Add new simplification rule

This adds the rule “(not (F and G)) === (not F or not G)” to the
simplification rule tableau.

src/anthem/Simplification.cpp

@@ -403,6 +403,33 @@ struct SimplificationRuleDoubleNegation
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
+struct SimplificationRuleDeMorganForConjunctions
+{
+	static constexpr const auto Description = "(not (F and G)) === (not F or not 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::And>())
+			return SimplificationResult::Unchanged;
+
+		auto &and_ = not_.argument.get<ast::And>();
+
+		for (auto &argument : and_.arguments)
+			argument = ast::Formula::make<ast::Not>(std::move(argument));
+
+		formula = ast::Formula::make<ast::Or>(std::move(and_.arguments));
+
+		return SimplificationResult::Simplified;
+	}
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
 const auto simplifyWithDefaultRules =
 	simplify
 	<
@@ -414,7 +441,8 @@ const auto simplifyWithDefaultRules =
 		SimplificationRuleOneElementConjunction,
 		SimplificationRuleExistsWithoutQuantifiedVariables,
 		SimplificationRuleInWithPrimitiveArguments,
-		SimplificationRuleSubsumptionInBiconditionals
+		SimplificationRuleSubsumptionInBiconditionals,
+		SimplificationRuleDeMorganForConjunctions
 	>;
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////

tests/TestCompletion.cpp

@@ -153,8 +153,8 @@ 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))\n"
-			"forall U2 not (U2 in 1..n and not covered(U2))\n"
+			"forall U2 (not U2 in 1..n or 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");
+			"forall U3, U4, U5 (not in(U3, U4) or not in(U5, U4) or not exists X1 (X1 in (U3 + U5) and in(X1, U4)))\n");
 	}
 
 	SECTION("binary operations with multiple variables")

tests/TestHiddenPredicateElimination.cpp

@@ -168,8 +168,8 @@ TEST_CASE("[hidden predicate elimination] Hidden predicates are correctly elimin
 		CHECK(output.str() ==
 			"(s -> not #false)\n"
 			"(t -> not #false)\n"
-			"not (s and not t)\n"
+			"(not s or t)\n"
-			"not (not #false and not #false and #false)\n");
+			"(#false or #false or not #false)\n");
 	}
 
 	SECTION("predicate with more than one argument is hidden correctly")

tests/TestPlaceholders.cpp

@@ -56,7 +56,7 @@ TEST_CASE("[placeholders] Programs with placeholders are correctly completed", "
 
 		CHECK(output.str() ==
 			"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 U1 (not vertex(U1) or exists U2 color(U1, U2))\n"
-			"forall U3, U4, U5 not (color(U3, U4) and color(U5, U4) and edge(U3, U5))\n");
+			"forall U3, U4, U5 (not color(U3, U4) or not color(U5, U4) or not edge(U3, U5))\n");
 	}
 }