github-actions[bot] commented on code in PR #67549:
URL: https://github.com/apache/doris/pull/67549#discussion_r4320638790


##########
fe/fe-core/src/main/java/org/apache/doris/nereids/stats/HboJoinConditions.java:
##########
@@ -0,0 +1,131 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+package org.apache.doris.nereids.stats;
+
+import org.apache.doris.nereids.trees.expressions.EqualTo;
+import org.apache.doris.nereids.trees.expressions.Expression;
+import org.apache.doris.nereids.trees.expressions.NullSafeEqual;
+import org.apache.doris.nereids.trees.expressions.Slot;
+import org.apache.doris.nereids.trees.expressions.SlotReference;
+import org.apache.doris.nereids.trees.plans.JoinType;
+import org.apache.doris.nereids.trees.plans.Plan;
+import org.apache.doris.nereids.trees.plans.algebra.Join;
+
+import com.google.common.hash.Hashing;
+
+import java.nio.charset.StandardCharsets;
+import java.util.ArrayList;
+import java.util.List;
+import java.util.Optional;
+import java.util.Set;
+import java.util.TreeSet;
+
+/**
+ * Canonical description and fingerprint of the equality conditions of a join, 
used as the key of
+ * manually injected join expansion entries ({@code HBO SET EXPANSION}).
+ *
+ * <p>The join type and the residual (non equality) conditions take part in 
the key next to the hash
+ * (equality) conjuncts, because the injected factor replaces the output rows 
of the whole join: an
+ * inner join which matches nothing and a left outer join of the same columns 
produce very different
+ * row counts, and a selective residual predicate changes the output by orders 
of magnitude. The
+ * shape of both sub trees is still excluded, so one injected entry stays 
reusable by every query
+ * which joins the same columns with the same join type and the same residual 
conditions.
+ *
+ * <p>The canonical form is {@code JE{<join type>;EqualTo(...);...}} with the 
pairs and the residual
+ * conditions sorted; a pair is rendered by {@link 
GroupStructInfo#normalizeExpression(Expression)}
+ * which already sorts the two operands of an equality (equality is 
commutative), so {@code a = b}
+ * and {@code b = a} collapse. A residual condition is rendered with its 
literal in both modes,
+ * because it decides how many partner rows a row finds ({@code b > c + 1} is 
not {@code b > c + 2}).
+ */
+public class HboJoinConditions {
+    private static final String PREFIX = "JE{";
+    private static final String SEP = ";";
+
+    private HboJoinConditions() {
+    }
+
+    /** True when the injected expansion of this join type is applicable at 
all. */
+    public static boolean isExpansionApplicable(JoinType joinType) {
+        // semi / anti / mark style joins can never produce more rows than 
their left input, and
+        // asof joins match at most one row per left row, so expansion can not 
happen there
+        return joinType == JoinType.INNER_JOIN
+                || joinType == JoinType.LEFT_OUTER_JOIN
+                || joinType == JoinType.RIGHT_OUTER_JOIN
+                || joinType == JoinType.FULL_OUTER_JOIN;
+    }
+
+    /**
+     * Canonical string of the equality conditions, empty when the join has no 
equality condition
+     * (e.g. a cross join). A null safe equality ({@code <=>}) is a hash 
conjunct as well, so it
+     * takes part in the canonical like a plain equality.
+     */
+    public static Optional<String> canonicalOf(Join join) {
+        List<String> pairs = new ArrayList<>();
+        for (Expression conjunct : join.getHashJoinConjuncts()) {
+            if (conjunct instanceof EqualTo || conjunct instanceof 
NullSafeEqual) {
+                pairs.add(GroupStructInfo.normalizeExpression(conjunct));

Review Comment:
   [P2] Bind expansion operands to their underlying relations
   
   For the reduced trees `Join(x.a=y.a AND x.b<y.b, Scan(t AS x), Scan(u AS 
y))` and the same join over `Scan(u AS x), Scan(t AS y)`, these bare slot 
expressions retain identical x/y qualifiers. With 1000 copies of (a=1,b=1) in t 
and 1000 copies of (a=1,b=2) in u, the joins return 1000000 versus zero rows, 
yet both JE keys match. A factor of 1000 pinned for the first therefore gives 
the second an estimate of 1000000. The OLAP J key's new `#ra` fields do not 
participate in this separate lookup. Unlike the existing computed-key-producer 
report, every operand here is a bare scan slot; its missing identity is the 
table that the SQL alias names. Resolve JE operands to stable relation/column 
identities before normalizing them.



##########
fe/fe-core/src/main/java/org/apache/doris/nereids/stats/HboUtils.java:
##########
@@ -502,27 +548,77 @@ private static InputTableStatisticsInfo 
buildHboInputTableStatisticsInfo(Physica
      * @param planToIdMap planToIdMap
      * @param scanToFilterMap scanToFilterMap
      * @param curPlanNodeRuntimeStats curPlanNodeRuntimeStats
+     * @param nodeFingerprints snapshot of nereids plan node id -> hbo 
fingerprint taken during
+     *        planning (only populated when the struct-info fingerprint is 
enabled)
      * @return plan statistics map
      */
     public static Map<PlanNodeAndHash, PlanStatisticsWithInputInfo> 
genPlanStatisticsMap(
             Map<Integer, PhysicalPlan> idToPlanMap, Map<PhysicalPlan, Integer> 
planToIdMap,
             Map<RelationId, Set<Expression>> scanToFilterMap,
-            List<TPlanNodeRuntimeStatsItem> curPlanNodeRuntimeStats) {
+            List<TPlanNodeRuntimeStatsItem> curPlanNodeRuntimeStats,
+            Map<Integer, String> nodeFingerprints) {
         Map<PlanNodeAndHash, PlanStatisticsWithInputInfo> 
outputPlanStatisticsMap = new HashMap<>();
+        // the fingerprint a plan node was published under, so a second node 
with the same fingerprint
+        // can be folded into it (the map above is keyed by the plan node 
identity as well)
+        Map<String, PlanNodeAndHash> publishedKeyByHash = new HashMap<>();
+        int missingFingerprints = 0;
+        int skippedWithoutSnapshot = 0;
         for (TPlanNodeRuntimeStatsItem nodeStats : curPlanNodeRuntimeStats) {
             int nodeId = nodeStats.node_id;
             PhysicalPlan planNode = idToPlanMap.get(nodeId);
-            if (planNode != null) {
-                PlanStatistics curPlanStatistics = 
PlanStatistics.buildFromStatsItem(
-                        nodeStats, planNode, scanToFilterMap);
-                InputTableStatisticsInfo inputTableStatisticsInfo = 
buildHboInputTableStatisticsInfo(
-                        planNode, planToIdMap, scanToFilterMap, 
curPlanNodeRuntimeStats);
-                Optional<String> hash = inputTableStatisticsInfo.getHash();
-                PlanNodeAndHash planNodeAndHash = new 
PlanNodeAndHash((AbstractPlan) planNode, hash);
-                PlanStatisticsWithInputInfo planHashWithInputInfo = new 
PlanStatisticsWithInputInfo(
-                        nodeId, curPlanStatistics, inputTableStatisticsInfo);
-                outputPlanStatisticsMap.put(planNodeAndHash, 
planHashWithInputInfo);
+            if (planNode == null) {
+                continue;
             }
+            PlanStatistics curPlanStatistics = 
PlanStatistics.buildFromStatsItem(
+                    nodeStats, planNode, scanToFilterMap);
+            InputTableStatisticsInfo inputTableStatisticsInfo = 
buildHboInputTableStatisticsInfo(
+                    planNode, planToIdMap, scanToFilterMap, 
curPlanNodeRuntimeStats);
+            Optional<String> hash;
+            if (nodeFingerprints != null && 
nodeFingerprints.containsKey(nodeId)) {
+                String snapshot = nodeFingerprints.get(nodeId);
+                if (GroupStructInfo.UNSUPPORTED_FINGERPRINT.equals(snapshot)) {
+                    // the node is deliberately excluded from the hbo 
fingerprint (its group is
+                    // unsupported), so its missing fingerprint is not a 
diagnostic gap
+                    continue;
+                }
+                hash = Optional.ofNullable(snapshot);
+            } else {
+                // no planning-time snapshot for this node: skip it
+                skippedWithoutSnapshot++;
+                if (nodeFingerprints != null && !nodeFingerprints.isEmpty()) {
+                    missingFingerprints++;
+                }
+                continue;
+            }
+            if (!hash.isPresent()) {
+                continue;
+            }
+            PlanNodeAndHash planNodeAndHash = new 
PlanNodeAndHash((AbstractPlan) planNode, hash);
+            PlanNodeAndHash publishedKey = publishedKeyByHash.get(hash.get());
+            if (publishedKey == null) {
+                publishedKeyByHash.put(hash.get(), planNodeAndHash);
+                outputPlanStatisticsMap.put(planNodeAndHash, new 
PlanStatisticsWithInputInfo(
+                        nodeId, curPlanStatistics, inputTableStatisticsInfo));
+                continue;
+            }
+            // a second runtime node with the same fingerprint (the two scans 
of a self join, for
+            // instance): the provider stores one entry per fingerprint, so 
the input statistics of both
+            // nodes are folded here - writing both would let the last write 
discard the other node's
+            // rows, and the drift comparison of the published entry expects 
the rows of every scan
+            PlanStatisticsWithInputInfo published = 
outputPlanStatisticsMap.get(publishedKey);
+            outputPlanStatisticsMap.put(publishedKey, new 
PlanStatisticsWithInputInfo(
+                    published.getId(), published.getPlanStatistics(),
+                    
published.getInputTableInfo().merge(inputTableStatisticsInfo)));

Review Comment:
   [P2] Preserve separate input populations for same-key scan runs
   
   Consider a qualifying execution with runtime filters OFF of `SELECT count(*) 
FROM (SELECT a FROM t WHERE b=1) x JOIN (SELECT a FROM t WHERE b=2) y ON 
x.a=y.a`. The derived aliases wrap Projects, so alias lowering leaves both 
underlying scan aliases empty and they share the S fingerprint. If both scans 
read all N mixed rows before filtering, this merge retains one node's output 
but concatenates both inputs into one run. On the identical next query, 
historical predicate matching accepts both recorded RelationIds, then scan 
fallback compares that run's recorded 2N with the single current scan's N and 
rejects it as STALE at the default tolerance. This is a new consequence of the 
same-key publication fix, distinct from the existing pruning-counter mismatch: 
each original scan population is individually comparable. Keep alternative node 
observations as separate runs under the fingerprint instead of concatenating 
their inputs.



##########
fe/fe-core/src/main/java/org/apache/doris/nereids/stats/GroupStructInfo.java:
##########
@@ -0,0 +1,2880 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+package org.apache.doris.nereids.stats;
+
+import org.apache.doris.catalog.TableIf;
+import org.apache.doris.nereids.memo.Group;
+import org.apache.doris.nereids.memo.GroupExpression;
+import org.apache.doris.nereids.properties.OrderKey;
+import org.apache.doris.nereids.trees.expressions.Alias;
+import org.apache.doris.nereids.trees.expressions.And;
+import org.apache.doris.nereids.trees.expressions.ArrayItemReference;
+import org.apache.doris.nereids.trees.expressions.EqualTo;
+import org.apache.doris.nereids.trees.expressions.ExprId;
+import org.apache.doris.nereids.trees.expressions.Expression;
+import org.apache.doris.nereids.trees.expressions.Match;
+import org.apache.doris.nereids.trees.expressions.NamedExpression;
+import org.apache.doris.nereids.trees.expressions.NullSafeEqual;
+import org.apache.doris.nereids.trees.expressions.Or;
+import org.apache.doris.nereids.trees.expressions.OrderExpression;
+import org.apache.doris.nereids.trees.expressions.SearchExpression;
+import org.apache.doris.nereids.trees.expressions.Slot;
+import org.apache.doris.nereids.trees.expressions.SlotReference;
+import org.apache.doris.nereids.trees.expressions.WindowExpression;
+import org.apache.doris.nereids.trees.expressions.functions.Function;
+import org.apache.doris.nereids.trees.expressions.functions.Udf;
+import 
org.apache.doris.nereids.trees.expressions.functions.agg.AggregateFunction;
+import org.apache.doris.nereids.trees.expressions.functions.scalar.Lambda;
+import org.apache.doris.nereids.trees.expressions.literal.ArrayLiteral;
+import org.apache.doris.nereids.trees.expressions.literal.DateLiteral;
+import org.apache.doris.nereids.trees.expressions.literal.Literal;
+import org.apache.doris.nereids.trees.expressions.literal.NullLiteral;
+import org.apache.doris.nereids.trees.plans.AbstractPlan;
+import org.apache.doris.nereids.trees.plans.JoinType;
+import org.apache.doris.nereids.trees.plans.Plan;
+import org.apache.doris.nereids.trees.plans.algebra.Aggregate;
+import org.apache.doris.nereids.trees.plans.algebra.Except;
+import org.apache.doris.nereids.trees.plans.algebra.Filter;
+import org.apache.doris.nereids.trees.plans.algebra.Generate;
+import org.apache.doris.nereids.trees.plans.algebra.Intersect;
+import org.apache.doris.nereids.trees.plans.algebra.Join;
+import org.apache.doris.nereids.trees.plans.algebra.Limit;
+import org.apache.doris.nereids.trees.plans.algebra.OlapScan;
+import org.apache.doris.nereids.trees.plans.algebra.Project;
+import org.apache.doris.nereids.trees.plans.algebra.Repeat;
+import org.apache.doris.nereids.trees.plans.algebra.SetOperation;
+import org.apache.doris.nereids.trees.plans.algebra.Sort;
+import org.apache.doris.nereids.trees.plans.algebra.TopN;
+import org.apache.doris.nereids.trees.plans.algebra.Union;
+import org.apache.doris.nereids.trees.plans.algebra.Window;
+import org.apache.doris.nereids.trees.plans.logical.LogicalCTEAnchor;
+import org.apache.doris.nereids.trees.plans.logical.LogicalCTEConsumer;
+import org.apache.doris.nereids.trees.plans.logical.LogicalCTEProducer;
+import org.apache.doris.nereids.trees.plans.logical.LogicalFileScan;
+import org.apache.doris.nereids.trees.plans.logical.LogicalGenerate;
+import org.apache.doris.nereids.trees.plans.logical.LogicalOlapScan;
+import org.apache.doris.nereids.trees.plans.physical.PhysicalAssertNumRows;
+import org.apache.doris.nereids.trees.plans.physical.PhysicalCTEAnchor;
+import org.apache.doris.nereids.trees.plans.physical.PhysicalCTEConsumer;
+import org.apache.doris.nereids.trees.plans.physical.PhysicalCTEProducer;
+import org.apache.doris.nereids.trees.plans.physical.PhysicalDistribute;
+import org.apache.doris.nereids.trees.plans.physical.PhysicalFileScan;
+import org.apache.doris.nereids.trees.plans.physical.PhysicalGenerate;
+import org.apache.doris.nereids.trees.plans.physical.PhysicalHashAggregate;
+import 
org.apache.doris.nereids.trees.plans.physical.PhysicalStorageLayerAggregate;
+import org.apache.doris.nereids.util.MutableState;
+import org.apache.doris.qe.ConnectContext;
+
+import com.google.common.annotations.VisibleForTesting;
+import com.google.common.hash.Hashing;
+import org.apache.logging.log4j.LogManager;
+import org.apache.logging.log4j.Logger;
+
+import java.nio.charset.StandardCharsets;
+import java.time.ZoneId;
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.Collection;
+import java.util.Collections;
+import java.util.Comparator;
+import java.util.HashSet;
+import java.util.LinkedHashMap;
+import java.util.List;
+import java.util.Map;
+import java.util.Optional;
+import java.util.Set;
+import java.util.TreeSet;
+import java.util.concurrent.atomic.AtomicInteger;
+
+/**
+ * Simplified struct info of a memo {@link Group}, used by History Based 
Optimization (HBO).
+ *
+ * <p>The struct info is a property of the <b>group</b>, not of one of its 
group expressions: all
+ * expressions of a group are logically equivalent, so they describe the same 
set of relations with
+ * the same predicates, and the canonical form below is deliberately 
insensitive to which expression
+ * is picked.
+ * <ul>
+ *   <li>join commutativity: children of a join are canonicalized by 
sorting;</li>
+ *   <li>join associativity: a whole inner / cross join chain is emitted as 
one node
+ *       ({@code J{inner,c:[...]}(...;...)}) whose children are the chain 
leaves sorted by their
+ *       canonical form and whose conditions are the sorted union of every 
condition of the chain,
+ *       so {@code (A join B) join C} and {@code A join (B join C)} produce 
the same descriptor;</li>
+ *   <li>aggregation: only the group by keys and the child participate, 
because the output row count
+ *       of an aggregation is the number of groups and cannot be changed by 
the aggregate functions
+ *       or by the output expressions;</li>
+ *   <li>project is transparent for structure matching.</li>
+ * </ul>
+ * This mirrors what the MV oriented {@code rules.exploration.mv.StructInfo} 
does (it identifies a
+ * sub tree by its relation set and by level independent - shuttled - 
predicates), with every MV
+ * specific field dropped: no hyper graph, no shuttle map, no equivalence 
class, no lineage.
+ *
+ * <p>What the canonical form keeps:
+ * <ul>
+ *   <li>for each scan: the table qualifier and - as an annotation only - the 
data state of the scan
+ *       (its visible version, the rows it reads and how many of the table 
partitions it selects,
+ *       see {@link HboScanDescriptor});</li>
+ *   <li>for filter / join / aggregate: the normalized predicates / join 
conditions / grouping keys,
+ *       i.e. the structural pattern only (slot and expression ids are 
stripped by
+ *       {@link #normalizeExpression}).</li>
+ * </ul>
+ * The string contains no per-query identifier, so it is reproducible across 
runs and queries for
+ * structurally identical sub trees, and its sha256 is used as the HBO cache 
key (fingerprint).
+ *
+ * <p>The sha256 is taken over the canonical string <b>without</b> the scan 
baselines
+ * ({@link #stripScanBaseline}): a hbo key identifies a plan pattern and the 
relation it reads, not a
+ * data state, so an entry whose table simply keeps growing stays matchable 
instead of silently never
+ * matching again. Whether an entry may still be applied is decided on the 
read side, by comparing
+ * the baseline of the entry with the data state of the current query (see
+ * {@link HboStructFreshness}).
+ *
+ * <p>The descriptor is derived from the group's logical expression and its 
child groups (memo level
+ * traversal, with a visited set to guard shared sub graphs such as CTE). 
Groups whose content is not
+ * supported (e.g. contains TVF / CTE consumer, or the head operator is not 
one of the supported
+ * kinds) are {@link #isValid() invalid} and callers must fall back to the 
legacy behavior.
+ *
+ * <p>This description is always built by the FE from the plan it is looking 
at, and every string it can
+ * produce is one of its renderings: {@link #getCanonical(LiteralMode)} is the 
text EXPLAIN prints and a
+ * user may paste into {@code HBO SET STATISTICS ... STRUCT='...'}, {@link 
#getShape(LiteralMode)} is the
+ * same text without the data state of the scans, and {@link 
#getFingerprint(LiteralMode)} is the sha256
+ * of that shape. Nothing is ever parsed to produce a fingerprint - in 
particular the text a user pasted
+ * is only compared with the fingerprint next to it, never taken as its source.
+ */
+public class GroupStructInfo {
+    /**
+     * The default of {@code hbo_max_scans_per_group}, used when no session is 
available. 20 keeps
+     * every TPC-DS shape observed in this repository (the largest single sub 
tree is query64's
+     * 19 scan join group) while refusing trees which are pathologically wide.
+     */
+    public static final int DEFAULT_MAX_SCANS_PER_GROUP = 20;
+    /**
+     * Snapshot value which marks a plan node that is deliberately excluded 
from the hbo
+     * fingerprint (its group is unsupported, e.g. a sort / topn). It is not a 
fingerprint and is
+     * never hashed: the publish path uses it to tell an expected gap from a 
lost snapshot. A
+     * concurrent map can not store a null marker, so an empty string is used.
+     */
+    public static final String UNSUPPORTED_FINGERPRINT = "";
+
+    /**
+     * The prefix of the reason a node whose kind the description does not 
support is reported with, and
+     * the two halves of the reason a node with an unsupported number of 
children is reported with. They
+     * are constants so that the corpus can bind the frozen skip texts to the 
formula which produces them
+     * instead of restating the prefix.
+     */
+    static final String UNSUPPORTED_REASON_PREFIX = "unsupported=";
+    static final String ARITY_REASON_PREFIX = "arity=";
+    static final String ARITY_REASON_MIDDLE = " of ";
+
+    private static final List<HboScanDescriptor> INVALID_SCANS = 
Collections.emptyList();
+
+    /**
+     * Characters which structure the canonical form and therefore can not 
appear raw inside a
+     * literal value (see {@link #encodeLiteralValue}).
+     */
+    private static final String RESERVED_LITERAL_CHARS = "\u0000\\%(){}[],;:|";
+
+    private static final char[] HEX_DIGITS = "0123456789ABCDEF".toCharArray();
+
+    /**
+     * How many groups this query described. A group is described once: the 
description is memoized on
+     * the group and composed by its parents, so this number only grows when a 
new group is reached.
+     */
+    private static final AtomicInteger describedGroupCount = new 
AtomicInteger();
+
+    /**
+     * How many descriptions were walked while materializing a string. A 
description whose string is
+     * already materialized is copied instead of being walked again, so this 
number does not grow for
+     * the sub tree of an already materialized child.
+     */
+    private static final AtomicInteger materializedGroupCount = new 
AtomicInteger();
+
+    /** Shared invalid instance: the group content is not supported by the 
simplified struct info. */
+    public static final GroupStructInfo INVALID = new GroupStructInfo(false, 
"", null, INVALID_SCANS);
+
+    private static final String SEP = ";";
+
+    /**
+     * The header letters whose arguments are part of the identity of their 
node (see
+     * {@link Kind#literalsAreIdentity()}): the fold of a pasted struct info 
copies those headers verbatim,
+     * because folding one of their literals would make the sha256 of the text 
differ from the fingerprint
+     * EXPLAIN printed. The set is derived from the kinds which render the 
text, so a kind whose literals
+     * stop being identity cannot be forgotten here.
+     */
+    private static final String PROTECTED_HEADERS = protectedHeaders();
+
+    /**
+     * The markers of the headers whose condition collection is sorted per 
literal mode, i.e. the ones the
+     * fold of a pasted struct info has to re-sort after it folded their 
literals (see
+     * {@code recanonicalizeFoldedConditions}): a filter, an aggregation, a 
join (which also de-duplicates)
+     * and the grouping sets of a repeat.
+     */
+    private static final String[] CONDITION_HEADER_MARKERS = {"F{", "A{gb:", 
"J{", "R{gs:["};
+
+    /**
+     * The functions whose value depends on the session time zone although 
neither their arguments nor
+     * their result are a date: an epoch value is read in that zone ({@code 
hour_from_unixtime(t.ts) = 0}
+     * keeps 1000 rows in one session and 1 row in another although its 
argument is the same integer).
+     * A function whose argument or result is a date or a datetime is covered 
by its type instead (see
+     * {@link #usesSessionTimeZone}).
+     */
+    private static final List<String> EPOCH_TIME_ZONE_FUNCTIONS = 
Arrays.asList(
+            "hour_from_unixtime", "minute_from_unixtime", 
"second_from_unixtime",
+            "microsecond_from_unixtime", "unix_timestamp");
+
+    private static final String NO_LOOKUP_PATH_REASON =
+            "storage layer aggregate: the read side applies the row count of 
the aggregation above it";
+
+    private static final String PARTIAL_STAGE_REASON =
+            "local (partial) aggregation stage: the read side applies the row 
count of the final"
+                    + " aggregation above it";
+
+    private static final Logger LOG = 
LogManager.getLogger(GroupStructInfo.class);
+
+    /**
+     * Whether literal values participate in the canonical string / 
fingerprint.
+     * <ul>
+     *   <li>{@link #WITH_LITERAL} keeps the literal value ({@code 
lit(10:int)}): the fingerprint is
+     *       bound to the exact constants, used for filter roots where the 
constant changes the
+     *       output row count;</li>
+     *   <li>{@link #NO_LITERAL} replaces every literal value with {@code *} 
({@code lit(*)}): the
+     *       fingerprint is constant agnostic. It is the primary key of a 
scan, of a constant-free
+     *       filter shape and of the key the publish path generates for a join 
/ aggregate root; every
+     *       root which is annotated also carries a literal carrying form.</li>
+     * </ul>
+     * The literal data type is intentionally not kept: nereids inserts an 
explicit {@code Cast}
+     * for mismatching operand types, so two semantically different literal 
forms already differ by
+     * the cast node, while equivalent forms (e.g. {@code d > 1} and {@code d 
> 1.0} on a decimal
+     * column) are allowed to collapse.
+     */
+    public enum LiteralMode {
+        WITH_LITERAL,
+        NO_LITERAL
+    }
+
+    /**
+     * Whether the description could be built. It is invalid - and the memo 
caches that answer, so every
+     * node above the sub tree gets no fingerprint for the whole query - when 
one of the following holds
+     * for the sub tree it covers:
+     * <ul>
+     *   <li>it contains an operator the canonical form does not describe, 
which the annotation prints as
+     *       {@code unsupported=<Operator>}: a table valued function relation 
({@code numbers},
+     *       {@code s3}), an apply, a recursive union, a partition top-n, 
...;</li>
+     *   <li>it reads more scans than {@code hbo_max_scans_per_group}:
+     *       {@code subtree scans=N > hbo_max_scans_per_group=M};</li>
+     *   <li>a table name carries a struct info delimiter ({@code ,} or {@code 
}}), so the printed token
+     *       could not be read back: {@code delimiter in table name 
<table>};</li>
+     *   <li>the memo does not look like a canonical form can express it: a 
unary operator whose group
+     *       expression has another arity, a CTE consumer which has no memo 
edge to its producer, a
+     *       reused sub tree whose description is not available;</li>
+     *   <li>the data state of a scan cannot be read (an external table whose 
metadata is not available,
+     *       a cloud rpc failure): {@code no data state for <table> 
(<cause>)}.</li>
+     * </ul>
+     * A node whose group cannot be resolved at all is not described either, 
which the annotation reports
+     * as {@code no group for <Operator>}.
+     */
+    private final boolean valid;
+    /**
+     * The tree of this description: the information of its own group and the 
descriptions of the groups
+     * below it, all as objects. Nothing is rendered while it is built - 
{@link #render} is the one place
+     * which knows the grammar - and every node remembers the forms it has 
rendered, so a parent which is
+     * rendered later composes the text of a child instead of walking its sub 
tree again.
+     */
+    private final Node root;
+    /** The scans of the sub tree, in the order their tokens appear in the 
canonical string. */
+    private final List<HboScanDescriptor> scans;
+    /** Why no struct info was built, when it was refused by a limit instead 
of being unsupported. */
+    private final String skipReason;
+    // the forms materialized on first request: the read side only needs a 
fingerprint, while the
+    // explain annotation needs the canonical string, so building all of them 
up front would be wasted
+    private String canonicalWithLiteral;
+    private String canonicalNoLiteral;
+    private String shapeWithLiteral;
+    private String shapeNoLiteral;
+    private String fingerprintWithLiteral;
+    private String fingerprintNoLiteral;
+
+    private GroupStructInfo(boolean valid, String skipReason, Node root,
+            List<HboScanDescriptor> scans) {
+        this.valid = valid;
+        this.skipReason = skipReason;
+        this.root = root;
+        this.scans = scans;
+    }
+
+    private static GroupStructInfo ofNode(Node root) {
+        List<HboScanDescriptor> scans = new ArrayList<>();
+        collectScans(root, scans);
+        return new GroupStructInfo(true, "", root, 
Collections.unmodifiableList(scans));
+    }
+
+    private static GroupStructInfo invalidStructInfo(String skipReason) {
+        return skipReason.isEmpty()
+                ? INVALID
+                : new GroupStructInfo(false, skipReason, null, INVALID_SCANS);
+    }
+
+    private static String protectedHeaders() {
+        StringBuilder letters = new StringBuilder();
+        for (Kind kind : Kind.values()) {
+            if (kind.literalsAreIdentity()) {
+                letters.append(kind.headerLetters());
+            }
+        }
+        return letters.toString();
+    }
+
+    /** The reason the struct info was refused by a limit, or empty. Only for 
diagnostics. */
+    public String getSkipReason() {
+        return skipReason;
+    }
+
+    public boolean isValid() {
+        return valid;
+    }
+
+    /** The node this description is made of; null when the description is 
invalid. */
+    private Node root() {
+        return root;
+    }
+
+    /**
+     * The row count and partition selection of every scan of the sub tree, in 
the order the scan tokens
+     * appear in the canonical string (i.e. the order a user sees when pasting 
the struct info). A sub
+     * tree which the canonical string writes twice - a child which is 
referenced more than once - keeps
+     * its token in the text twice while its tables are read once, so its 
descriptors appear here once;
+     * a caller which compares this list with the tokens of a text has to 
expect that difference (the
+     * learned freshness comparison folds the tokens of a text per table for 
the same reason). Empty when
+     * the struct info is invalid.
+     */
+    public List<HboScanDescriptor> getScans() {
+        return scans;
+    }
+
+    /** The canonical string of one literal mode, with the data state of every 
scan. */
+    public String getCanonical(LiteralMode mode) {
+        boolean noLiteral = mode == LiteralMode.NO_LITERAL;
+        String materialized = noLiteral ? canonicalNoLiteral : 
canonicalWithLiteral;
+        if (materialized != null) {
+            return materialized;
+        }
+        materialized = root == null ? "" : render(root, mode, false);
+        if (noLiteral) {
+            canonicalNoLiteral = materialized;
+        } else {
+            canonicalWithLiteral = materialized;
+        }
+        return materialized;
+    }
+
+    /**
+     * The fingerprint input of one literal mode: the canonical string with 
the data state of every scan
+     * removed ({@code S{db.t}}). It is rendered from the same tree as the 
canonical string, with the scan
+     * tokens reduced to their identity, and never parsed out of the text, so 
no text inside a table name
+     * or a literal can be mistaken for a scan token.
+     */
+    public String getShape(LiteralMode mode) {
+        boolean noLiteral = mode == LiteralMode.NO_LITERAL;
+        String materialized = noLiteral ? shapeNoLiteral : shapeWithLiteral;
+        if (materialized != null) {
+            return materialized;
+        }
+        materialized = root == null ? "" : render(root, mode, true);
+        if (noLiteral) {
+            shapeNoLiteral = materialized;
+        } else {
+            shapeWithLiteral = materialized;
+        }
+        return materialized;
+    }
+
+    /** The sha256 of {@link #getShape(LiteralMode)}: the key an hbo entry is 
registered under. */
+    public String getFingerprint(LiteralMode mode) {
+        boolean noLiteral = mode == LiteralMode.NO_LITERAL;
+        String materialized = noLiteral ? fingerprintNoLiteral : 
fingerprintWithLiteral;
+        if (materialized != null) {
+            return materialized;
+        }
+        materialized = sha256(getShape(mode));
+        if (noLiteral) {
+            fingerprintNoLiteral = materialized;
+        } else {
+            fingerprintWithLiteral = materialized;
+        }
+        return materialized;
+    }
+
+    private static String sha256(String value) {
+        return Hashing.sha256().hashString(value, 
StandardCharsets.UTF_8).toString();
+    }
+
+    /**
+     * Resolve the fingerprint of the memo group that {@code planNode} belongs 
to, when the node
+     * still carries its {@link GroupExpression} back reference (memo inner 
plans, or plans from
+     * {@code chooseBestPlan}). Empty when the group content is unsupported 
(invalid struct info).
+     */
+    public static Optional<String> fingerprintOfPlanNode(AbstractPlan 
planNode) {
+        return fingerprintOfPlanNode(planNode, LiteralMode.WITH_LITERAL);
+    }
+
+    /**
+     * Resolve the group fingerprint of a plan node in the given literal mode.
+     */
+    public static Optional<String> fingerprintOfPlanNode(AbstractPlan 
planNode, LiteralMode mode) {
+        Group group = 
planNode.getGroupExpression().map(GroupExpression::getOwnerGroup).orElse(null);
+        if (hasNoHboLookupPath(planNode, group)) {
+            return Optional.empty();
+        }
+        return fingerprintOfGroup(group, mode);
+    }
+
+    /**
+     * Resolve the fingerprint of the group that {@code planNode} belongs to, 
with a fallback to
+     * the {@link MutableState#KEY_GROUP} group-id state that post processors 
propagate to their
+     * rewritten copies (see {@code copyStatsAndGroupIdFrom}). {@code 
groupsById} maps memo group
+     * id to group, and is looked up only when the back reference is absent.
+     */
+    public static Optional<String> fingerprintOfPlanNode(AbstractPlan 
planNode, Map<Integer, Group> groupsById) {
+        return fingerprintOfPlanNode(planNode, groupsById, 
LiteralMode.WITH_LITERAL);
+    }
+
+    /**
+     * Resolve the group fingerprint of a plan node in the given literal mode, 
with the
+     * {@link MutableState#KEY_GROUP} fallback for post-processed copies.
+     */
+    public static Optional<String> fingerprintOfPlanNode(AbstractPlan 
planNode, Map<Integer, Group> groupsById,
+            LiteralMode mode) {
+        Group group = resolveGroup(planNode, groupsById);
+        if (hasNoHboLookupPath(planNode, group)) {
+            return Optional.empty();
+        }
+        return fingerprintOfGroup(group, mode);
+    }
+
+    private static Optional<String> fingerprintOfGroup(Group group, 
LiteralMode mode) {
+        GroupStructInfo structInfo = group == null ? INVALID : 
group.getOrComputeHboStructInfo();
+        return structInfo.isValid() ? 
Optional.of(structInfo.getFingerprint(mode)) : Optional.empty();
+    }
+
+    /**
+     * Resolve the description of the group a plan node belongs to, using the 
group-expression back
+     * reference or the KEY_GROUP group-id state propagated by post processors 
(see
+     * {@link #fingerprintOfPlanNode}). Empty when the group content is 
unsupported.
+     */
+    public static Optional<GroupStructInfo> structInfoOfPlanNode(AbstractPlan 
planNode,
+            Map<Integer, Group> groupsById) {
+        Group group = resolveGroup(planNode, groupsById);
+        if (hasNoHboLookupPath(planNode, group)) {
+            // the annotation asks for the struct info first: without this 
guard the node would advertise
+            // a key which no read path ever looks up (see hasNoHboLookupPath)
+            return Optional.empty();
+        }
+        return structInfoOfGroup(group);
+    }
+
+    private static Optional<GroupStructInfo> structInfoOfGroup(Group group) {
+        if (group == null) {
+            return Optional.empty();
+        }
+        GroupStructInfo structInfo = group.getOrComputeHboStructInfo();
+        return structInfo.isValid() ? Optional.of(structInfo) : 
Optional.empty();
+    }
+
+    /**
+     * The description of a group: computed once per query and memoized on the 
group (see
+     * {@link Group#getOrComputeHboStructInfo}), so that a parent composes the 
description of its
+     * children instead of describing their sub trees again.
+     */
+    public static GroupStructInfo of(Group group) {
+        return describeGroup(group);
+    }
+
+    public static GroupStructInfo describeGroup(Group group) {
+        return describeGroup(group, new Ctx());
+    }
+
+    private static GroupStructInfo describeGroup(Group group, Ctx ctx) {
+        if (!ctx.visited.add(group)) {
+            // the same group is reached twice (a CTE which is consumed twice, 
a scan which feeds two
+            // consumers, a shared sub tree): a tree cannot express the reuse, 
so the sub tree is
+            // described again - the description is the one of a plan which 
writes that sub tree twice
+            // (a self join for instance), and the read side of a query builds 
the same description, so
+            // an entry recorded from one form applies to the other. The sub 
tree was read once, so the
+            // repeated reference composes its canonical form but not its 
scans again (the drift guard
+            // compares the scan states of the tables a query actually reads).
+            GroupStructInfo memoized = group.getHboStructInfoOrNull();
+            if (memoized != null) {
+                return memoized;
+            }
+            invalid(ctx, "sharing=group " + group.getGroupId().asInt() + " 
reached twice");
+            return INVALID;
+        }
+        return describeVisited(group, ctx);
+    }
+
+    /**
+     * The description of a group which the caller already marked visited (the 
join chain marks the
+     * groups it descends through itself, so that a group is never added twice 
within one build).
+     */
+    private static GroupStructInfo describeVisited(Group group, Ctx ctx) {
+        GroupStructInfo memoized = group.getHboStructInfoOrNull();
+        if (memoized != null) {
+            return memoized;
+        }
+        GroupStructInfo computed = build(group, ctx);
+        group.setHboStructInfo(computed);
+        return computed;
+    }
+
+    /**
+     * The first logical expression of a group, or null when it holds none: 
{@link
+     * Group#getFirstLogicalExpression()} asserts that there is one, so a 
group which only holds
+     * physical expressions (an enforcer group, or a group a rule filled with 
physical plans) cannot be
+     * asked that way.
+     */
+    private static GroupExpression firstLogicalExpression(Group group) {
+        List<GroupExpression> logical = group.getLogicalExpressions();
+        return logical.isEmpty() ? null : logical.get(0);
+    }
+
+    /** Why a group has nothing to describe: its chosen id and how many 
expressions it holds. */
+    private static String describeGroupState(Group group) {
+        return group.getGroupId().asInt()
+                + " (logical=" + group.getLogicalExpressions().size()
+                + ", physical=" + group.getPhysicalExpressions().size()
+                + ", enforcers=" + group.getEnforcers().size() + ")";
+    }
+
+    /**
+     * The expression which is described for a group. The first logical 
expression is used, and the logical
+     * form is what the key of a group has to be made of: the read side looks 
an entry up while the plan is
+     * still being optimized, i.e. before any expression is chosen, and a 
physical plan may hold nodes the
+     * logical plan abstracts away (the two staged aggregation of a {@code 
count(*)}, for instance), which
+     * would move the key of every such group and make a pinned entry miss. 
The expression the plan chooser
+     * picked is deliberately not consulted for the same reason - a key must 
not depend on when it is
+     * computed. The method is package visible so that a test can pin that the 
recorded choice of the plan
+     * chooser is not consulted.
+     */
+    static GroupExpression getRepresentativeExpression(Group group) {
+        GroupExpression logical = firstLogicalExpression(group);
+        if (logical != null) {
+            return logical;
+        }
+        // Some groups have no logical plan at all, for instance the group of a
+        // {@link PhysicalStorageLayerAggregate} (an aggregation answered from 
the storage layer is a
+        // catalog relation a rule inserts, there is no logical aggregation 
left to describe) or a group
+        // which only holds an enforcer. Such a group is described through the 
physical expression it
+        // holds: it is the only form it has, so both sides - the read side 
and the annotation - see the
+        // same one, and giving the whole struct info up would hide every node 
above it.
+        List<GroupExpression> physical = group.getPhysicalExpressions();
+        if (!physical.isEmpty()) {
+            return physical.get(0);
+        }
+        // an enforcer group keeps its expression in the enforcer list, not 
among the physical ones
+        return group.getEnforcers().isEmpty() ? null : 
group.getEnforcers().keySet().iterator().next();
+    }
+
+    /**
+     * Describe one group by composing the descriptions of its children (which 
are memoized, so each
+     * group of a plan is described exactly once per query), in both literal 
modes at once.
+     */
+    private static GroupStructInfo build(Group group, Ctx ctx) {
+        describedGroupCount.incrementAndGet();
+        HboStructSummary summary = group.getOrComputeHboStructSummary();
+        int maxScansPerGroup = hboMaxScansPerGroup();
+        if (maxScansPerGroup > 0 && summary.getScanCount() > maxScansPerGroup) 
{
+            // The canonical string of a group describes its whole sub tree, 
so a cheap structural
+            // summary is used as a gate: a sub tree with more scan tokens than
+            // hbo_max_scans_per_group is not described at all (the read side 
falls back to the
+            // optimizer estimation and EXPLAIN reports why).
+            return invalidStructInfo("subtree scans=" + summary.getScanCount()
+                    + " > hbo_max_scans_per_group=" + maxScansPerGroup);
+        }
+        GroupExpression logical = firstLogicalExpression(group);
+        if (logical != null) {
+            return describeExpression(group, logical, ctx);
+        }
+        GroupExpression representative = getRepresentativeExpression(group);
+        if (representative == null) {
+            // a group without any expression (no logical one, no physical 
one, no enforcer): there is
+            // nothing to describe
+            return invalidStructInfo("no expression in group " + 
describeGroupState(group));
+        }
+        return describeExpression(group, representative, ctx);
+    }
+
+    /** Describe one expression of a group: the body of {@link #build} without 
the choice of it. */
+    private static GroupStructInfo describeExpression(Group group, 
GroupExpression ge, Ctx ctx) {
+        Node root;
+        try {
+            root = buildNode(ge.getPlan(), ge, ctx);
+            if (root != null) {
+                applyColumnDefinitions(ge.getPlan(), root);
+            }
+        } catch (RuntimeException e) {
+            // memo content which the simplified struct info cannot describe 
(an unexpected plan node, a
+            // cast of a named expression which is not the alias of a window 
expression): treat the group as
+            // invalid and fall back to the legacy behavior instead of failing 
the optimizer on the hot
+            // path. Rendering cannot throw for a description which was built: 
it only concatenates.
+            LOG.debug("failed to compute hbo struct info for group {}", 
group.getGroupId(), e);
+            return invalidStructInfo(ctx.reason);
+        }
+        if (!ctx.valid || root == null) {
+            return invalidStructInfo(ctx.reason);
+        }
+        return ofNode(root);
+    }
+
+    /**
+     * Bind the columns the children of a node compute to the expression which 
produces them, and
+     * substitute a reference to such a column in the expressions of this node.
+     *
+     * <p>A project is transparent for structure matching and an aggregation 
keeps only its grouping
+     * keys in its header, so a column whose value they compute is 
<em>named</em> by every node above
+     * them and <em>defined</em> by none: {@code Aggregate(group by x) -> 
Project(a % 2 AS x) ->
+     * Scan(t)} and the same plan with {@code % 3} render one {@code 
A{gb:col(x)}} although their group
+     * counts differ, and a pinned row count of one is then applied to the 
other. The definition is
+     * therefore carried up: the expressions of this node are rewritten so 
that a column defined by a
+     * child renders as the expression which computes it, and the map is 
handed to the nodes above.
+     */
+    private static void applyColumnDefinitions(Plan plan, Node node) {
+        Map<ExprId, Expression> childDefinitions = 
childColumnDefinitions(node);
+        resolveNodeExpressions(node, childDefinitions);
+        if (plan instanceof Project) {
+            node.columnDefinitions = projectColumnDefinitions((Project) plan, 
childDefinitions);
+        } else if (plan instanceof Aggregate) {
+            node.columnDefinitions = aggregateColumnDefinitions((Aggregate<?>) 
plan, childDefinitions);
+        } else {
+            node.columnDefinitions = childDefinitions;
+        }
+    }
+
+    /**
+     * The columns an aggregation computes. Its header keeps the grouping keys 
- the number of groups,
+     * which is the row count of the node, depends on them alone - so the 
values its aggregate
+     * functions produce are defined nowhere: {@code Filter(s = 1) -> 
Aggregate(group by k, MIN(v) AS
+     * s)} and the same tree with {@code MAX(v) AS s} render one filter key 
although one k group whose
+     * values are 1 and 2 keeps zero and one rows. A definition is the 
aggregate function under the
+     * name of the alias which exposes it, resolved against the columns of the 
child like the header of
+     * the aggregation itself.
+     */
+    private static Map<ExprId, Expression> 
aggregateColumnDefinitions(Aggregate<?> aggregate,
+            Map<ExprId, Expression> childDefinitions) {
+        Map<ExprId, Expression> definitions = new LinkedHashMap<>();
+        for (NamedExpression output : aggregate.getOutputExpressions()) {
+            if (output instanceof Alias) {
+                definitions.put(output.getExprId(),
+                        resolveColumnDefinitions(((Alias) output).child(), 
childDefinitions));
+            }
+        }
+        return Collections.unmodifiableMap(definitions);
+    }
+
+    /** The definitions the children of a node expose: a join forwards the 
columns of both sides. */
+    private static Map<ExprId, Expression> childColumnDefinitions(Node node) {
+        if (node.children.size() == 1) {
+            return node.children.get(0).node.columnDefinitions;
+        }
+        if (node.children.isEmpty()) {
+            return Collections.emptyMap();
+        }
+        Map<ExprId, Expression> definitions = new LinkedHashMap<>();
+        for (Child child : node.children) {
+            definitions.putAll(child.node.columnDefinitions);
+        }
+        return Collections.unmodifiableMap(definitions);
+    }
+
+    /**
+     * The columns a project computes: an alias names the expression it wraps, 
and that expression is
+     * the value a node above the project reads. A plain slot of the 
projection is a forwarded column,
+     * which keeps the definition it already had below the project (a project 
of plain slots over a
+     * project of aliases forwards exactly those definitions).
+     */
+    private static Map<ExprId, Expression> projectColumnDefinitions(Project 
project,
+            Map<ExprId, Expression> childDefinitions) {
+        Map<ExprId, Expression> definitions = new LinkedHashMap<>();
+        for (NamedExpression output : project.getProjects()) {
+            if (output instanceof Alias) {
+                definitions.put(output.getExprId(),
+                        resolveColumnDefinitions(((Alias) output).child(), 
childDefinitions));
+            } else if (childDefinitions.containsKey(output.getExprId())) {
+                definitions.put(output.getExprId(), 
childDefinitions.get(output.getExprId()));
+            }
+        }
+        return Collections.unmodifiableMap(definitions);
+    }
+
+    /** Substitute every reference to a defined column with the expression 
which computes it. */
+    private static Expression resolveColumnDefinitions(Expression expression,
+            Map<ExprId, Expression> definitions) {
+        if (definitions.isEmpty()) {
+            return expression;
+        }
+        return expression.rewriteUp(rewritten -> {
+            if (!(rewritten instanceof Slot)) {
+                return rewritten;
+            }
+            Expression definition = definitions.get(((Slot) 
rewritten).getExprId());
+            return definition == null ? rewritten : definition;
+        });
+    }
+
+    private static List<Expression> resolveColumnDefinitions(List<Expression> 
expressions,
+            Map<ExprId, Expression> definitions) {
+        if (definitions.isEmpty()) {
+            return expressions;
+        }
+        List<Expression> resolved = new ArrayList<>(expressions.size());
+        for (Expression expression : expressions) {
+            resolved.add(resolveColumnDefinitions(expression, definitions));
+        }
+        return resolved;
+    }
+
+    /** Rewrite the expressions a node keeps, in place: they are rendered 
exactly once, later. */
+    private static void resolveNodeExpressions(Node node, Map<ExprId, 
Expression> definitions) {
+        if (definitions.isEmpty()) {
+            return;
+        }
+        if (node.conditions != null) {
+            node.conditions = resolveColumnDefinitions(node.conditions, 
definitions);
+        }
+        if (node.orderKeys != null) {
+            List<OrderKey> orderKeys = new ArrayList<>(node.orderKeys.size());
+            for (OrderKey orderKey : node.orderKeys) {
+                orderKeys.add(orderKey.withExpression(
+                        resolveColumnDefinitions(orderKey.getExpr(), 
definitions)));
+            }
+            node.orderKeys = orderKeys;
+        }
+        if (node.windowExpressions != null) {
+            List<NamedExpression> windowExpressions = new 
ArrayList<>(node.windowExpressions.size());
+            for (NamedExpression windowExpression : node.windowExpressions) {
+                windowExpressions.add((NamedExpression)
+                        resolveColumnDefinitions(windowExpression, 
definitions));
+            }
+            node.windowExpressions = windowExpressions;
+        }
+        if (node.generators != null) {
+            node.generators = resolveColumnDefinitions(node.generators, 
definitions);
+        }
+        if (node.generatorConjuncts != null) {
+            node.generatorConjuncts = 
resolveColumnDefinitions(node.generatorConjuncts, definitions);
+        }
+        if (node.groupingSets != null) {
+            List<List<Expression>> groupingSets = new 
ArrayList<>(node.groupingSets.size());
+            for (List<Expression> groupingSet : node.groupingSets) {
+                groupingSets.add(resolveColumnDefinitions(groupingSet, 
definitions));
+            }
+            node.groupingSets = groupingSets;
+        }
+    }
+
+    /** The memo group a plan node belongs to: its back reference, or the post 
processed group id. */
+    private static Group resolveGroup(AbstractPlan planNode, Map<Integer, 
Group> groupsById) {
+        Group group = 
planNode.getGroupExpression().map(GroupExpression::getOwnerGroup).orElse(null);
+        if (group != null) {
+            return group;
+        }
+        Optional<Object> groupState = 
planNode.getMutableState(MutableState.KEY_GROUP);
+        if (groupState.isPresent() && groupsById != null) {
+            try {
+                return 
groupsById.get(Integer.valueOf(groupState.get().toString()));
+            } catch (NumberFormatException ignored) {
+                return null;
+            }
+        }
+        return null;
+    }
+
+    /**
+     * Step 1 of a node build: describe one child of this node. The child is 
described once per query -
+     * its memoized description is returned - and a child which cannot be 
described invalidates this
+     * node with the reason of the child, so that the first reason of the 
failing sub tree is the one
+     * which is reported.
+     */
+    private static GroupStructInfo describeChild(GroupExpression ge, int 
index, Ctx ctx) {
+        if (!ctx.valid) {
+            return null;
+        }
+        GroupStructInfo child = describeGroup(ge.child(index), ctx);
+        if (!child.isValid()) {
+            invalid(ctx, child.getSkipReason());
+            return null;
+        }
+        return child;
+    }
+
+    /**
+     * The conditions and the leaves of a join chain, memoized per group: a 
chain of n joins used to walk
+     * its own sub tree once per member (O(n^2) condition renderings for the 
whole query), while the
+     * structure of a chain does not depend on the build which reads it - only 
the bookkeeping of a sub
+     * tree which is reached more than once does, and that is done while 
composing the chain.
+     */
+    public static final class ChainInfo {
+        /** the conditions of the chain, de-duplicated by their literal 
carrying text */
+        private final List<Expression> conditions;
+        /** the groups the chain is made of, without its leaves: they detect a 
chain which is reused */
+        private final List<Group> members;
+        /** the groups which are not flattened into the chain, in traversal 
order */
+        private final List<Group> leaves;
+        private final boolean valid;
+        private final String skipReason;
+
+        private ChainInfo(List<Expression> conditions, List<Group> members, 
List<Group> leaves,
+                boolean valid, String skipReason) {
+            this.conditions = conditions;
+            this.members = members;
+            this.leaves = leaves;
+            this.valid = valid;
+            this.skipReason = skipReason;
+        }
+
+        private static ChainInfo of(List<Expression> conditions, List<Group> 
members, List<Group> leaves) {
+            return new ChainInfo(conditions, members, leaves, true, "");
+        }
+
+        private static ChainInfo failed(String skipReason) {
+            return new ChainInfo(new ArrayList<>(), new ArrayList<>(), new 
ArrayList<>(), false, skipReason);
+        }
+    }
+
+    /** The memoized chain info of a group, computed at most once per query. */
+    private static ChainInfo chainInfoOf(Group group) {
+        ChainInfo memoized = group.getHboChainInfoOrNull();
+        if (memoized != null) {
+            return memoized;
+        }
+        ChainInfo computed = buildChainInfo(group);
+        group.setHboChainInfo(computed);
+        return computed;
+    }
+
+    /**
+     * The chain structure of a group: a flattenable join contributes its own 
conditions and the chains
+     * of its children, a transparent operator contributes the chain below it, 
anything else is a leaf.
+     */
+    private static ChainInfo buildChainInfo(Group group) {
+        GroupExpression ge = getRepresentativeExpression(group);
+        if (ge == null) {
+            return ChainInfo.failed("no logical expression in group " + 
describeGroupState(group));
+        }
+        Plan plan = ge.getPlan();
+        if (plan instanceof Join && isFlattenableJoinType(((Join) 
plan).getJoinType())) {
+            List<Expression> conditions = joinConditions((Join) plan);
+            List<Group> members = new ArrayList<>();
+            List<Group> leaves = new ArrayList<>();
+            members.add(group);
+            for (int i = 0; i < ge.arity(); i++) {
+                ChainInfo child = chainInfoOf(ge.child(i));
+                if (!child.valid) {
+                    return ChainInfo.failed(child.skipReason);
+                }
+                mergeConditions(conditions, child.conditions);
+                members.addAll(child.members);
+                leaves.addAll(child.leaves);
+            }
+            return ChainInfo.of(conditions, members, leaves);
+        }
+        // a top-n must not be flattened into the chain although it is a sort: 
it keeps a bounded number
+        // of rows, so it is a boundary of the chain like a limit, and the 
ordering it keeps them by is
+        // part of the identity of every node above it. A window is a boundary 
as well: it keeps every
+        // row, but the values of the columns it computes depend on its 
definition, and a node above it
+        // reads those values.
+        // a top-n is a sort but must not be flattened (it keeps a bounded 
number of rows, so it is a
+        // boundary of the chain), and a window is neither a project nor a 
sort, so it reaches the leaf
+        // branch below without a negation which a cleanup could drop
+        // a project is transparent only while it forwards its columns: one 
which computes a value is a
+        // leaf, so that its definitions reach the conditions of the join 
above it (a flattened project
+        // would be skipped and its definitions would be lost)
+        if ((plan instanceof Sort && !(plan instanceof TopN) || 
isTransparentProject(plan)) && ge.arity() == 1) {
+            ChainInfo child = chainInfoOf(ge.child(0));
+            if (!child.valid) {
+                return child;
+            }
+            List<Group> members = new ArrayList<>();
+            members.add(group);
+            members.addAll(child.members);
+            return ChainInfo.of(child.conditions, members, child.leaves);
+        }
+        List<Group> leaves = new ArrayList<>();
+        leaves.add(group);
+        return ChainInfo.of(new ArrayList<>(), new ArrayList<>(), leaves);
+    }
+
+    /**
+     * Add the leaves of a chain to the leaves of the build which is being 
described: a sub tree which the
+     * build already reached contributes its canonical form again, but not its 
scans (its tables are read
+     * once), and a chain which is reused makes all of its leaves repeated.
+     */
+    private static boolean composeChain(ChainInfo chain, List<Leaf> leaves, 
Ctx ctx) {
+        boolean firstUse = true;
+        for (Group member : chain.members) {
+            if (!ctx.visited.add(member)) {
+                firstUse = false;
+            }
+        }
+        for (Group group : chain.leaves) {
+            boolean repeated = !firstUse || !ctx.visited.add(group);
+            GroupStructInfo leaf = describeVisited(group, ctx);
+            if (!leaf.isValid()) {
+                invalid(ctx, leaf.getSkipReason());
+                return false;
+            }
+            leaves.add(new Leaf(leaf, repeated));
+        }
+        return true;
+    }
+
+    /** One leaf of a flattened join chain: the memoized description of that 
sub tree. */
+    private static class Leaf {
+        private final GroupStructInfo leaf;
+        /** whether the sub tree of this leaf is referenced by another leaf as 
well */
+        private final boolean repeated;
+
+        Leaf(GroupStructInfo leaf) {
+            this(leaf, false);
+        }
+
+        Leaf(GroupStructInfo leaf, boolean repeated) {
+            this.leaf = leaf;
+            this.repeated = repeated;
+        }
+
+        GroupStructInfo getLeaf() {
+            return leaf;
+        }
+
+        boolean isRepeated() {
+            return repeated;
+        }
+
+        /** The key the leaves of a chain are ordered by: the identity of the 
sub tree, no data state. */
+        String sortKey() {
+            return leaf.getShape(LiteralMode.WITH_LITERAL);
+        }
+    }
+
+    /**
+     * The conditions of a join as expressions, de-duplicated by their literal 
carrying text - the key the
+     * two per-mode string sets used. The rendering happens once per mode in
+     * {@link #conditions(List, LiteralMode)}, which sorts and de-duplicates 
each mode on its own, exactly
+     * like the two {@link TreeSet}s did.
+     */
+    private static List<Expression> joinConditions(Join join) {
+        List<Expression> conditions = new ArrayList<>();
+        addConditions(conditions, join.getHashJoinConjuncts());
+        addConditions(conditions, join.getOtherJoinConjuncts());
+        // a mark join carries its correlation condition in the mark 
conjuncts, and the translator turns
+        // them into the hash condition of the executed null aware join: they 
decide which rows the node
+        // keeps, so two mark joins which differ only in that condition must 
not share a key
+        addConditions(conditions, join.getMarkJoinConjuncts());
+        return conditions;
+    }
+
+    private static void addConditions(List<Expression> conditions, 
Collection<Expression> conjuncts) {
+        mergeConditions(conditions, new ArrayList<>(conjuncts));
+    }
+
+    /** Append the conditions which are not in {@code into} yet, keyed by 
their literal carrying text. */
+    private static void mergeConditions(List<Expression> into, 
List<Expression> from) {
+        Set<String> seen = new HashSet<>();
+        for (Expression condition : into) {
+            seen.add(identityText(condition));
+        }
+        for (Expression condition : from) {
+            if (seen.add(identityText(condition))) {
+                into.add(condition);
+            }
+        }
+    }
+
+    /** Inner and cross joins may be reordered, reassociated and therefore 
flattened. */
+    private static boolean isFlattenableJoinType(JoinType joinType) {
+        return joinType == JoinType.INNER_JOIN || joinType == 
JoinType.CROSS_JOIN;
+    }
+
+    // 
------------------------------------------------------------------------------------------
+    // the description of one group: a tree of nodes, and the one renderer of 
the grammar
+    // 
------------------------------------------------------------------------------------------
+
+    /** What a node of a description is; {@link #appendNode} switches on it. */
+    private enum Kind {
+        SCAN("", false),
+        FILE_SCAN("", false),
+        STORAGE_AGGREGATE("A", false),
+        FILTER("F", false),
+        AGGREGATE("A", false),
+        // a join's residual conditions decide which rows the join keeps (a 
range bound, a function of both
+        // sides), so their literals are identity: the published and learned 
keys of a join must not fold
+        // `t.b > u.b + 1000` and `t.b > u.b + 1` into one entry
+        JOIN("J", true),
+        TOPN("T", true),
+        LIMIT("L", true),
+        WINDOW("W", true),
+        GENERATE("G", true),
+        REPEAT("R", false),
+        SET_OPERATION("UIE", true),
+        PASSTHROUGH("", false);
+
+        /** The letters the renderer writes in front of the header of this 
kind (a set operation has three). */
+        private final String headerLetters;
+        /**
+         * Whether the literals inside the header of this kind are part of its 
identity, which means the
+         * renderer writes them in both literal modes: a generator's delimiter 
decides how many rows a row
+         * expands into, a top-n's ordering and a window's definition decide 
which rows reach the node
+         * above, a set operation's constant and a limit bound decide the rows 
of the operation itself.
+         */
+        private final boolean literalsAreIdentity;
+
+        Kind(String headerLetters, boolean literalsAreIdentity) {
+            this.headerLetters = headerLetters;
+            this.literalsAreIdentity = literalsAreIdentity;
+        }
+
+        private String headerLetters() {
+            return headerLetters;
+        }
+
+        private boolean literalsAreIdentity() {
+            return literalsAreIdentity;
+        }
+    }
+
+    /**
+     * One node of a description: the information of the group itself, held as 
objects (an expression
+     * list, a bound, an ordering, a scan descriptor, ...), plus the children 
it composes. Nothing is
+     * rendered while a node is built: {@link #appendNode} is the only place 
which knows the grammar, and
+     * it renders the literals in the mode the caller asks for, which is why a 
node has no "with literal"
+     * and "no literal" variant of its own.
+     */
+    private static final class Node {
+        private final Kind kind;
+        /** FILTER / AGGREGATE / JOIN: the predicates, the grouping keys or 
the conjuncts. */
+        private List<Expression> conditions;
+        /** JOIN: a flattened inner / cross join chain is rendered as `inner`, 
like a cross join. */
+        private boolean flattenable;
+        /** JOIN: the type of a join which is not flattened. */
+        private JoinType joinType;
+        /** TOPN / LIMIT: the bound. */
+        private long limit;
+        private long offset;
+        /** TOPN: the ordering which decides which rows survive. */
+        private List<OrderKey> orderKeys;
+        /** WINDOW: the named expressions of the window (each child is the 
window expression). */
+        private List<NamedExpression> windowExpressions;
+        /** GENERATE: the table functions, whose arguments decide how many 
rows come out. */
+        private List<Expression> generators;
+        /** GENERATE: the aliases of the columns those functions produce, in 
order. */
+        private List<Slot> generatorOutputs;
+        /** GENERATE: the lateral ON conditions, which decide which produced 
rows survive. */
+        private List<Expression> generatorConjuncts;
+        /** REPEAT: the grouping sets, in the order they were written. */
+        private List<List<Expression>> groupingSets;
+        /** SET_OPERATION: the plan node and the operation, which know the 
kind, the qualifier and more. */
+        private Plan setOperationPlan;
+        private SetOperation setOperation;
+        /** SCAN / FILE_SCAN / STORAGE_AGGREGATE: the token of the relation 
which is read. */
+        private HboScanDescriptor scan;
+        /** STORAGE_AGGREGATE: the pushed down aggregation. */
+        private PhysicalStorageLayerAggregate storageAggregate;
+        /**
+         * The columns this node or a node below it computes, keyed by the id 
of the column which
+         * exposes the value: an alias of a transparent project and an output 
of an aggregation are
+         * the two definitions a node above them cannot see in the canonical 
form of its children.
+         */
+        private Map<ExprId, Expression> columnDefinitions = 
Collections.emptyMap();
+        /** The children, in the order the canonical string prints them. */
+        private List<Child> children = new ArrayList<>();
+        /** The rendered forms of this node, filled on the first request of 
each of them. */
+        private String canonicalWithLiteral;
+        private String canonicalNoLiteral;
+        private String shapeWithLiteral;
+        private String shapeNoLiteral;
+
+        private Node(Kind kind) {
+            this.kind = kind;
+        }
+
+        private String materialized(LiteralMode mode, boolean shape) {
+            if (shape) {
+                return mode == LiteralMode.NO_LITERAL ? shapeNoLiteral : 
shapeWithLiteral;
+            }
+            return mode == LiteralMode.NO_LITERAL ? canonicalNoLiteral : 
canonicalWithLiteral;
+        }
+
+        private void setMaterialized(LiteralMode mode, boolean shape, String 
text) {
+            if (shape) {
+                if (mode == LiteralMode.NO_LITERAL) {
+                    shapeNoLiteral = text;
+                } else {
+                    shapeWithLiteral = text;
+                }
+                return;
+            }
+            if (mode == LiteralMode.NO_LITERAL) {
+                canonicalNoLiteral = text;
+            } else {
+                canonicalWithLiteral = text;
+            }
+        }
+    }
+
+    /**
+     * One child of a node: its description, and whether the sub tree is 
referenced by another child as
+     * well - such a child writes its canonical form again (a query which 
reuses a sub tree and a query
+     * which writes it twice share one entry) while its tables are read once, 
so its scan tokens are
+     * inherited by the first reference only. A set operation branch also 
writes the mapping of its
+     * columns, which is per parent and can therefore not live in the shared 
child node.
+     */
+    private static final class Child {
+        private final Node node;
+        private final boolean repeated;
+        /** SET_OPERATION: the expressions the branch feeds its outputs with, 
empty for every other child. */
+        private final List<Expression> mapping;
+
+        private Child(Node node, boolean repeated) {
+            this(node, repeated, Collections.emptyList());
+        }
+
+        private Child(Node node, boolean repeated, List<Expression> mapping) {
+            this.node = node;
+            this.repeated = repeated;
+            this.mapping = mapping;
+        }
+    }
+
+    // ---------------------------------------------------------------- build 
(memo level)
+
+    /**
+     * Build the description of one node. Every branch follows the same three 
steps: the node's own
+     * information is collected as objects, its children are described by 
{@link #describeChild} (the
+     * memoized description of a child group, never its sub tree again), and 
both are put into a
+     * {@link Node} - the rendering happens later and elsewhere.
+     */
+    private static Node buildNode(Plan plan, GroupExpression ge, Ctx ctx) {
+        if (!ctx.valid) {
+            return null;
+        }
+        // the order of the checks matters: a top-n is a sort and a window is 
neither a project nor a
+        // sort, so the boundaries of a join chain are recognised before the 
transparent operators
+        if (plan instanceof OlapScan) {
+            return olapScanNode((OlapScan) plan, ctx);
+        }
+        if (plan instanceof Filter) {
+            return conditionsNode(Kind.FILTER, ((Filter) plan).getConjuncts(), 
ge, ctx);
+        }
+        if (plan instanceof LogicalCTEConsumer || plan instanceof 
PhysicalCTEConsumer) {
+            // both consumers are leaves which reference their producer by id, 
and neither has a sub tree
+            // which this description could follow: the producer is reachable 
only from its anchor, and a
+            // group is described bottom-up (DeriveStatsJob, 
collectHboPlanInfo, the explain annotation),
+            // so the consumer side is visited before the anchor and no 
producer is known there yet. A plan
+            // which contains a consumer therefore stays undescribed - the 
same message for both classes,
+            // because the reason is the same.
+            return invalidNode("unsupported=cte consumer without a memo edge", 
ctx);
+        }
+        if (plan instanceof LogicalCTEProducer || plan instanceof 
PhysicalCTEProducer) {
+            // a producer materializes the sub tree it was given: transparent
+            if (ge.arity() != 1) {
+                return invalidNode(ARITY_REASON_PREFIX + ge.arity() + 
ARITY_REASON_MIDDLE
+                        + plan.getClass().getSimpleName(), ctx);
+            }
+            return passthroughNode(ge, 0, ctx);
+        }
+        if (plan instanceof LogicalCTEAnchor || plan instanceof 
PhysicalCTEAnchor) {
+            // the value of an anchor is its consumer side: the producer is 
the first child and the plan
+            // which consumes it is the second one 
(LogicalCTEAnchor.computeOutput is right().getOutput())
+            if (ge.arity() < 2) {
+                return invalidNode(ARITY_REASON_PREFIX + ge.arity() + 
ARITY_REASON_MIDDLE
+                        + plan.getClass().getSimpleName(), ctx);
+            }
+            return passthroughNode(ge, 1, ctx);
+        }
+        if (plan instanceof LogicalFileScan) {
+            LogicalFileScan fileScan = (LogicalFileScan) plan;
+            return fileScanNode(fileScan.getTable(), 
fileScan.getTableSnapshot().isPresent()
+                    || fileScan.getScanParams().isPresent() || 
fileScan.getTableSample().isPresent(), ctx);
+        }
+        if (plan instanceof PhysicalFileScan) {
+            PhysicalFileScan fileScan = (PhysicalFileScan) plan;
+            return fileScanNode(fileScan.getTable(), 
fileScan.getTableSnapshot().isPresent()
+                    || fileScan.getScanParams().isPresent(), ctx);
+        }
+        if (plan instanceof PhysicalStorageLayerAggregate) {
+            // the optimizer answers an aggregation over a scan from the 
storage layer itself: the node is
+            // a catalog relation without children, and its identity is the 
aggregation together with the
+            // relation it reads. The argument expressions are referenced by 
expression id there, which is
+            // not stable across queries, so they are left out: they do not 
change the number of rows this
+            // node produces (one row, the query has no grouping).
+            PhysicalStorageLayerAggregate aggregate = 
(PhysicalStorageLayerAggregate) plan;
+            Node node = new Node(Kind.STORAGE_AGGREGATE);
+            node.storageAggregate = aggregate;
+            if (aggregate.getRelation() instanceof OlapScan) {
+                node.scan = scanDescriptor((OlapScan) aggregate.getRelation(), 
ctx);
+                if (node.scan == null) {
+                    return null;
+                }
+            }
+            return node;
+        }
+        if (plan instanceof TopN) {
+            if (ge.arity() != 1) {
+                return invalidNode(ARITY_REASON_PREFIX + ge.arity() + 
ARITY_REASON_MIDDLE
+                        + plan.getClass().getSimpleName(), ctx);
+            }
+            // a top-n keeps its bound and its ordering out of the folding: 
the bound is written in both
+            // modes so that the constant agnostic form cannot fold two 
different bounds into one entry,
+            // and the ordering is part of the identity because it decides 
*which* rows survive
+            TopN topN = (TopN) plan;
+            Node node = new Node(Kind.TOPN);
+            node.limit = topN.getLimit();
+            node.offset = topN.getOffset();
+            node.orderKeys = new ArrayList<>(topN.getOrderKeys());
+            node.children = children(ge, ctx, 0);
+            return node.children == null ? null : node;
+        }
+        if (plan instanceof Limit) {
+            if (ge.arity() != 1) {
+                return invalidNode(ARITY_REASON_PREFIX + ge.arity() + 
ARITY_REASON_MIDDLE
+                        + plan.getClass().getSimpleName(), ctx);
+            }
+            Limit limit = (Limit) plan;
+            Node node = new Node(Kind.LIMIT);
+            node.limit = limit.getLimit();
+            node.offset = limit.getOffset();
+            node.children = children(ge, ctx, 0);
+            return node.children == null ? null : node;
+        }
+        if (plan instanceof Generate) {
+            if (ge.arity() != 1) {
+                return invalidNode(ARITY_REASON_PREFIX + ge.arity() + 
ARITY_REASON_MIDDLE
+                        + plan.getClass().getSimpleName(), ctx);
+            }
+            // a generate expands a row into the rows of its table functions, 
so its identity is the
+            // identity of those functions: the function and its arguments 
decide how many rows come out,
+            // and the arguments are rendered with their literals (see 
identityText)
+            Node node = new Node(Kind.GENERATE);
+            node.generators = new ArrayList<>(((Generate) 
plan).getGenerators());
+            node.generatorOutputs = generatorOutputsOf(plan);
+            node.generatorConjuncts = generatorConjunctsOf(plan);
+            node.children = children(ge, ctx, 0);
+            return node.children == null ? null : node;
+        }
+        if (plan instanceof Repeat) {
+            if (ge.arity() != 1) {
+                return invalidNode(ARITY_REASON_PREFIX + ge.arity() + 
ARITY_REASON_MIDDLE
+                        + plan.getClass().getSimpleName(), ctx);
+            }
+            // a repeat produces the rows of several grouping sets, so its 
identity is the list of those
+            // sets; the order of the sets is part of the identity (the 
grouping id values depend on it)
+            // and is kept as written, while the expressions of one set are 
sorted (their order does not
+            // change the groups)
+            Node node = new Node(Kind.REPEAT);
+            node.groupingSets = new ArrayList<>();
+            for (List<Expression> set : ((Repeat<?>) plan).getGroupingSets()) {
+                node.groupingSets.add(new ArrayList<>(set));
+            }
+            node.children = children(ge, ctx, 0);
+            return node.children == null ? null : node;
+        }
+        if (plan instanceof Union || plan instanceof Intersect || plan 
instanceof Except) {
+            return setOperationNode(plan, (SetOperation) plan, ge, ctx);
+        }
+        if (plan instanceof PhysicalDistribute || plan instanceof 
PhysicalAssertNumRows
+                || plan instanceof Project || plan instanceof Sort) {
+            // an enforcer, a project and a sort are transparent for structure 
matching: none of them
+            // changes the number of rows, so the nodes above them are 
described by the shape below and
+            // they must not make the struct info of those nodes disappear
+            if (ge.arity() != 1) {
+                return invalidNode(ARITY_REASON_PREFIX + ge.arity() + 
ARITY_REASON_MIDDLE
+                        + plan.getClass().getSimpleName(), ctx);
+            }
+            return passthroughNode(ge, 0, ctx);
+        }
+        if (plan instanceof Window) {
+            if (ge.arity() != 1) {
+                return invalidNode(ARITY_REASON_PREFIX + ge.arity() + 
ARITY_REASON_MIDDLE
+                        + plan.getClass().getSimpleName(), ctx);
+            }
+            // a window computes its columns from the rows of its partition, 
so its definition decides the
+            // values a node above it reads and is part of the identity; the 
window itself adds no rows
+            Node node = new Node(Kind.WINDOW);
+            node.windowExpressions = new ArrayList<>(((Window) 
plan).getWindowExpressions());
+            node.children = children(ge, ctx, 0);
+            return node.children == null ? null : node;
+        }
+        if (plan instanceof Join) {
+            return joinNode((Join) plan, ge, ctx);
+        }
+        if (plan instanceof Aggregate) {
+            // only the grouping keys take part: the output row count of an 
aggregation is the number of
+            // groups, which the aggregate functions and the output 
expressions cannot change, so keeping
+            // them would only split one plan pattern into several cache 
entries
+            return conditionsNode(Kind.AGGREGATE, ((Aggregate<?>) 
plan).getGroupByExpressions(), ge, ctx);
+        }
+        return invalidNode(UNSUPPORTED_REASON_PREFIX + 
plan.getClass().getSimpleName(), ctx);
+    }
+
+    /** A filter or an aggregation: a header made of its conditions, then its 
single child. */
+    private static Node conditionsNode(Kind kind, Collection<Expression> 
conditions, GroupExpression ge,
+            Ctx ctx) {
+        if (ge.arity() != 1) {
+            return invalidNode("arity=" + ge.arity() + " of " + 
ge.getPlan().getClass().getSimpleName(), ctx);
+        }
+        Node node = new Node(kind);
+        node.conditions = new ArrayList<>(conditions);
+        node.children = children(ge, ctx, 0);
+        return node.children == null ? null : node;
+    }
+
+    /**
+     * A join. An inner or cross join is flattened together with every 
flattenable join below it into one
+     * node whose conditions are the merged conditions of the chain and whose 
children are the leaves of
+     * the chain (the first sub tree which is not part of it), while an outer 
/ semi / anti / asof join
+     * keeps its type and the memo order of its two sides, because it cannot 
be reassociated.
+     */
+    private static Node joinNode(Join join, GroupExpression ge, Ctx ctx) {
+        if (!isFlattenableJoinType(join.getJoinType())) {
+            Node node = new Node(Kind.JOIN);
+            node.joinType = join.getJoinType();
+            node.conditions = joinConditions(join);
+            node.children = children(ge, ctx, 0);
+            if (node.children == null) {
+                return null;
+            }
+            for (int i = 1; i < ge.arity(); i++) {
+                List<Child> more = children(ge, ctx, i);
+                if (more == null) {
+                    return null;
+                }
+                node.children.addAll(more);
+            }
+            return node;
+        }
+        return joinChainNode(join, ge, ctx);
+    }
+
+    /**
+     * A whole inner / cross join chain as one node: inner and cross joins are 
associative and
+     * commutative, so the grouping of the chain is an artifact of the 
explored expression and must not be
+     * part of the fingerprint. The conditions of every join of the chain are 
merged (de-duplicated by
+     * their literal carrying text) and the leaves are sorted by their own 
identity - an order which is
+     * part of the fingerprint and must therefore not depend on a data state.
+     */
+    private static Node joinChainNode(Join join, GroupExpression ge, Ctx ctx) {
+        List<Expression> conditions = joinConditions(join);
+        List<Leaf> leaves = new ArrayList<>();
+        for (int i = 0; i < ge.arity(); i++) {
+            ChainInfo child = chainInfoOf(ge.child(i));
+            if (!child.valid) {
+                return invalidNode(child.skipReason, ctx);
+            }
+            mergeConditions(conditions, child.conditions);
+            if (!composeChain(child, leaves, ctx)) {
+                return null;
+            }
+        }
+        if (!ctx.valid) {
+            return null;
+        }
+        leaves.sort(Comparator.comparing(Leaf::sortKey));
+        Node node = new Node(Kind.JOIN);
+        node.flattenable = true;
+        node.conditions = conditions;
+        for (Leaf leaf : leaves) {
+            node.children.add(new Child(leaf.getLeaf().root(), 
leaf.isRepeated()));
+        }
+        return node;
+    }
+
+    /**
+     * A set operation: its header carries the kind, the qualifier and the 
compared columns, and every
+     * branch writes the mapping of the columns it feeds the outputs with (see 
{@link #branchMapping}).
+     * The branches are sorted - the memo may reorder them - together with 
their mapping, because the
+     * mapping belongs to one branch and two branches of the same shape can 
still feed different columns.
+     */
+    private static Node setOperationNode(Plan plan, SetOperation setOperation, 
GroupExpression ge, Ctx ctx) {
+        Node node = new Node(Kind.SET_OPERATION);
+        node.setOperationPlan = plan;
+        node.setOperation = setOperation;
+        List<GroupStructInfo> branches = describeBranches(ge, ctx);
+        if (branches == null) {
+            return null;
+        }
+        List<List<SlotReference>> mappings = 
setOperation.getRegularChildrenOutputs();
+        if (plan instanceof Except) {
+            // the first branch is the minuend: it keeps its position, the 
subtrahends are sorted below
+            node.children.add(branchChild(branches.get(0), mappings, 0));
+            List<Integer> subtrahends = new ArrayList<>();
+            for (int i = 1; i < branches.size(); i++) {
+                subtrahends.add(i);
+            }
+            subtrahends.sort(Comparator.comparing(
+                    index -> branchSortKey(branches.get(index), mappings, 
index)));
+            for (int index : subtrahends) {
+                node.children.add(branchChild(branches.get(index), mappings, 
index));
+            }
+            return node;
+        }
+        // the branches are sorted because the memo may reorder them
+        List<Integer> order = new ArrayList<>();
+        for (int i = 0; i < branches.size(); i++) {
+            order.add(i);
+        }
+        order.sort(Comparator.comparing(index -> 
branchSortKey(branches.get(index), mappings, index)));
+        for (int index : order) {
+            node.children.add(branchChild(branches.get(index), mappings, 
index));
+        }
+        return node;
+    }
+
+    private static Child branchChild(GroupStructInfo branch, 
List<List<SlotReference>> mappings, int index) {
+        return new Child(branch.root(), false, branchMapping(mappings, index, 
branch.root()));
+    }
+
+    /** The mapping of one branch followed by its shape: the key the branches 
of a node are sorted by. */
+    private static String branchSortKey(GroupStructInfo branch, 
List<List<SlotReference>> mappings, int index) {
+        return branchMappingText(branchMapping(mappings, index, 
branch.root()), LiteralMode.WITH_LITERAL)
+                + branch.getShape(LiteralMode.WITH_LITERAL);
+    }
+
+    /**
+     * The columns one branch of a set operation feeds its outputs with. The 
branches are children of the
+     * node, but the projects which select those columns are transparent and 
the output slots of the
+     * operation are new ones, so this mapping is the only place where an 
output column is tied to a
+     * column of the branch: {@code SELECT a FROM t UNION SELECT a FROM u} and 
the same query selecting
+     * {@code u.b} read the same two tables and produce a different number of 
distinct rows.
+     */
+    private static List<Expression> branchMapping(List<List<SlotReference>> 
mappings, int index, Node branchNode) {
+        if (index >= mappings.size() || mappings.get(index).isEmpty()) {
+            return Collections.emptyList();
+        }
+        Map<ExprId, Expression> definitions = branchNode == null
+                ? Collections.emptyMap() : branchNode.columnDefinitions;
+        List<Expression> mapping = new ArrayList<>(mappings.get(index).size());
+        for (SlotReference mapped : mappings.get(index)) {
+            // the mapped slot may be the output of a computed project inside 
the branch: the value the
+            // branch feeds the output with is that definition, not the name 
of the slot
+            mapping.add(resolveColumnDefinitions(mapped, definitions));
+        }
+        return mapping;
+    }
+
+    /** The mapping of one branch, rendered in the literal mode of the node 
above it. */
+    private static String branchMappingText(List<Expression> mapping, 
LiteralMode mode) {
+        if (mapping.isEmpty()) {
+            return "";
+        }
+        StringBuilder text = new StringBuilder("[");
+        for (int i = 0; i < mapping.size(); i++) {
+            if (i > 0) {
+                text.append(',');
+            }
+            text.append(renderExpression(mapping.get(i), mode));
+        }
+        return text.append(']').toString();
+    }
+
+    /** Whether a project only forwards the columns of its child (no output of 
it is an alias). */
+    private static boolean isTransparentProject(Plan plan) {
+        if (!(plan instanceof Project)) {
+            return false;
+        }
+        for (NamedExpression expression : ((Project) plan).getProjects()) {
+            if (expression instanceof Alias) {
+                return false;
+            }
+        }
+        return true;
+    }
+
+    /** A node which only composes the child at {@code index} (an enforcer, a 
project, a CTE edge). */
+    private static Node passthroughNode(GroupExpression ge, int index, Ctx 
ctx) {
+        Node node = new Node(Kind.PASSTHROUGH);
+        node.children = children(ge, ctx, index);
+        return node.children == null ? null : node;
+    }
+
+    /**
+     * A scan of an internal table: its descriptor carries what the read side 
needs to compare the data
+     * state, so a scan whose state cannot be read leaves the whole group 
undescribed.
+     */
+    private static Node olapScanNode(OlapScan scan, Ctx ctx) {
+        HboScanDescriptor descriptor = scanDescriptor(scan, ctx);
+        return descriptor == null ? null : scanRecord(Kind.SCAN, descriptor);
+    }
+
+    /**
+     * A scan of an external table. Its identity is the table name only, which 
is why a scan which reads an
+     * explicit snapshot or a sampled part of one would share it although it 
holds different rows: such a
+     * scan is not described until the selector is part of the identity.
+     */
+    private static Node fileScanNode(TableIf table, boolean 
explicitlyVersioned, Ctx ctx) {
+        String name = HboScanDescriptor.qualifiedNameOf(table);
+        if (name.indexOf(',') >= 0 || name.indexOf('}') >= 0) {
+            // the token delimiters cannot appear in a table name: the printed 
struct info could not be
+            // read back, and a pasted one could resolve to another table
+            return invalidNode("delimiter in table name " + name, ctx);
+        }
+        if (explicitlyVersioned) {
+            return invalidNode("selected file scan " + name, ctx);
+        }
+        return scanRecord(Kind.FILE_SCAN, 
HboScanDescriptor.ofUnreadableState(table));

Review Comment:
   [P2] Preserve alias bindings in external scan keys
   
   The OLAP `#ra` fix does not cover this FileScan branch. Compare these 
reduced trees in one external catalog/database:
   ```text
   Join(x.a=y.a AND x.b<y.b, FileScan(t AS x), FileScan(u AS y))
   Join(x.a=y.a AND x.b<y.b, FileScan(u AS x), FileScan(t AS y))
   ```
   For NOT NULL BIGINT `(a,b)` data t=(1,1), u=(1,2), they return one versus 
zero rows. Alias lowering preserves x/y in forwarding Projects, but 
`ofUnreadableState(table)` drops `tableAlias`; sorting the t/u leaves therefore 
gives identical exact J keys. The relation prefilter matches, and UNKNOWN 
external freshness permits the first pin to override the second estimate. This 
is the separate external-scan instance left after the existing OLAP 
alias-binding report. Carry the file scan's alias-to-table binding into its 
descriptor, or resolve predicates to scan occurrences before sorting.



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