diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/namedExpressions.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/namedExpressions.scala
index f80bcfcb0b0bf..e3daddace241d 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/namedExpressions.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/namedExpressions.scala
@@ -194,7 +194,9 @@ case class AttributeReference(
   def sameRef(other: AttributeReference): Boolean = this.exprId == other.exprId
 
   override def equals(other: Any): Boolean = other match {
-    case ar: AttributeReference => name == ar.name && exprId == ar.exprId && dataType == ar.dataType
+    case ar: AttributeReference =>
+      name == ar.name && dataType == ar.dataType && nullable == ar.nullable &&
+        metadata == ar.metadata && exprId == ar.exprId && qualifiers == ar.qualifiers
     case _ => false
   }
 
diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/logical/basicOperators.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/logical/basicOperators.scala
index e2b97b27a6c2c..45630a591d349 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/logical/basicOperators.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/logical/basicOperators.scala
@@ -23,7 +23,7 @@ import org.apache.spark.sql.catalyst.expressions._
 import org.apache.spark.sql.catalyst.expressions.aggregate.AggregateExpression
 import org.apache.spark.sql.catalyst.plans._
 import org.apache.spark.sql.types._
-import org.apache.spark.util.collection.OpenHashSet
+import scala.collection.mutable.ArrayBuffer
 
 case class Project(projectList: Seq[NamedExpression], child: LogicalPlan) extends UnaryNode {
   override def output: Seq[Attribute] = projectList.map(_.toAttribute)
@@ -244,12 +244,12 @@ private[sql] object Expand {
    */
   private def buildNonSelectExprSet(
       bitmask: Int,
-      exprs: Seq[Expression]): OpenHashSet[Expression] = {
-    val set = new OpenHashSet[Expression](2)
+      exprs: Seq[Expression]): ArrayBuffer[Expression] = {
+    val set = new ArrayBuffer[Expression](2)
 
     var bit = exprs.length - 1
     while (bit >= 0) {
-      if (((bitmask >> bit) & 1) == 0) set.add(exprs(bit))
+      if (((bitmask >> bit) & 1) == 0) set += exprs(bit)
       bit -= 1
     }
 
@@ -279,7 +279,7 @@ private[sql] object Expand {
 
       (child.output :+ gid).map(expr => expr transformDown {
         // TODO this causes a problem when a column is used both for grouping and aggregation.
-        case x: Expression if nonSelectedGroupExprSet.contains(x) =>
+        case x: Expression if nonSelectedGroupExprSet.exists(_.semanticEquals(x)) =>
           // if the input attribute in the Invalid Grouping Expression set of for this group
           // replace it with constant null
           Literal.create(null, expr.dataType)
diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala
index 86b9417477ba3..f6fb31a2af594 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala
@@ -235,17 +235,17 @@ case class HashPartitioning(expressions: Seq[Expression], numPartitions: Int)
   override def satisfies(required: Distribution): Boolean = required match {
     case UnspecifiedDistribution => true
     case ClusteredDistribution(requiredClustering) =>
-      expressions.toSet.subsetOf(requiredClustering.toSet)
+      expressions.forall(x => requiredClustering.exists(_.semanticEquals(x)))
     case _ => false
   }
 
   override def compatibleWith(other: Partitioning): Boolean = other match {
-    case o: HashPartitioning => this == o
+    case o: HashPartitioning => this.semanticEquals(o)
     case _ => false
   }
 
   override def guarantees(other: Partitioning): Boolean = other match {
-    case o: HashPartitioning => this == o
+    case o: HashPartitioning => this.semanticEquals(o)
     case _ => false
   }
 
@@ -276,17 +276,17 @@ case class RangePartitioning(ordering: Seq[SortOrder], numPartitions: Int)
       val minSize = Seq(requiredOrdering.size, ordering.size).min
       requiredOrdering.take(minSize) == ordering.take(minSize)
     case ClusteredDistribution(requiredClustering) =>
-      ordering.map(_.child).toSet.subsetOf(requiredClustering.toSet)
+      ordering.map(_.child).forall(x => requiredClustering.exists(_.semanticEquals(x)))
     case _ => false
   }
 
   override def compatibleWith(other: Partitioning): Boolean = other match {
-    case o: RangePartitioning => this == o
+    case o: RangePartitioning => this.semanticEquals(o)
     case _ => false
   }
 
   override def guarantees(other: Partitioning): Boolean = other match {
-    case o: RangePartitioning => this == o
+    case o: RangePartitioning => this.semanticEquals(o)
     case _ => false
   }
 }