Add new simplification rule

This adds the rule “(F <-> (F and G)) === (F -> G)” to the
simplification rule tableau.

include/anthem/Equality.h

@@ -0,0 +1,417 @@
+#ifndef __ANTHEM__EQUALITY_H
+#define __ANTHEM__EQUALITY_H
+
+#include <anthem/AST.h>
+#include <anthem/ASTUtils.h>
+
+namespace anthem
+{
+namespace ast
+{
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+//
+// Equality
+//
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+// TODO: move to separate class
+enum class Tristate
+{
+	True,
+	False,
+	Unknown,
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+Tristate equal(const Formula &lhs, const Formula &rhs);
+Tristate equal(const Term &lhs, const Term &rhs);
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+struct FormulaEqualityVisitor
+{
+	Tristate visit(const And &and_, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<And>())
+			return Tristate::Unknown;
+
+		const auto &otherAnd = otherFormula.get<And>();
+
+		for (const auto &argument : and_.arguments)
+		{
+			const auto match = std::find_if(
+				otherAnd.arguments.cbegin(), otherAnd.arguments.cend(),
+				[&](const auto &otherArgument)
+				{
+					return equal(argument, otherArgument) == Tristate::True;
+				});
+
+			if (match == otherAnd.arguments.cend())
+				return Tristate::Unknown;
+		}
+
+		for (const auto &otherArgument : otherAnd.arguments)
+		{
+			const auto match = std::find_if(
+				and_.arguments.cbegin(), and_.arguments.cend(),
+				[&](const auto &argument)
+				{
+					return equal(otherArgument, argument) == Tristate::True;
+				});
+
+			if (match == and_.arguments.cend())
+				return Tristate::Unknown;
+		}
+
+		return Tristate::True;
+	}
+
+	Tristate visit(const Biconditional &biconditional, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<Biconditional>())
+			return Tristate::Unknown;
+
+		const auto &otherBiconditional = otherFormula.get<Biconditional>();
+
+		if (equal(biconditional.left, otherBiconditional.left) == Tristate::True
+		    && equal(biconditional.right, otherBiconditional.right) == Tristate::True)
+		{
+			return Tristate::True;
+		}
+
+		if (equal(biconditional.left, otherBiconditional.right) == Tristate::True
+		    && equal(biconditional.right, otherBiconditional.left) == Tristate::True)
+		{
+			return Tristate::True;
+		}
+
+		return Tristate::Unknown;
+	}
+
+	Tristate visit(const Boolean &boolean, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<Boolean>())
+			return Tristate::Unknown;
+
+		const auto &otherBoolean = otherFormula.get<Boolean>();
+
+		return (boolean.value == otherBoolean.value)
+			? Tristate::True
+			: Tristate::False;
+	}
+
+	Tristate visit(const Comparison &comparison, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<Comparison>())
+			return Tristate::Unknown;
+
+		const auto &otherComparison = otherFormula.get<Comparison>();
+
+		if (comparison.operator_ != otherComparison.operator_)
+			return Tristate::Unknown;
+
+		if (equal(comparison.left, otherComparison.left) == Tristate::True
+		    && equal(comparison.right, otherComparison.right) == Tristate::True)
+		{
+			return Tristate::True;
+		}
+
+		// Only = and != are commutative operators, all others don’t need to be checked with exchanged arguments
+		if (comparison.operator_ != Comparison::Operator::Equal
+		    && comparison.operator_ != Comparison::Operator::NotEqual)
+		{
+			return Tristate::Unknown;
+		}
+
+		if (equal(comparison.left, otherComparison.right) == Tristate::True
+		    && equal(comparison.right, otherComparison.left) == Tristate::True)
+		{
+			return Tristate::True;
+		}
+
+		return Tristate::Unknown;
+	}
+
+	Tristate visit(const Exists &, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<Exists>())
+			return Tristate::Unknown;
+
+		// TODO: implement stronger check
+		return Tristate::Unknown;
+	}
+
+	Tristate visit(const ForAll &, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<ForAll>())
+			return Tristate::Unknown;
+
+		// TODO: implement stronger check
+		return Tristate::Unknown;
+	}
+
+	Tristate visit(const Implies &implies, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<Implies>())
+			return Tristate::Unknown;
+
+		const auto &otherImplies = otherFormula.get<Implies>();
+
+		if (equal(implies.antecedent, otherImplies.antecedent) == Tristate::True
+		    && equal(implies.consequent, otherImplies.consequent) == Tristate::True)
+		{
+			return Tristate::True;
+		}
+
+		return Tristate::Unknown;
+	}
+
+	Tristate visit(const In &in, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<In>())
+			return Tristate::Unknown;
+
+		const auto &otherIn = otherFormula.get<In>();
+
+		if (equal(in.element, otherIn.element) == Tristate::True
+		    && equal(in.set, otherIn.set) == Tristate::True)
+		{
+			return Tristate::True;
+		}
+
+		return Tristate::Unknown;
+	}
+
+	Tristate visit(const Not &not_, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<Not>())
+			return Tristate::Unknown;
+
+		const auto &otherNot = otherFormula.get<Not>();
+
+		return equal(not_.argument, otherNot.argument);
+	}
+
+	Tristate visit(const Or &or_, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<Or>())
+			return Tristate::Unknown;
+
+		const auto &otherOr = otherFormula.get<Or>();
+
+		for (const auto &argument : or_.arguments)
+		{
+			const auto match = std::find_if(
+				otherOr.arguments.cbegin(), otherOr.arguments.cend(),
+				[&](const auto &otherArgument)
+				{
+					return equal(argument, otherArgument) == Tristate::True;
+				});
+
+			if (match == otherOr.arguments.cend())
+				return Tristate::Unknown;
+		}
+
+		for (const auto &otherArgument : otherOr.arguments)
+		{
+			const auto match = std::find_if(
+				or_.arguments.cbegin(), or_.arguments.cend(),
+				[&](const auto &argument)
+				{
+					return equal(otherArgument, argument) == Tristate::True;
+				});
+
+			if (match == or_.arguments.cend())
+				return Tristate::Unknown;
+		}
+
+		return Tristate::True;
+	}
+
+	Tristate visit(const Predicate &predicate, const Formula &otherFormula)
+	{
+		if (!otherFormula.is<Predicate>())
+			return Tristate::Unknown;
+
+		const auto &otherPredicate = otherFormula.get<Predicate>();
+
+		if (!matches(predicate, otherPredicate))
+			return Tristate::False;
+
+		assert(predicate.arguments.size() == otherPredicate.arguments.size());
+
+		for (size_t i = 0; i < predicate.arguments.size(); i++)
+			if (equal(predicate.arguments[i], otherPredicate.arguments[i]) != Tristate::True)
+				return Tristate::Unknown;
+
+		return Tristate::True;
+	}
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+struct TermEqualityVisitor
+{
+	Tristate visit(const BinaryOperation &binaryOperation, const Term &otherTerm)
+	{
+		if (!otherTerm.is<BinaryOperation>())
+			return Tristate::Unknown;
+
+		const auto &otherBinaryOperation = otherTerm.get<BinaryOperation>();
+
+		if (binaryOperation.operator_ != otherBinaryOperation.operator_)
+			return Tristate::Unknown;
+
+		if (equal(binaryOperation.left, otherBinaryOperation.left) == Tristate::True
+		    && equal(binaryOperation.right, otherBinaryOperation.right) == Tristate::True)
+		{
+			return Tristate::True;
+		}
+
+		// Only + and * are commutative operators, all others don’t need to be checked with exchanged arguments
+		if (binaryOperation.operator_ != BinaryOperation::Operator::Plus
+		    && binaryOperation.operator_ != BinaryOperation::Operator::Multiplication)
+		{
+			return Tristate::Unknown;
+		}
+
+		if (equal(binaryOperation.left, binaryOperation.right) == Tristate::True
+		    && equal(binaryOperation.right, binaryOperation.left) == Tristate::True)
+		{
+			return Tristate::True;
+		}
+
+		return Tristate::Unknown;
+	}
+
+	Tristate visit(const Boolean &boolean, const Term &otherTerm)
+	{
+		if (!otherTerm.is<Boolean>())
+			return Tristate::Unknown;
+
+		const auto &otherBoolean = otherTerm.get<Boolean>();
+
+		return (boolean.value == otherBoolean.value)
+			? Tristate::True
+			: Tristate::False;
+	}
+
+	Tristate visit(const Constant &constant, const Term &otherTerm)
+	{
+		if (!otherTerm.is<Constant>())
+			return Tristate::Unknown;
+
+		const auto &otherConstant = otherTerm.get<Constant>();
+
+		return (constant.name == otherConstant.name)
+			? Tristate::True
+			: Tristate::False;
+	}
+
+	Tristate visit(const Function &function, const Term &otherTerm)
+	{
+		if (!otherTerm.is<Function>())
+			return Tristate::Unknown;
+
+		const auto &otherFunction = otherTerm.get<Function>();
+
+		if (function.name != otherFunction.name)
+			return Tristate::False;
+
+		if (function.arguments.size() != otherFunction.arguments.size())
+			return Tristate::False;
+
+		for (size_t i = 0; i < function.arguments.size(); i++)
+			if (equal(function.arguments[i], otherFunction.arguments[i]) != Tristate::True)
+				return Tristate::Unknown;
+
+		return Tristate::True;
+	}
+
+	Tristate visit(const Integer &integer, const Term &otherTerm)
+	{
+		if (!otherTerm.is<Integer>())
+			return Tristate::Unknown;
+
+		const auto &otherInteger = otherTerm.get<Integer>();
+
+		return (integer.value == otherInteger.value)
+			? Tristate::True
+			: Tristate::False;
+	}
+
+	Tristate visit(const Interval &interval, const Term &otherTerm)
+	{
+		if (!otherTerm.is<Interval>())
+			return Tristate::Unknown;
+
+		const auto &otherInterval = otherTerm.get<Interval>();
+
+		if (equal(interval.from, otherInterval.from) != Tristate::True)
+			return Tristate::Unknown;
+
+		if (equal(interval.to, otherInterval.to) != Tristate::True)
+			return Tristate::Unknown;
+
+		return Tristate::True;
+	}
+
+	Tristate visit(const SpecialInteger &specialInteger, const Term &otherTerm)
+	{
+		if (!otherTerm.is<SpecialInteger>())
+			return Tristate::Unknown;
+
+		const auto &otherSpecialInteger = otherTerm.get<SpecialInteger>();
+
+		return (specialInteger.type == otherSpecialInteger.type)
+			? Tristate::True
+			: Tristate::False;
+	}
+
+	Tristate visit(const String &string, const Term &otherTerm)
+	{
+		if (!otherTerm.is<String>())
+			return Tristate::Unknown;
+
+		const auto &otherString = otherTerm.get<String>();
+
+		return (string.text == otherString.text)
+			? Tristate::True
+			: Tristate::False;
+	}
+
+	Tristate visit(const Variable &variable, const Term &otherTerm)
+	{
+		if (!otherTerm.is<Variable>())
+			return Tristate::Unknown;
+
+		const auto &otherVariable = otherTerm.get<Variable>();
+
+		return (variable.declaration == otherVariable.declaration)
+			? Tristate::True
+			: Tristate::False;
+	}
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+Tristate equal(const Formula &lhs, const Formula &rhs)
+{
+	return lhs.accept(FormulaEqualityVisitor(), rhs);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+Tristate equal(const Term &lhs, const Term &rhs)
+{
+	return lhs.accept(TermEqualityVisitor(), rhs);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+}
+}
+
+#endif

src/anthem/Simplification.cpp

@@ -3,6 +3,8 @@
 #include <optional>
 
 #include <anthem/ASTCopy.h>
+#include <anthem/Equality.h>
+#include <anthem/output/AST.h>
 #include <anthem/SimplificationVisitors.h>
 
 namespace anthem
@@ -333,6 +335,50 @@ struct SimplificationRuleInWithPrimitiveArguments
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
+struct SimplificationRuleSubsumptionInBiconditionals
+{
+	static constexpr const auto Description = "(F <-> (F and G)) === (F -> G)";
+
+	static SimplificationResult apply(ast::Formula &formula)
+	{
+		if (!formula.is<ast::Biconditional>())
+			return SimplificationResult::Unchanged;
+
+		auto &biconditional = formula.get<ast::Biconditional>();
+
+		const auto leftIsPredicate = biconditional.left.is<ast::Predicate>();
+		const auto rightIsPredicate = biconditional.right.is<ast::Predicate>();
+
+		const auto leftIsAnd = biconditional.left.is<ast::And>();
+		const auto rightIsAnd = biconditional.right.is<ast::And>();
+
+		if (!(leftIsPredicate && rightIsAnd) && !(rightIsPredicate && leftIsAnd))
+			return SimplificationResult::Unchanged;
+
+		auto &predicateSide = (leftIsPredicate ? biconditional.left : biconditional.right);
+		auto &andSide = (leftIsPredicate ? biconditional.right : biconditional.left);
+		auto &and_ = andSide.get<ast::And>();
+
+		const auto matchingPredicate =
+			std::find_if(and_.arguments.cbegin(), and_.arguments.cend(),
+			[&](const auto &argument)
+			{
+				return (ast::equal(predicateSide, argument) == ast::Tristate::True);
+			});
+
+		if (matchingPredicate == and_.arguments.cend())
+			return SimplificationResult::Unchanged;
+
+		and_.arguments.erase(matchingPredicate);
+
+		formula = ast::Formula::make<ast::Implies>(std::move(predicateSide), std::move(andSide));
+
+		return SimplificationResult::Simplified;
+	}
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
 const auto simplifyWithDefaultRules =
 	simplify
 	<
@@ -342,7 +388,8 @@ const auto simplifyWithDefaultRules =
 		SimplificationRuleTrivialExists,
 		SimplificationRuleOneElementConjunction,
 		SimplificationRuleExistsWithoutQuantifiedVariables,
-		SimplificationRuleInWithPrimitiveArguments
+		SimplificationRuleInWithPrimitiveArguments,
+		SimplificationRuleSubsumptionInBiconditionals
 	>;
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////

tests/TestCompletion.cpp

@@ -152,7 +152,7 @@ TEST_CASE("[completion] Rules are completed", "[completion]")
 
 		CHECK(output.str() ==
 			"forall V1 (covered(V1) <-> exists U1 in(V1, U1))\n"
-			"forall V2, V3 (in(V2, V3) <-> (V2 in 1..n and V3 in 1..r and in(V2, V3)))\n"
+			"forall V2, V3 (in(V2, V3) -> (V2 in 1..n and V3 in 1..r))\n"
 			"forall U2 not (U2 in 1..n and not covered(U2))\n"
 			"forall U3, U4, U5 not (in(U3, U4) and in(U5, U4) and exists X1 (X1 in (U3 + U5) and in(X1, U4)))\n");
 	}

tests/TestHiddenPredicateElimination.cpp

@@ -164,10 +164,9 @@ TEST_CASE("[hidden predicate elimination] Hidden predicates are correctly elimin
 			"#show t/0.";
 		anthem::translate("input", input, context);
 
-		// TODO: simplify further
 		CHECK(output.str() ==
-			"(s <-> (not #false and s))\n"
+			"(s -> not #false)\n"
-			"(t <-> (not #false and t))\n"
+			"(t -> not #false)\n"
 			"not (s and not t)\n"
 			"not (not #false and not #false and #false)\n");
 	}

tests/TestPlaceholders.cpp

@@ -55,7 +55,7 @@ TEST_CASE("[placeholders] Programs with placeholders are correctly completed", "
 		anthem::translate("input", input, context);
 
 		CHECK(output.str() ==
-			"forall V1, V2 (color(V1, V2) <-> (vertex(V1) and color(V2) and color(V1, V2)))\n"
+			"forall V1, V2 (color(V1, V2) -> (vertex(V1) and color(V2)))\n"
 			"forall U1 not (vertex(U1) and not exists U2 color(U1, U2))\n"
 			"forall U3, U4, U5 not (color(U3, U4) and color(U5, U4) and edge(U3, U5))\n");
 	}