opt: improve FDs for Intersect and Except variants

We can pass through FDs from the left side on Intersect/IntersectAll, and we can pass through FDs from both sides on Except/ExceptAll. Release note: None
cockroachdb · Jun 14, 2021 · 491690a · 491690a
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diff --git a/pkg/sql/opt/exec/execbuilder/testdata/fk b/pkg/sql/opt/exec/execbuilder/testdata/fk
@@ -487,6 +487,7 @@ vectorized: true
 │       │
 │       └── • hash join
 │           │ equality: (p) = (p)
+│           │ left cols are key
 │           │ right cols are key
 │           │
 │           ├── • except all
@@ -512,6 +513,7 @@ vectorized: true
         │
         └── • hash join
             │ equality: (p) = (p)
+            │ left cols are key
             │ right cols are key
             │
             ├── • except all
@@ -618,6 +620,7 @@ vectorized: true
         │
         └── • hash join
             │ equality: (c) = (c)
+            │ left cols are key
             │ right cols are key
             │
             ├── • except all
@@ -758,6 +761,7 @@ vectorized: true
         │
         └── • hash join
             │ equality: (c) = (c)
+            │ left cols are key
             │ right cols are key
             │
             ├── • except all
@@ -890,6 +894,7 @@ vectorized: true
         │
         └── • hash join
             │ equality: (x) = (y)
+            │ left cols are key
             │ right cols are key
             │
             ├── • except all

diff --git a/pkg/sql/opt/exec/execbuilder/testdata/union b/pkg/sql/opt/exec/execbuilder/testdata/union
@@ -595,7 +595,7 @@ vectorized: true
 ·
 • intersect
 │ columns: (b, c, d, e)
-│ ordering: +b,+c,+d,+e
+│ ordering: +b,+d,+c,+e
 │ estimated row count: 1 (missing stats)
 │
 ├── • filter
@@ -624,7 +624,7 @@ vectorized: true
           table: abcde@abcde_b_c_d_e_idx
           spans: FULL SCAN
 ·
-Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJy0lF-L2kAUxd_7KS73KcEpbv7olgFhdmuWBlyzTUL_UERi5tYG0iSdjLBF_O4lSdtVu6Z12b4Ic2Z-95x7kGyx_pYjR-_D3ezKn4Mx9aM4ejtj8M4Lr4PIMyHyZt7rGFYMUgaSAcFNGNyCcUJPVqkk8OexF0bNfd8zE96_8UIPjBQmYJlwNZ-CIWECZEIQTr0Qrj_CChkWpaR58pVq5J_QwgXDSpUp1XWpGmnbPvDlPfILhllRbXQjLximpSLkW9SZzgk5xskqp5ASSWp4gQwl6STL27FtItH-LlfLdCmXtMzkPTKMqqSoObxEhsFGcxA2Ew4TLhMjXOwYlhv94FjrZE3IrR3791Q3Wa5JkRpah5E6nYMh7KYgzrk_j1_97Ek4MAHhmicj2OdE2C_G_p_FOE8qxnnOYtxzIkyzWmdFqofuYQRhsV_rNusrSYokh0Z2TjqPnuQ8egbn8UnnB8NNUXbDDvwWDfm3J4_EvyW1poh0UA3HhwvE3yvie5-Iq9kMGeb0WRvCGjBhD5hwBky4A3OisvWXP-Xff7i9Kk5tfnlO5yHVVVnUdNzAo5MvmrVJrqmrsS43KqU7VaatTXcMWq4VJNW6u7W6g190V03AfdjqhUf9sN0LO_2w0wu7_bDbC48PYOsYHp0B28fwuBe-PIq92L34EQAA___K-yzi
+Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJy0lF-L2kAUxd_7KS73KcEpbv7olgFhdmuWBlyzTUL_UERi5tYG0iSdjLBF_O4lSdtVu6Z12b4Ic2Z-95x7kGyx_pYjR-_D3ezKn4Mx9aM4ejtj8M4Lr4PIMyHyZt7rGFYMUgaSAcFNGNyCcUJPVqkk8OexF0bNfd8zE96_8UIPjBQmYJlwNZ-CIWECZEIQTr0Qrj_CChkWpaR58pVq5J_QwgXDSpUp1XWpGmnbPvDlPfILhllRbXQjLximpSLkW9SZzgk5xskqp5ASSWp4gQwl6STL27FtItH-LlfLdCmXtMzkPTKMqqSoObxEhsFGcxA2Ew4TLhMjXOwYlhv94FjrZE3IrR3791Q3Wa5JkRpah5E6nYMh7KYgzrk_j1_97Ek4MAHhmicj2OdE2C_G_p_FOE8qxnnOYtxzIkyzWmdFqofuYQRhsV_rNusrSYokh0Z2TjqPnuQ8egbn8UnnB8NNUXbDDvwWDfm3J4_EvyW1poh0UA3HhwvE3yvie5-Iq9kMGeb0WRvCGjDhDJiwB0y4A3OisvWXP-Xff7i9Kk5tfnlO5yHVVVnUdNzAo5MvmrVJrqmrsS43KqU7VaatTXcMWq4VJNW6u7W6g190V03AfdjqhUf9sN0LO_2w0wu7_bDbC48PYOsYHp0B28fwuBe-PIq92L34EQAA___LAyzi
 
 query T
 EXPLAIN (DISTSQL,VERBOSE) SELECT b, c, d, e FROM (SELECT b, c, d, e FROM abcde EXCEPT SELECT b, c, d, e FROM abcde) WHERE c = 1 AND d = e ORDER BY b, c, d, e
@@ -634,7 +634,7 @@ vectorized: true
 ·
 • except
 │ columns: (b, c, d, e)
-│ ordering: +b,+c,+d,+e
+│ ordering: +b,+d,+c,+e
 │ estimated row count: 1 (missing stats)
 │
 ├── • filter
@@ -663,7 +663,7 @@ vectorized: true
           table: abcde@abcde_b_c_d_e_idx
           spans: FULL SCAN
 ·
-Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJy0lN9q20wQxe-_pxjmSsL74eiPnbJg2CRWqMGxUkm0KcUYWTt1BaqkrtaQEvzuRVLT2G6k1iG9MezZ_c05czB6wOpbhhy9u9v5xWwBxnQWRuG7OYP3XnDph54JoTf3riJYM0gYSAYE14F_A0aHHq8TSeDdXXm3URfbvDHhw1sv8MBIYAKWCReLKRgSJkAm-MHUC-Dy4x6JDPNC0iL-ShXyT2jhkmGpioSqqlC19NA8mMl75GcM07zc6lpeMkwKRcgfUKc6I-QYxeuMAoolqeEZMpSk4zRrxjbRRPO7Wq-SlVzRKpX3yDAs47zi8D8y9Leag7CZcJhwmRjhcsew2Oonx0rHG0Ju7djfp7pOM02K1NA6jNTqHAxh101xzmeL6M3PwoQDExCu2RnBPiXCfjH2vyzGeVExzmsW454SYZpWOs0TPXQPIwiLPa5br68kKZIcatnpdB69yHn0Cs7jTucnw21etMMO_JY1-acnz8S_IbWhkLRfDseHC0TfS-KPH4qL-RwZZvRZG8IaMGEPmHAGTLgDc6LSzZff5V__tr0eutY-P6XwgKqyyCs6Xv_ZyWf1ziQ31HZYFVuV0K0qksamPfoN1wiSKt3eWu1hlrdXdcB92OqF3X7Y7oWdftjphUf9sNsLjw9g6xgenQDbx_C4Fz4_ir3c_fcjAAD__7UbLSI=
+Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJy0lN9q20wQxe-_pxjmSsL74eiPnbJg2CRWqMGxUkm0KcUYWTt1BaqkrtaQEvzuRVLT2G6k1iG9MezZ_c05czB6wOpbhhy9u9v5xWwBxnQWRuG7OYP3XnDph54JoTf3riJYM0gYSAYE14F_A0aHHq8TSeDdXXm3URfbvDHhw1sv8MBIYAKWCReLKRgSJkAm-MHUC-Dy4x6JDPNC0iL-ShXyT2jhkmGpioSqqlC19NA8mMl75GcM07zc6lpeMkwKRcgfUKc6I-QYxeuMAoolqeEZMpSk4zRrxjbRRPO7Wq-SlVzRKpX3yDAs47zi8D8y9Leag7CZcJhwmRjhcsew2Oonx0rHG0Ju7djfp7pOM02K1NA6jNTqHAxh101xzmeL6M3PwoQDExCu2RnBPiXCfjH2vyzGeVExzmsW454SYZpWOs0TPXQPIwiLPa5br68kKZIcatnpdB69yHn0Cs7jTucnw21etMMO_JY1-acnz8S_IbWhkLRfDseHC0TfS-KPH4qL-RwZZvRZG8IaMOEMmLAHTLgDc6LSzZff5V__tr0eutY-P6XwgKqyyCs6Xv_ZyWf1ziQ31HZYFVuV0K0qksamPfoN1wiSKt3eWu1hlrdXdcB92OqF3X7Y7oWdftjphUf9sNsLjw9g6xgenQDbx_C4Fz4_ir3c_fcjAAD__7UjLSI=
 
 query T
 EXPLAIN (DISTSQL,VERBOSE) SELECT * FROM (SELECT * FROM abcde EXCEPT ALL SELECT * FROM abcde) WHERE c = 1 AND d = e ORDER BY a
@@ -712,7 +712,7 @@ vectorized: true
 ·
 • intersect all
 │ columns: (a, b, c, d, e)
-│ ordering: +b,+c,+d,+a,+e
+│ ordering: +b,+d,+a,+c,+e
 │ estimated row count: 1 (missing stats)
 │
 ├── • filter
@@ -741,7 +741,7 @@ vectorized: true
           table: abcde@abcde_b_c_d_e_idx
           spans: FULL SCAN
 ·
-Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJysk9uLm1AQxt_7VwzzpM2UjZdAORA42calQjZuVXqhhGA801Swao8GtoT870Ut7BqStCn7EpjLN993fsE91j9zFOh9fljM_CUYcz-Kow8Lgo9eeBtEngmRt_DexfAa7sLgHoxhmWxSxeAvYy-M2vZssYATGyZ8eu-FHhgpTMEyYbacg6FgCmxCEM69EG6_wIYgJVAETJAgYVEqXiY_uEbxFS1cEVa6TLmuS9229t2Crx5RjAmzoto1bXtFmJaaUeyxyZqcUWCcbHIOOVGsb8ZIqLhJsrw726WT3e96s07Xas3rTD0iYVQlRS3gDa4OhOWueTpfN8mWUVgH-vcId1nesGZ9Yw39-74AQzotGSGEv4zf_gEkXZiCnJhnI9jXRHhOwX4xCs5_UXBekoJ7NsKT864otWLNamC8apV_WznxjnvWW464Caobd_iS-FfFYvg9IGHO3xpD2iOSzoikOyJpjUhORuZUZ9vvp0dIGOwaAdIiaZN0SLokJ2chTK75H0Kuq7Ko-RjGycvjlgCrLfdE63KnU37QZdrZ9GXQ6bqG4rrpp1Zf-EU_agM-F1sXxe5AbB-L7Yti57Kzc4WzdSx2L4onR86rw6vfAQAA___SNa8C
+Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJysk9uLm1AQxt_7VwzzpM2UjZdAORA42calQjZuVXqhhGA801Swao8GtoT870Ut7BqStCn7EpjLN993fsE91j9zFOh9fljM_CUYcz-Kow8Lgo9eeBtEngmRt_DexfAa7sLgHoxhmWxSxeAvYy-M2vZssYATGyZ8eu-FHhgpTMEyYbacg6FgCmxCEM69EG6_wIYgJVAETJAgYVEqXiY_uEbxFS1cEVa6TLmuS9229t2Crx5RjAmzoto1bXtFmJaaUeyxyZqcUWCcbHIOOVGsb8ZIqLhJsrw726WT3e96s07Xas3rTD0iYVQlRS3gDa4OhOWueTpfN8mWUVgH-vcId1nesGZ9Yw39-74AQzotGSGEv4zf_gEkXZiCnJhnI9jXRHhOwX4xCs5_UXBekoJ7NsKT864otWLNamC8apV_WznxjnvWW464Caobd_iS-FfFYvg9IGHO3xpD2iOS7oikNSLpjEhORuZUZ9vvp0dIGOwaAdIiaZN0SLokJ2chTK75H0Kuq7Ko-RjGycvjlgCrLfdE63KnU37QZdrZ9GXQ6bqG4rrpp1Zf-EU_agM-F1sXxe5AbB-L7Yti57Kzc4WzdSx2L4onR86rw6vfAQAA___SLa8C
 
 # Regression test for #64181. Ensure that a projection on top of an ordered
 # UNION ALL correctly projects away ordering columns.

diff --git a/pkg/sql/opt/memo/logical_props_builder.go b/pkg/sql/opt/memo/logical_props_builder.go
@@ -685,6 +685,7 @@ func (b *logicalPropsBuilder) buildLocalityOptimizedSearchProps(
 func (b *logicalPropsBuilder) buildSetProps(setNode RelExpr, rel *props.Relational) {
 	BuildSharedProps(setNode, &rel.Shared)
 
+	op := setNode.Op()
 	leftProps := setNode.Child(0).(RelExpr).Relational()
 	rightProps := setNode.Child(1).(RelExpr).Relational()
 	setPrivate := setNode.Private().(*SetPrivate)
@@ -720,12 +721,7 @@ func (b *logicalPropsBuilder) buildSetProps(setNode RelExpr, rel *props.Relation
 
 	// Functional Dependencies
 	// -----------------------
-	switch setNode.Op() {
-	case opt.UnionOp, opt.IntersectOp, opt.ExceptOp:
-		// These operators eliminate duplicates, so a strict key exists.
-		rel.FuncDeps.AddStrictKey(rel.OutputCols, rel.OutputCols)
-	}
-	switch setNode.Op() {
+	switch op {
 	case opt.UnionOp, opt.UnionAllOp, opt.LocalityOptimizedSearchOp:
 		// If columns at ordinals (i, j) are equivalent in both the left input
 		// and right input, then the output columns at ordinals at (i, j) are
@@ -738,27 +734,48 @@ func (b *logicalPropsBuilder) buildSetProps(setNode RelExpr, rel *props.Relation
 				}
 			}
 		}
+
 	case opt.IntersectOp, opt.IntersectAllOp, opt.ExceptOp, opt.ExceptAllOp:
-		// Intersect, IntersectAll, Except and ExceptAll only output rows from
-		// the left input, so if columns at ordinals (i, j) are equivalent in
-		// the left input, then they are equivalent in the output.
-		// TODO(mgartner): The entire FD set on the left side can be used, but
-		// columns may need to be mapped. Intersections can combine FD
-		// information from both the left and the right.
-		for i := range setPrivate.OutCols {
-			for j := i + 1; j < len(setPrivate.OutCols); j++ {
-				if leftProps.FuncDeps.AreColsEquiv(setPrivate.LeftCols[i], setPrivate.LeftCols[j]) {
-					rel.FuncDeps.AddEquivalency(setPrivate.OutCols[i], setPrivate.OutCols[j])
+		// With these operators, the output is a subset of the left input, so all
+		// the left FDs still hold (similar to a Select).
+		rel.FuncDeps.RemapFrom(&leftProps.FuncDeps, func(in opt.ColumnID) opt.ColumnID {
+			for i, leftCol := range setPrivate.LeftCols {
+				if in == leftCol {
+					return setPrivate.OutCols[i]
 				}
 			}
+			panic(errors.AssertionFailedf("invalid column %d in left FD", in))
+		})
+
+		if op == opt.IntersectOp || op == opt.IntersectAllOp {
+			// With Intersect operators, the output is also a subset of the right input,
+			// so all the right FDs apply as well.
+			var remapped props.FuncDepSet
+			remapped.RemapFrom(&rightProps.FuncDeps, func(in opt.ColumnID) opt.ColumnID {
+				for i, rightCol := range setPrivate.RightCols {
+					if in == rightCol {
+						return setPrivate.OutCols[i]
+					}
+				}
+				panic(errors.AssertionFailedf("invalid column %d in right FD", in))
+			})
+			rel.FuncDeps.AddFrom(&remapped)
 		}
 	}
 
+	// Add a strict key for variants that eliminate duplicates.
+	switch op {
+	case opt.UnionOp, opt.IntersectOp, opt.ExceptOp:
+		rel.FuncDeps.AddStrictKey(rel.OutputCols, rel.OutputCols)
+	}
+
 	// Cardinality
 	// -----------
 	// Calculate cardinality of the set operator.
-	rel.Cardinality = b.makeSetCardinality(
-		setNode.Op(), leftProps.Cardinality, rightProps.Cardinality)
+	rel.Cardinality = b.makeSetCardinality(op, leftProps.Cardinality, rightProps.Cardinality)
+	if rel.FuncDeps.HasMax1Row() {
+		rel.Cardinality = rel.Cardinality.Limit(1)
+	}
 
 	// Statistics
 	// ----------

diff --git a/pkg/sql/opt/memo/testdata/logprops/set b/pkg/sql/opt/memo/testdata/logprops/set
@@ -48,7 +48,8 @@ intersect
  ├── columns: x:1(int!null) y:2(int) x:1(int!null)
  ├── left columns: x:1(int!null) y:2(int) x:1(int!null)
  ├── right columns: v:6(int) u:5(int) rowid:7(int)
- ├── key: (1,2)
+ ├── key: (1)
+ ├── fd: ()-->(2)
  ├── interesting orderings: (+1)
  ├── project
  │    ├── columns: x:1(int!null) y:2(int)
@@ -92,7 +93,8 @@ except
  ├── columns: x:1(int!null) x:1(int!null) y:2(int)
  ├── left columns: x:1(int!null) x:1(int!null) y:2(int)
  ├── right columns: u:5(int) v:6(int) v:6(int)
- ├── key: (1,2)
+ ├── key: (1)
+ ├── fd: (1)-->(2)
  ├── interesting orderings: (+1)
  ├── project
  │    ├── columns: x:1(int!null) y:2(int)
@@ -489,7 +491,8 @@ intersect-all
  ├── columns: a:1(int!null) b:2(int) c:3(int)
  ├── left columns: a:1(int!null) b:2(int) c:3(int)
  ├── right columns: a:6(int) b:7(int) c:8(int)
- ├── fd: (1)==(3), (3)==(1)
+ ├── key: (1)
+ ├── fd: (1)==(2,3), (3)==(1,2), (2)==(1,3)
  ├── interesting orderings: (+1)
  ├── select
  │    ├── columns: a:1(int!null) b:2(int) c:3(int!null)
@@ -541,7 +544,8 @@ except-all
  ├── columns: a:1(int!null) b:2(int) c:3(int)
  ├── left columns: a:1(int!null) b:2(int) c:3(int)
  ├── right columns: a:6(int) b:7(int) c:8(int)
- ├── fd: (1)==(3), (3)==(1)
+ ├── key: (1)
+ ├── fd: (1)-->(2), (1)==(3), (3)==(1)
  ├── interesting orderings: (+1)
  ├── select
  │    ├── columns: a:1(int!null) b:2(int) c:3(int!null)

diff --git a/pkg/sql/opt/memo/testdata/stats/set b/pkg/sql/opt/memo/testdata/stats/set
@@ -241,7 +241,8 @@ intersect
  ├── left columns: a.x:1(int!null) y:2(int) a.x:1(int!null)
  ├── right columns: z:7(int) b.x:6(int) rowid:9(int)
  ├── stats: [rows=2, distinct(1,2)=2, null(1,2)=0]
- ├── key: (1,2)
+ ├── key: (1)
+ ├── fd: ()-->(2)
  ├── project
  │    ├── columns: a.x:1(int!null) y:2(int)
  │    ├── stats: [rows=5000, distinct(1,2)=5000, null(1,2)=0]
@@ -283,6 +284,8 @@ intersect-all
  ├── left columns: a.x:1(int!null) y:2(int) a.x:1(int!null)
  ├── right columns: z:7(int) b.x:6(int) rowid:9(int)
  ├── stats: [rows=2]
+ ├── key: (1)
+ ├── fd: ()-->(2)
  ├── project
  │    ├── columns: a.x:1(int!null) y:2(int)
  │    ├── stats: [rows=5000]
@@ -401,7 +404,8 @@ except
  ├── left columns: a.x:1(int!null) a.x:1(int!null) y:2(int)
  ├── right columns: b.x:6(int) z:7(int) z:7(int)
  ├── stats: [rows=5000, distinct(1,2)=5000, null(1,2)=0]
- ├── key: (1,2)
+ ├── key: (1)
+ ├── fd: (1)-->(2)
  ├── project
  │    ├── columns: a.x:1(int!null) y:2(int)
  │    ├── stats: [rows=5000, distinct(1,2)=5000, null(1,2)=0]
@@ -441,6 +445,8 @@ except-all
  ├── left columns: a.x:1(int!null) a.x:1(int!null) y:2(int)
  ├── right columns: b.x:6(int) z:7(int) z:7(int)
  ├── stats: [rows=5000]
+ ├── key: (1)
+ ├── fd: (1)-->(2)
  ├── project
  │    ├── columns: a.x:1(int!null) y:2(int)
  │    ├── stats: [rows=5000]
@@ -878,9 +884,10 @@ except
  ├── columns: a:1(int) b:2(bool!null)
  ├── left columns: column1:1(int) column2:2(bool!null)
  ├── right columns: column1:3(int) column2:4(bool)
- ├── cardinality: [0 - 2]
+ ├── cardinality: [0 - 1]
  ├── stats: [rows=1, distinct(1,2)=1, null(1,2)=0, distinct(2,5)=1, null(2,5)=0]
- ├── key: (1,2)
+ ├── key: ()
+ ├── fd: ()-->(1,2)
  ├── select
  │    ├── columns: column1:1(int) column2:2(bool!null)
  │    ├── cardinality: [0 - 2]
@@ -922,7 +929,8 @@ except
  ├── right columns: column1:3(int) column2:4(int)
  ├── cardinality: [0 - 3]
  ├── stats: [rows=2, distinct(1,2)=2, null(1,2)=0.666666667]
- ├── key: (1,2)
+ ├── key: (2)
+ ├── fd: ()-->(1)
  ├── select
  │    ├── columns: column1:1(int) column2:2(int)
  │    ├── cardinality: [0 - 3]
@@ -956,29 +964,24 @@ except
 opt disable=SimplifyIntersectRight
 VALUES (1), (2) INTERSECT VALUES (NULL) ORDER BY 1
 ----
-sort
+intersect
  ├── columns: column1:1(int)
+ ├── left columns: column1:1(int)
+ ├── right columns: column1:2(int)
  ├── cardinality: [0 - 1]
  ├── stats: [rows=1, distinct(1)=1, null(1)=0]
- ├── key: (1)
- ├── ordering: +1
- └── intersect
-      ├── columns: column1:1(int)
-      ├── left columns: column1:1(int)
-      ├── right columns: column1:2(int)
-      ├── cardinality: [0 - 1]
-      ├── stats: [rows=1, distinct(1)=1, null(1)=0]
-      ├── key: (1)
-      ├── values
-      │    ├── columns: column1:1(int!null)
-      │    ├── cardinality: [2 - 2]
-      │    ├── stats: [rows=2, distinct(1)=2, null(1)=0]
-      │    ├── (1,) [type=tuple{int}]
-      │    └── (2,) [type=tuple{int}]
-      └── values
-           ├── columns: column1:2(int)
-           ├── cardinality: [1 - 1]
-           ├── stats: [rows=1, distinct(2)=1, null(2)=1]
-           ├── key: ()
-           ├── fd: ()-->(2)
-           └── (NULL,) [type=tuple{int}]
+ ├── key: ()
+ ├── fd: ()-->(1)
+ ├── values
+ │    ├── columns: column1:1(int!null)
+ │    ├── cardinality: [2 - 2]
+ │    ├── stats: [rows=2, distinct(1)=2, null(1)=0]
+ │    ├── (1,) [type=tuple{int}]
+ │    └── (2,) [type=tuple{int}]
+ └── values
+      ├── columns: column1:2(int)
+      ├── cardinality: [1 - 1]
+      ├── stats: [rows=1, distinct(2)=1, null(2)=1]
+      ├── key: ()
+      ├── fd: ()-->(2)
+      └── (NULL,) [type=tuple{int}]
diff --git a/pkg/sql/opt/memo/testdata/stats_quality/tpcc b/pkg/sql/opt/memo/testdata/stats_quality/tpcc
@@ -1177,6 +1177,7 @@ except-all
  ├── left columns: no_w_id:3(int!null) no_d_id:2(int!null) no_o_id:1(int!null)
  ├── right columns: o_w_id:8(int) o_d_id:7(int) o_id:6(int)
  ├── stats: [rows=90000, distinct(1)=900, null(1)=0, distinct(2)=10, null(2)=0, distinct(3)=10, null(3)=0]
+ ├── key: (1-3)
  ├── scan new_order
  │    ├── save-table-name: consistency_08_scan_2
  │    ├── columns: no_o_id:1(int!null) no_d_id:2(int!null) no_w_id:3(int!null)
@@ -1290,6 +1291,7 @@ except-all
  ├── left columns: o_w_id:3(int!null) o_d_id:2(int!null) o_id:1(int!null)
  ├── right columns: no_w_id:13(int) no_d_id:12(int) no_o_id:11(int)
  ├── stats: [rows=90000, distinct(1)=2999, null(1)=0, distinct(2)=10, null(2)=0, distinct(3)=10, null(3)=0]
+ ├── key: (1-3)
  ├── project
  │    ├── save-table-name: consistency_09_project_2
  │    ├── columns: o_id:1(int!null) o_d_id:2(int!null) o_w_id:3(int!null)
@@ -1412,6 +1414,8 @@ except-all
  ├── left columns: o_w_id:3(int!null) o_d_id:2(int!null) o_id:1(int!null) o_ol_cnt:7(int)
  ├── right columns: ol_w_id:13(int) ol_d_id:12(int) ol_o_id:11(int) count_rows:23(int)
  ├── stats: [rows=300000, distinct(1)=2999, null(1)=0, distinct(2)=10, null(2)=0, distinct(3)=10, null(3)=0, distinct(7)=11, null(7)=0]
+ ├── key: (1-3)
+ ├── fd: (1-3)-->(7)
  ├── scan order
  │    ├── save-table-name: consistency_10_scan_2
  │    ├── columns: o_id:1(int!null) o_d_id:2(int!null) o_w_id:3(int!null) o_ol_cnt:7(int)
@@ -1521,6 +1525,8 @@ except-all
  ├── left columns: ol_w_id:3(int!null) ol_d_id:2(int!null) ol_o_id:1(int!null) count_rows:13(int)
  ├── right columns: o_w_id:16(int) o_d_id:15(int) o_id:14(int) o_ol_cnt:20(int)
  ├── stats: [rows=295745, distinct(1)=2999, null(1)=0, distinct(2)=10, null(2)=0, distinct(3)=10, null(3)=0, distinct(13)=295745, null(13)=0]
+ ├── key: (1-3)
+ ├── fd: (1-3)-->(13)
  ├── group-by
  │    ├── save-table-name: consistency_11_group_by_2
  │    ├── columns: ol_o_id:1(int!null) ol_d_id:2(int!null) ol_w_id:3(int!null) count_rows:13(int!null)