[SPARK-20350] Add optimization rules to apply Complementation Laws.

## What changes were proposed in this pull request?

Apply Complementation Laws during boolean expression simplification.

## How was this patch tested?

Tested using unit tests, integration tests, and manual tests.

Author: ptkool <michael.styles@shopify.com>
Author: Michael Styles <michael.styles@shopify.com>

Closes #17650 from ptkool/apply_complementation_laws.

sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/expressions.scala

@@ -154,6 +154,11 @@ object BooleanSimplification extends Rule[LogicalPlan] with PredicateHelper {
       case TrueLiteral Or _ => TrueLiteral
       case _ Or TrueLiteral => TrueLiteral
 
+      case a And b if Not(a).semanticEquals(b) => FalseLiteral
+      case a Or b if Not(a).semanticEquals(b) => TrueLiteral
+      case a And b if a.semanticEquals(Not(b)) => FalseLiteral
+      case a Or b if a.semanticEquals(Not(b)) => TrueLiteral
+
       case a And b if a.semanticEquals(b) => a
       case a Or b if a.semanticEquals(b) => a
 

sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/BooleanSimplificationSuite.scala

@@ -26,6 +26,7 @@ import org.apache.spark.sql.catalyst.plans.PlanTest
 import org.apache.spark.sql.catalyst.plans.logical._
 import org.apache.spark.sql.catalyst.rules._
 import org.apache.spark.sql.internal.SQLConf
+import org.apache.spark.sql.Row
 
 class BooleanSimplificationSuite extends PlanTest with PredicateHelper {
 
@@ -42,6 +43,16 @@ class BooleanSimplificationSuite extends PlanTest with PredicateHelper {
 
   val testRelation = LocalRelation('a.int, 'b.int, 'c.int, 'd.string)
 
+  val testRelationWithData = LocalRelation.fromExternalRows(
+    testRelation.output, Seq(Row(1, 2, 3, "abc"))
+  )
+
+  private def checkCondition(input: Expression, expected: LogicalPlan): Unit = {
+    val plan = testRelationWithData.where(input).analyze
+    val actual = Optimize.execute(plan)
+    comparePlans(actual, expected)
+  }
+
   private def checkCondition(input: Expression, expected: Expression): Unit = {
     val plan = testRelation.where(input).analyze
     val actual = Optimize.execute(plan)
@@ -160,4 +171,12 @@ class BooleanSimplificationSuite extends PlanTest with PredicateHelper {
       testRelation.where('a > 2 || ('b > 3 && 'b < 5)))
     comparePlans(actual, expected)
   }
+
+  test("Complementation Laws") {
+    checkCondition('a && !'a, testRelation)
+    checkCondition(!'a && 'a, testRelation)
+
+    checkCondition('a || !'a, testRelationWithData)
+    checkCondition(!'a || 'a, testRelationWithData)
+  }
 }