case EvaluationResult::Error:
+					return EvaluationResult::Error;
+				case EvaluationResult::True:
+					someTrue = true;
+					break;
+				case EvaluationResult::False:
+					break;
+				case EvaluationResult::Unknown:
+					someUnknown = true;
+					break;
+			}
+		}
+
+		if (someTrue)
+			return EvaluationResult::True;
+
+		if (someUnknown)
+			return EvaluationResult::Unknown;
+
+		return EvaluationResult::False;
+	}
+
+	template <class... Arguments>
+	static EvaluationResult visit(const ast::Predicate &predicate, Arguments &&... arguments)
+	{
+		assert(predicate.arguments.size() == predicate.declaration->arity());
+
+		for (size_t i = 0; i < predicate.arguments.size(); i++)
+		{
+			const auto &argument = predicate.arguments[i];
+			const auto &parameter = predicate.declaration->parameters[i];
+
+			if (parameter.domain != Domain::Integer)
+				continue;
+
+			const auto argumentType = type(argument, std::forward<Arguments>(arguments)...);
+
+			if (argumentType.domain == Domain::Noninteger || argumentType.setSize == SetSize::Empty)
+				return EvaluationResult::Error;
+		}
+
+		return EvaluationResult::Unknown;
+	}
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+template <class VariableDomainAccessor = DefaultVariableDomainAccessor, class... Arguments>
+EvaluationResult evaluate(const ast::Formula &formula, Arguments &&... arguments)
+{
+	return formula.accept(EvaluateFormulaVisitor<VariableDomainAccessor>(), std::forward<Arguments>(arguments)...);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+}
+
+#endif

include/anthem/Type.h

@@ -2,6 +2,7 @@
 #define __ANTHEM__TYPE_H
 
 #include <anthem/AST.h>
+#include <anthem/ASTUtils.h>
 #include <anthem/Utils.h>
 
 namespace anthem
@@ -13,16 +14,6 @@ namespace anthem
 //
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
-struct DefaultVariableDomainAccessor
-{
-	Domain operator()(const ast::Variable &variable)
-	{
-		return variable.declaration->domain;
-	}
-};
-
-////////////////////////////////////////////////////////////////////////////////////////////////////
-
 template <class VariableDomainAccessor = DefaultVariableDomainAccessor, class... Arguments>
 Type type(const ast::Term &term, Arguments &&... arguments);
 

include/anthem/Utils.h

@@ -33,6 +33,16 @@ enum class OperationResult
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
+enum class EvaluationResult
+{
+	True,
+	False,
+	Unknown,
+	Error,
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
 enum class Domain
 {
 	Noninteger,