Add new simplification rule

This adds the rule “(not F [comparison] G) === (F [negated comparison]
G)” to the simplification rule tableau.

src/anthem/Simplification.cpp

@@ -466,6 +466,52 @@ struct SimplificationRuleImplicationFromDisjunction
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
+struct SimplificationRuleNegatedComparison
+{
+	static constexpr const auto Description = "(not F [comparison] G) === (F [negated comparison] G)";
+
+	static SimplificationResult apply(ast::Formula &formula)
+	{
+		if (!formula.is<ast::Not>())
+			return SimplificationResult::Unchanged;
+
+		auto &not_ = formula.get<ast::Not>();
+
+		if (!not_.argument.is<ast::Comparison>())
+			return SimplificationResult::Unchanged;
+
+		auto &comparison = not_.argument.get<ast::Comparison>();
+
+		switch (comparison.operator_)
+		{
+			case ast::Comparison::Operator::GreaterThan:
+				comparison.operator_ = ast::Comparison::Operator::LessEqual;
+				break;
+			case ast::Comparison::Operator::LessThan:
+				comparison.operator_ = ast::Comparison::Operator::GreaterEqual;
+				break;
+			case ast::Comparison::Operator::LessEqual:
+				comparison.operator_ = ast::Comparison::Operator::GreaterThan;
+				break;
+			case ast::Comparison::Operator::GreaterEqual:
+				comparison.operator_ = ast::Comparison::Operator::LessThan;
+				break;
+			case ast::Comparison::Operator::NotEqual:
+				comparison.operator_ = ast::Comparison::Operator::Equal;
+				break;
+			case ast::Comparison::Operator::Equal:
+				comparison.operator_ = ast::Comparison::Operator::NotEqual;
+				break;
+		}
+
+		formula = std::move(comparison);
+
+		return SimplificationResult::Simplified;
+	}
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
 const auto simplifyWithDefaultRules =
 	simplify
 	<
@@ -479,7 +525,8 @@ const auto simplifyWithDefaultRules =
 		SimplificationRuleInWithPrimitiveArguments,
 		SimplificationRuleSubsumptionInBiconditionals,
 		SimplificationRuleDeMorganForConjunctions,
-		SimplificationRuleImplicationFromDisjunction
+		SimplificationRuleImplicationFromDisjunction,
+		SimplificationRuleNegatedComparison
 	>;
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////

tests/TestCompletion.cpp

@@ -176,4 +176,12 @@ TEST_CASE("[completion] Rules are completed", "[completion]")
 		CHECK(output.str() ==
 			"forall V1, V2, V3 (p(V1, V2, V3) <-> #true)\n");
 	}
+
+	SECTION("negated comparisons")
+	{
+		input << ":- color(V, C1), color(V, C2), C1 != C2.";
+		anthem::translate("input", input, context);
+
+		CHECK(output.str() == "forall V1, V2 not color(V1, V2)\nforall U1, U2, U3 (not color(U1, U2) or not color(U1, U3) or U2 = U3)\n");
+	}
 }