equivclass.c

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/*-------------------------------------------------------------------------
 *
 * equivclass.c
 *    Routines for managing EquivalenceClasses
 *
 * See src/backend/optimizer/README for discussion of EquivalenceClasses.
 *
 *
 * Portions Copyright (c) 1996-2017, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *    src/backend/optimizer/path/equivclass.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include <limits.h>

#include "access/stratnum.h"
#include "catalog/pg_type.h"
#include "nodes/makefuncs.h"
#include "nodes/nodeFuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/pathnode.h"
#include "optimizer/paths.h"
#include "optimizer/planmain.h"
#include "optimizer/prep.h"
#include "optimizer/var.h"
#include "utils/lsyscache.h"


static EquivalenceMember *add_eq_member(EquivalenceClass *ec,
              Expr *expr, Relids relids, Relids nullable_relids,
              bool is_child, Oid datatype);
static void generate_base_implied_equalities_const(PlannerInfo *root,
                                       EquivalenceClass *ec);
static void generate_base_implied_equalities_no_const(PlannerInfo *root,
                                          EquivalenceClass *ec);
static void generate_base_implied_equalities_broken(PlannerInfo *root,
                                        EquivalenceClass *ec);
static List *generate_join_implied_equalities_normal(PlannerInfo *root,
                                        EquivalenceClass *ec,
                                        Relids join_relids,
                                        Relids outer_relids,
                                        Relids inner_relids);
static List *generate_join_implied_equalities_broken(PlannerInfo *root,
                                        EquivalenceClass *ec,
                                        Relids nominal_join_relids,
                                        Relids outer_relids,
                                        Relids nominal_inner_relids,
                                        RelOptInfo *inner_rel);
static Oid select_equality_operator(EquivalenceClass *ec,
                         Oid lefttype, Oid righttype);
static RestrictInfo *create_join_clause(PlannerInfo *root,
                   EquivalenceClass *ec, Oid opno,
                   EquivalenceMember *leftem,
                   EquivalenceMember *rightem,
                   EquivalenceClass *parent_ec);
static bool reconsider_outer_join_clause(PlannerInfo *root,
                             RestrictInfo *rinfo,
                             bool outer_on_left);
static bool reconsider_full_join_clause(PlannerInfo *root,
                            RestrictInfo *rinfo);


/*
 * process_equivalence
 *    The given clause has a mergejoinable operator and can be applied without
 *    any delay by an outer join, so its two sides can be considered equal
 *    anywhere they are both computable; moreover that equality can be
 *    extended transitively.  Record this knowledge in the EquivalenceClass
 *    data structure.  Returns TRUE if successful, FALSE if not (in which
 *    case caller should treat the clause as ordinary, not an equivalence).
 *
 * If below_outer_join is true, then the clause was found below the nullable
 * side of an outer join, so its sides might validly be both NULL rather than
 * strictly equal.  We can still deduce equalities in such cases, but we take
 * care to mark an EquivalenceClass if it came from any such clauses.  Also,
 * we have to check that both sides are either pseudo-constants or strict
 * functions of Vars, else they might not both go to NULL above the outer
 * join.  (This is the main reason why we need a failure return.  It's more
 * convenient to check this case here than at the call sites...)
 *
 * We also reject proposed equivalence clauses if they contain leaky functions
 * and have security_level above zero.  The EC evaluation rules require us to
 * apply certain tests at certain joining levels, and we can't tolerate
 * delaying any test on security_level grounds.  By rejecting candidate clauses
 * that might require security delays, we ensure it's safe to apply an EC
 * clause as soon as it's supposed to be applied.
 *
 * On success return, we have also initialized the clause's left_ec/right_ec
 * fields to point to the EquivalenceClass representing it.  This saves lookup
 * effort later.
 *
 * Note: constructing merged EquivalenceClasses is a standard UNION-FIND
 * problem, for which there exist better data structures than simple lists.
 * If this code ever proves to be a bottleneck then it could be sped up ---
 * but for now, simple is beautiful.
 *
 * Note: this is only called during planner startup, not during GEQO
 * exploration, so we need not worry about whether we're in the right
 * memory context.
 */
bool
process_equivalence(PlannerInfo *root, RestrictInfo *restrictinfo,
                    bool below_outer_join)
{
    Expr       *clause = restrictinfo->clause;
    Oid         opno,
                collation,
                item1_type,
                item2_type;
    Expr       *item1;
    Expr       *item2;
    Relids      item1_relids,
                item2_relids,
                item1_nullable_relids,
                item2_nullable_relids;
    List       *opfamilies;
    EquivalenceClass *ec1,
               *ec2;
    EquivalenceMember *em1,
               *em2;
    ListCell   *lc1;

    /* Should not already be marked as having generated an eclass */
    Assert(restrictinfo->left_ec == NULL);
    Assert(restrictinfo->right_ec == NULL);

    /* Reject if it is potentially postponable by security considerations */
    if (restrictinfo->security_level > 0 && !restrictinfo->leakproof)
        return false;

    /* Extract info from given clause */
    Assert(is_opclause(clause));
    opno = ((OpExpr *) clause)->opno;
    collation = ((OpExpr *) clause)->inputcollid;
    item1 = (Expr *) get_leftop(clause);
    item2 = (Expr *) get_rightop(clause);
    item1_relids = restrictinfo->left_relids;
    item2_relids = restrictinfo->right_relids;

    /*
     * Ensure both input expressions expose the desired collation (their types
     * should be OK already); see comments for canonicalize_ec_expression.
     */
    item1 = canonicalize_ec_expression(item1,
                                       exprType((Node *) item1),
                                       collation);
    item2 = canonicalize_ec_expression(item2,
                                       exprType((Node *) item2),
                                       collation);

    /*
     * Reject clauses of the form X=X.  These are not as redundant as they
     * might seem at first glance: assuming the operator is strict, this is
     * really an expensive way to write X IS NOT NULL.  So we must not risk
     * just losing the clause, which would be possible if there is already a
     * single-element EquivalenceClass containing X.  The case is not common
     * enough to be worth contorting the EC machinery for, so just reject the
     * clause and let it be processed as a normal restriction clause.
     */
    if (equal(item1, item2))
        return false;           /* X=X is not a useful equivalence */

    /*
     * If below outer join, check for strictness, else reject.
     */
    if (below_outer_join)
    {
        if (!bms_is_empty(item1_relids) &&
            contain_nonstrict_functions((Node *) item1))
            return false;       /* LHS is non-strict but not constant */
        if (!bms_is_empty(item2_relids) &&
            contain_nonstrict_functions((Node *) item2))
            return false;       /* RHS is non-strict but not constant */
    }

    /* Calculate nullable-relid sets for each side of the clause */
    item1_nullable_relids = bms_intersect(item1_relids,
                                          restrictinfo->nullable_relids);
    item2_nullable_relids = bms_intersect(item2_relids,
                                          restrictinfo->nullable_relids);

    /*
     * We use the declared input types of the operator, not exprType() of the
     * inputs, as the nominal datatypes for opfamily lookup.  This presumes
     * that btree operators are always registered with amoplefttype and
     * amoprighttype equal to their declared input types.  We will need this
     * info anyway to build EquivalenceMember nodes, and by extracting it now
     * we can use type comparisons to short-circuit some equal() tests.
     */
    op_input_types(opno, &item1_type, &item2_type);

    opfamilies = restrictinfo->mergeopfamilies;

    /*
     * Sweep through the existing EquivalenceClasses looking for matches to
     * item1 and item2.  These are the possible outcomes:
     *
     * 1. We find both in the same EC.  The equivalence is already known, so
     * there's nothing to do.
     *
     * 2. We find both in different ECs.  Merge the two ECs together.
     *
     * 3. We find just one.  Add the other to its EC.
     *
     * 4. We find neither.  Make a new, two-entry EC.
     *
     * Note: since all ECs are built through this process or the similar
     * search in get_eclass_for_sort_expr(), it's impossible that we'd match
     * an item in more than one existing nonvolatile EC.  So it's okay to stop
     * at the first match.
     */
    ec1 = ec2 = NULL;
    em1 = em2 = NULL;
    foreach(lc1, root->eq_classes)
    {
        EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
        ListCell   *lc2;

        /* Never match to a volatile EC */
        if (cur_ec->ec_has_volatile)
            continue;

        /*
         * The collation has to match; check this first since it's cheaper
         * than the opfamily comparison.
         */
        if (collation != cur_ec->ec_collation)
            continue;

        /*
         * A "match" requires matching sets of btree opfamilies.  Use of
         * equal() for this test has implications discussed in the comments
         * for get_mergejoin_opfamilies().
         */
        if (!equal(opfamilies, cur_ec->ec_opfamilies))
            continue;

        foreach(lc2, cur_ec->ec_members)
        {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

            Assert(!cur_em->em_is_child);   /* no children yet */

            /*
             * If below an outer join, don't match constants: they're not as
             * constant as they look.
             */
            if ((below_outer_join || cur_ec->ec_below_outer_join) &&
                cur_em->em_is_const)
                continue;

            if (!ec1 &&
                item1_type == cur_em->em_datatype &&
                equal(item1, cur_em->em_expr))
            {
                ec1 = cur_ec;
                em1 = cur_em;
                if (ec2)
                    break;
            }

            if (!ec2 &&
                item2_type == cur_em->em_datatype &&
                equal(item2, cur_em->em_expr))
            {
                ec2 = cur_ec;
                em2 = cur_em;
                if (ec1)
                    break;
            }
        }

        if (ec1 && ec2)
            break;
    }

    /* Sweep finished, what did we find? */

    if (ec1 && ec2)
    {
        /* If case 1, nothing to do, except add to sources */
        if (ec1 == ec2)
        {
            ec1->ec_sources = lappend(ec1->ec_sources, restrictinfo);
            ec1->ec_below_outer_join |= below_outer_join;
            ec1->ec_min_security = Min(ec1->ec_min_security,
                                       restrictinfo->security_level);
            ec1->ec_max_security = Max(ec1->ec_max_security,
                                       restrictinfo->security_level);
            /* mark the RI as associated with this eclass */
            restrictinfo->left_ec = ec1;
            restrictinfo->right_ec = ec1;
            /* mark the RI as usable with this pair of EMs */
            restrictinfo->left_em = em1;
            restrictinfo->right_em = em2;
            return true;
        }

        /*
         * Case 2: need to merge ec1 and ec2.  This should never happen after
         * we've built any canonical pathkeys; if it did, those pathkeys might
         * be rendered non-canonical by the merge.
         */
        if (root->canon_pathkeys != NIL)
            elog(ERROR, "too late to merge equivalence classes");

        /*
         * We add ec2's items to ec1, then set ec2's ec_merged link to point
         * to ec1 and remove ec2 from the eq_classes list.  We cannot simply
         * delete ec2 because that could leave dangling pointers in existing
         * PathKeys.  We leave it behind with a link so that the merged EC can
         * be found.
         */
        ec1->ec_members = list_concat(ec1->ec_members, ec2->ec_members);
        ec1->ec_sources = list_concat(ec1->ec_sources, ec2->ec_sources);
        ec1->ec_derives = list_concat(ec1->ec_derives, ec2->ec_derives);
        ec1->ec_relids = bms_join(ec1->ec_relids, ec2->ec_relids);
        ec1->ec_has_const |= ec2->ec_has_const;
        /* can't need to set has_volatile */
        ec1->ec_below_outer_join |= ec2->ec_below_outer_join;
        ec1->ec_min_security = Min(ec1->ec_min_security,
                                   ec2->ec_min_security);
        ec1->ec_max_security = Max(ec1->ec_max_security,
                                   ec2->ec_max_security);
        ec2->ec_merged = ec1;
        root->eq_classes = list_delete_ptr(root->eq_classes, ec2);
        /* just to avoid debugging confusion w/ dangling pointers: */
        ec2->ec_members = NIL;
        ec2->ec_sources = NIL;
        ec2->ec_derives = NIL;
        ec2->ec_relids = NULL;
        ec1->ec_sources = lappend(ec1->ec_sources, restrictinfo);
        ec1->ec_below_outer_join |= below_outer_join;
        ec1->ec_min_security = Min(ec1->ec_min_security,
                                   restrictinfo->security_level);
        ec1->ec_max_security = Max(ec1->ec_max_security,
                                   restrictinfo->security_level);
        /* mark the RI as associated with this eclass */
        restrictinfo->left_ec = ec1;
        restrictinfo->right_ec = ec1;
        /* mark the RI as usable with this pair of EMs */
        restrictinfo->left_em = em1;
        restrictinfo->right_em = em2;
    }
    else if (ec1)
    {
        /* Case 3: add item2 to ec1 */
        em2 = add_eq_member(ec1, item2, item2_relids, item2_nullable_relids,
                            false, item2_type);
        ec1->ec_sources = lappend(ec1->ec_sources, restrictinfo);
        ec1->ec_below_outer_join |= below_outer_join;
        ec1->ec_min_security = Min(ec1->ec_min_security,
                                   restrictinfo->security_level);
        ec1->ec_max_security = Max(ec1->ec_max_security,
                                   restrictinfo->security_level);
        /* mark the RI as associated with this eclass */
        restrictinfo->left_ec = ec1;
        restrictinfo->right_ec = ec1;
        /* mark the RI as usable with this pair of EMs */
        restrictinfo->left_em = em1;
        restrictinfo->right_em = em2;
    }
    else if (ec2)
    {
        /* Case 3: add item1 to ec2 */
        em1 = add_eq_member(ec2, item1, item1_relids, item1_nullable_relids,
                            false, item1_type);
        ec2->ec_sources = lappend(ec2->ec_sources, restrictinfo);
        ec2->ec_below_outer_join |= below_outer_join;
        ec2->ec_min_security = Min(ec2->ec_min_security,
                                   restrictinfo->security_level);
        ec2->ec_max_security = Max(ec2->ec_max_security,
                                   restrictinfo->security_level);
        /* mark the RI as associated with this eclass */
        restrictinfo->left_ec = ec2;
        restrictinfo->right_ec = ec2;
        /* mark the RI as usable with this pair of EMs */
        restrictinfo->left_em = em1;
        restrictinfo->right_em = em2;
    }
    else
    {
        /* Case 4: make a new, two-entry EC */
        EquivalenceClass *ec = makeNode(EquivalenceClass);

        ec->ec_opfamilies = opfamilies;
        ec->ec_collation = collation;
        ec->ec_members = NIL;
        ec->ec_sources = list_make1(restrictinfo);
        ec->ec_derives = NIL;
        ec->ec_relids = NULL;
        ec->ec_has_const = false;
        ec->ec_has_volatile = false;
        ec->ec_below_outer_join = below_outer_join;
        ec->ec_broken = false;
        ec->ec_sortref = 0;
        ec->ec_min_security = restrictinfo->security_level;
        ec->ec_max_security = restrictinfo->security_level;
        ec->ec_merged = NULL;
        em1 = add_eq_member(ec, item1, item1_relids, item1_nullable_relids,
                            false, item1_type);
        em2 = add_eq_member(ec, item2, item2_relids, item2_nullable_relids,
                            false, item2_type);

        root->eq_classes = lappend(root->eq_classes, ec);

        /* mark the RI as associated with this eclass */
        restrictinfo->left_ec = ec;
        restrictinfo->right_ec = ec;
        /* mark the RI as usable with this pair of EMs */
        restrictinfo->left_em = em1;
        restrictinfo->right_em = em2;
    }

    return true;
}

/*
 * canonicalize_ec_expression
 *
 * This function ensures that the expression exposes the expected type and
 * collation, so that it will be equal() to other equivalence-class expressions
 * that it ought to be equal() to.
 *
 * The rule for datatypes is that the exposed type should match what it would
 * be for an input to an operator of the EC's opfamilies; which is usually
 * the declared input type of the operator, but in the case of polymorphic
 * operators no relabeling is wanted (compare the behavior of parse_coerce.c).
 * Expressions coming in from quals will generally have the right type
 * already, but expressions coming from indexkeys may not (because they are
 * represented without any explicit relabel in pg_index), and the same problem
 * occurs for sort expressions (because the parser is likewise cavalier about
 * putting relabels on them).  Such cases will be binary-compatible with the
 * real operators, so adding a RelabelType is sufficient.
 *
 * Also, the expression's exposed collation must match the EC's collation.
 * This is important because in comparisons like "foo < bar COLLATE baz",
 * only one of the expressions has the correct exposed collation as we receive
 * it from the parser.  Forcing both of them to have it ensures that all
 * variant spellings of such a construct behave the same.  Again, we can
 * stick on a RelabelType to force the right exposed collation.  (It might
 * work to not label the collation at all in EC members, but this is risky
 * since some parts of the system expect exprCollation() to deliver the
 * right answer for a sort key.)
 *
 * Note this code assumes that the expression has already been through
 * eval_const_expressions, so there are no CollateExprs and no redundant
 * RelabelTypes.
 */
Expr *
canonicalize_ec_expression(Expr *expr, Oid req_type, Oid req_collation)
{
    Oid         expr_type = exprType((Node *) expr);

    /*
     * For a polymorphic-input-type opclass, just keep the same exposed type.
     */
    if (IsPolymorphicType(req_type))
        req_type = expr_type;

    /*
     * No work if the expression exposes the right type/collation already.
     */
    if (expr_type != req_type ||
        exprCollation((Node *) expr) != req_collation)
    {
        /*
         * Strip any existing RelabelType, then add a new one if needed. This
         * is to preserve the invariant of no redundant RelabelTypes.
         *
         * If we have to change the exposed type of the stripped expression,
         * set typmod to -1 (since the new type may not have the same typmod
         * interpretation).  If we only have to change collation, preserve the
         * exposed typmod.
         */
        while (expr && IsA(expr, RelabelType))
            expr = (Expr *) ((RelabelType *) expr)->arg;

        if (exprType((Node *) expr) != req_type)
            expr = (Expr *) makeRelabelType(expr,
                                            req_type,
                                            -1,
                                            req_collation,
                                            COERCE_IMPLICIT_CAST);
        else if (exprCollation((Node *) expr) != req_collation)
            expr = (Expr *) makeRelabelType(expr,
                                            req_type,
                                            exprTypmod((Node *) expr),
                                            req_collation,
                                            COERCE_IMPLICIT_CAST);
    }

    return expr;
}

/*
 * add_eq_member - build a new EquivalenceMember and add it to an EC
 */
static EquivalenceMember *
add_eq_member(EquivalenceClass *ec, Expr *expr, Relids relids,
              Relids nullable_relids, bool is_child, Oid datatype)
{
    EquivalenceMember *em = makeNode(EquivalenceMember);

    em->em_expr = expr;
    em->em_relids = relids;
    em->em_nullable_relids = nullable_relids;
    em->em_is_const = false;
    em->em_is_child = is_child;
    em->em_datatype = datatype;

    if (bms_is_empty(relids))
    {
        /*
         * No Vars, assume it's a pseudoconstant.  This is correct for entries
         * generated from process_equivalence(), because a WHERE clause can't
         * contain aggregates or SRFs, and non-volatility was checked before
         * process_equivalence() ever got called.  But
         * get_eclass_for_sort_expr() has to work harder.  We put the tests
         * there not here to save cycles in the equivalence case.
         */
        Assert(!is_child);
        em->em_is_const = true;
        ec->ec_has_const = true;
        /* it can't affect ec_relids */
    }
    else if (!is_child)         /* child members don't add to ec_relids */
    {
        ec->ec_relids = bms_add_members(ec->ec_relids, relids);
    }
    ec->ec_members = lappend(ec->ec_members, em);

    return em;
}


/*
 * get_eclass_for_sort_expr
 *    Given an expression and opfamily/collation info, find an existing
 *    equivalence class it is a member of; if none, optionally build a new
 *    single-member EquivalenceClass for it.
 *
 * expr is the expression, and nullable_relids is the set of base relids
 * that are potentially nullable below it.  We actually only care about
 * the set of such relids that are used in the expression; but for caller
 * convenience, we perform that intersection step here.  The caller need
 * only be sure that nullable_relids doesn't omit any nullable rels that
 * might appear in the expr.
 *
 * sortref is the SortGroupRef of the originating SortGroupClause, if any,
 * or zero if not.  (It should never be zero if the expression is volatile!)
 *
 * If rel is not NULL, it identifies a specific relation we're considering
 * a path for, and indicates that child EC members for that relation can be
 * considered.  Otherwise child members are ignored.  (Note: since child EC
 * members aren't guaranteed unique, a non-NULL value means that there could
 * be more than one EC that matches the expression; if so it's order-dependent
 * which one you get.  This is annoying but it only happens in corner cases,
 * so for now we live with just reporting the first match.  See also
 * generate_implied_equalities_for_column and match_pathkeys_to_index.)
 *
 * If create_it is TRUE, we'll build a new EquivalenceClass when there is no
 * match.  If create_it is FALSE, we just return NULL when no match.
 *
 * This can be used safely both before and after EquivalenceClass merging;
 * since it never causes merging it does not invalidate any existing ECs
 * or PathKeys.  However, ECs added after path generation has begun are
 * of limited usefulness, so usually it's best to create them beforehand.
 *
 * Note: opfamilies must be chosen consistently with the way
 * process_equivalence() would do; that is, generated from a mergejoinable
 * equality operator.  Else we might fail to detect valid equivalences,
 * generating poor (but not incorrect) plans.
 */
EquivalenceClass *
get_eclass_for_sort_expr(PlannerInfo *root,
                         Expr *expr,
                         Relids nullable_relids,
                         List *opfamilies,
                         Oid opcintype,
                         Oid collation,
                         Index sortref,
                         Relids rel,
                         bool create_it)
{
    Relids      expr_relids;
    EquivalenceClass *newec;
    EquivalenceMember *newem;
    ListCell   *lc1;
    MemoryContext oldcontext;

    /*
     * Ensure the expression exposes the correct type and collation.
     */
    expr = canonicalize_ec_expression(expr, opcintype, collation);

    /*
     * Get the precise set of nullable relids appearing in the expression.
     */
    expr_relids = pull_varnos((Node *) expr);
    nullable_relids = bms_intersect(nullable_relids, expr_relids);

    /*
     * Scan through the existing EquivalenceClasses for a match
     */
    foreach(lc1, root->eq_classes)
    {
        EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
        ListCell   *lc2;

        /*
         * Never match to a volatile EC, except when we are looking at another
         * reference to the same volatile SortGroupClause.
         */
        if (cur_ec->ec_has_volatile &&
            (sortref == 0 || sortref != cur_ec->ec_sortref))
            continue;

        if (collation != cur_ec->ec_collation)
            continue;
        if (!equal(opfamilies, cur_ec->ec_opfamilies))
            continue;

        foreach(lc2, cur_ec->ec_members)
        {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

            /*
             * Ignore child members unless they match the request.
             */
            if (cur_em->em_is_child &&
                !bms_equal(cur_em->em_relids, rel))
                continue;

            /*
             * If below an outer join, don't match constants: they're not as
             * constant as they look.
             */
            if (cur_ec->ec_below_outer_join &&
                cur_em->em_is_const)
                continue;

            if (opcintype == cur_em->em_datatype &&
                equal(expr, cur_em->em_expr))
                return cur_ec;  /* Match! */
        }
    }

    /* No match; does caller want a NULL result? */
    if (!create_it)
        return NULL;

    /*
     * OK, build a new single-member EC
     *
     * Here, we must be sure that we construct the EC in the right context.
     */
    oldcontext = MemoryContextSwitchTo(root->planner_cxt);

    newec = makeNode(EquivalenceClass);
    newec->ec_opfamilies = list_copy(opfamilies);
    newec->ec_collation = collation;
    newec->ec_members = NIL;
    newec->ec_sources = NIL;
    newec->ec_derives = NIL;
    newec->ec_relids = NULL;
    newec->ec_has_const = false;
    newec->ec_has_volatile = contain_volatile_functions((Node *) expr);
    newec->ec_below_outer_join = false;
    newec->ec_broken = false;
    newec->ec_sortref = sortref;
    newec->ec_min_security = UINT_MAX;
    newec->ec_max_security = 0;
    newec->ec_merged = NULL;

    if (newec->ec_has_volatile && sortref == 0) /* should not happen */
        elog(ERROR, "volatile EquivalenceClass has no sortref");

    newem = add_eq_member(newec, copyObject(expr), expr_relids,
                          nullable_relids, false, opcintype);

    /*
     * add_eq_member doesn't check for volatile functions, set-returning
     * functions, aggregates, or window functions, but such could appear in
     * sort expressions; so we have to check whether its const-marking was
     * correct.
     */
    if (newec->ec_has_const)
    {
        if (newec->ec_has_volatile ||
            expression_returns_set((Node *) expr) ||
            contain_agg_clause((Node *) expr) ||
            contain_window_function((Node *) expr))
        {
            newec->ec_has_const = false;
            newem->em_is_const = false;
        }
    }

    root->eq_classes = lappend(root->eq_classes, newec);

    MemoryContextSwitchTo(oldcontext);

    return newec;
}


/*
 * generate_base_implied_equalities
 *    Generate any restriction clauses that we can deduce from equivalence
 *    classes.
 *
 * When an EC contains pseudoconstants, our strategy is to generate
 * "member = const1" clauses where const1 is the first constant member, for
 * every other member (including other constants).  If we are able to do this
 * then we don't need any "var = var" comparisons because we've successfully
 * constrained all the vars at their points of creation.  If we fail to
 * generate any of these clauses due to lack of cross-type operators, we fall
 * back to the "ec_broken" strategy described below.  (XXX if there are
 * multiple constants of different types, it's possible that we might succeed
 * in forming all the required clauses if we started from a different const
 * member; but this seems a sufficiently hokey corner case to not be worth
 * spending lots of cycles on.)
 *
 * For ECs that contain no pseudoconstants, we generate derived clauses
 * "member1 = member2" for each pair of members belonging to the same base
 * relation (actually, if there are more than two for the same base relation,
 * we only need enough clauses to link each to each other).  This provides
 * the base case for the recursion: each row emitted by a base relation scan
 * will constrain all computable members of the EC to be equal.  As each
 * join path is formed, we'll add additional derived clauses on-the-fly
 * to maintain this invariant (see generate_join_implied_equalities).
 *
 * If the opfamilies used by the EC do not provide complete sets of cross-type
 * equality operators, it is possible that we will fail to generate a clause
 * that must be generated to maintain the invariant.  (An example: given
 * "WHERE a.x = b.y AND b.y = a.z", the scheme breaks down if we cannot
 * generate "a.x = a.z" as a restriction clause for A.)  In this case we mark
 * the EC "ec_broken" and fall back to regurgitating its original source
 * RestrictInfos at appropriate times.  We do not try to retract any derived
 * clauses already generated from the broken EC, so the resulting plan could
 * be poor due to bad selectivity estimates caused by redundant clauses.  But
 * the correct solution to that is to fix the opfamilies ...
 *
 * Equality clauses derived by this function are passed off to
 * process_implied_equality (in plan/initsplan.c) to be inserted into the
 * restrictinfo datastructures.  Note that this must be called after initial
 * scanning of the quals and before Path construction begins.
 *
 * We make no attempt to avoid generating duplicate RestrictInfos here: we
 * don't search ec_sources for matches, nor put the created RestrictInfos
 * into ec_derives.  Doing so would require some slightly ugly changes in
 * initsplan.c's API, and there's no real advantage, because the clauses
 * generated here can't duplicate anything we will generate for joins anyway.
 */
void
generate_base_implied_equalities(PlannerInfo *root)
{
    ListCell   *lc;
    Index       rti;

    foreach(lc, root->eq_classes)
    {
        EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc);

        Assert(ec->ec_merged == NULL);  /* else shouldn't be in list */
        Assert(!ec->ec_broken); /* not yet anyway... */

        /* Single-member ECs won't generate any deductions */
        if (list_length(ec->ec_members) <= 1)
            continue;

        if (ec->ec_has_const)
            generate_base_implied_equalities_const(root, ec);
        else
            generate_base_implied_equalities_no_const(root, ec);

        /* Recover if we failed to generate required derived clauses */
        if (ec->ec_broken)
            generate_base_implied_equalities_broken(root, ec);
    }

    /*
     * This is also a handy place to mark base rels (which should all exist by
     * now) with flags showing whether they have pending eclass joins.
     */
    for (rti = 1; rti < root->simple_rel_array_size; rti++)
    {
        RelOptInfo *brel = root->simple_rel_array[rti];

        if (brel == NULL)
            continue;

        brel->has_eclass_joins = has_relevant_eclass_joinclause(root, brel);
    }
}

/*
 * generate_base_implied_equalities when EC contains pseudoconstant(s)
 */
static void
generate_base_implied_equalities_const(PlannerInfo *root,
                                       EquivalenceClass *ec)
{
    EquivalenceMember *const_em = NULL;
    ListCell   *lc;

    /*
     * In the trivial case where we just had one "var = const" clause, push
     * the original clause back into the main planner machinery.  There is
     * nothing to be gained by doing it differently, and we save the effort to
     * re-build and re-analyze an equality clause that will be exactly
     * equivalent to the old one.
     */
    if (list_length(ec->ec_members) == 2 &&
        list_length(ec->ec_sources) == 1)
    {
        RestrictInfo *restrictinfo = (RestrictInfo *) linitial(ec->ec_sources);

        if (bms_membership(restrictinfo->required_relids) != BMS_MULTIPLE)
        {
            distribute_restrictinfo_to_rels(root, restrictinfo);
            return;
        }
    }

    /*
     * Find the constant member to use.  We prefer an actual constant to
     * pseudo-constants (such as Params), because the constraint exclusion
     * machinery might be able to exclude relations on the basis of generated
     * "var = const" equalities, but "var = param" won't work for that.
     */
    foreach(lc, ec->ec_members)
    {
        EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);

        if (cur_em->em_is_const)
        {
            const_em = cur_em;
            if (IsA(cur_em->em_expr, Const))
                break;
        }
    }
    Assert(const_em != NULL);

    /* Generate a derived equality against each other member */
    foreach(lc, ec->ec_members)
    {
        EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);
        Oid         eq_op;

        Assert(!cur_em->em_is_child);   /* no children yet */
        if (cur_em == const_em)
            continue;
        eq_op = select_equality_operator(ec,
                                         cur_em->em_datatype,
                                         const_em->em_datatype);
        if (!OidIsValid(eq_op))
        {
            /* failed... */
            ec->ec_broken = true;
            break;
        }
        process_implied_equality(root, eq_op, ec->ec_collation,
                                 cur_em->em_expr, const_em->em_expr,
                                 bms_copy(ec->ec_relids),
                                 bms_union(cur_em->em_nullable_relids,
                                           const_em->em_nullable_relids),
                                 ec->ec_min_security,
                                 ec->ec_below_outer_join,
                                 cur_em->em_is_const);
    }
}

/*
 * generate_base_implied_equalities when EC contains no pseudoconstants
 */
static void
generate_base_implied_equalities_no_const(PlannerInfo *root,
                                          EquivalenceClass *ec)
{
    EquivalenceMember **prev_ems;
    ListCell   *lc;

    /*
     * We scan the EC members once and track the last-seen member for each
     * base relation.  When we see another member of the same base relation,
     * we generate "prev_mem = cur_mem".  This results in the minimum number
     * of derived clauses, but it's possible that it will fail when a
     * different ordering would succeed.  XXX FIXME: use a UNION-FIND
     * algorithm similar to the way we build merged ECs.  (Use a list-of-lists
     * for each rel.)
     */
    prev_ems = (EquivalenceMember **)
        palloc0(root->simple_rel_array_size * sizeof(EquivalenceMember *));

    foreach(lc, ec->ec_members)
    {
        EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);
        int         relid;

        Assert(!cur_em->em_is_child);   /* no children yet */
        if (!bms_get_singleton_member(cur_em->em_relids, &relid))
            continue;
        Assert(relid < root->simple_rel_array_size);

        if (prev_ems[relid] != NULL)
        {
            EquivalenceMember *prev_em = prev_ems[relid];
            Oid         eq_op;

            eq_op = select_equality_operator(ec,
                                             prev_em->em_datatype,
                                             cur_em->em_datatype);
            if (!OidIsValid(eq_op))
            {
                /* failed... */
                ec->ec_broken = true;
                break;
            }
            process_implied_equality(root, eq_op, ec->ec_collation,
                                     prev_em->em_expr, cur_em->em_expr,
                                     bms_copy(ec->ec_relids),
                                     bms_union(prev_em->em_nullable_relids,
                                               cur_em->em_nullable_relids),
                                     ec->ec_min_security,
                                     ec->ec_below_outer_join,
                                     false);
        }
        prev_ems[relid] = cur_em;
    }

    pfree(prev_ems);

    /*
     * We also have to make sure that all the Vars used in the member clauses
     * will be available at any join node we might try to reference them at.
     * For the moment we force all the Vars to be available at all join nodes
     * for this eclass.  Perhaps this could be improved by doing some
     * pre-analysis of which members we prefer to join, but it's no worse than
     * what happened in the pre-8.3 code.
     */
    foreach(lc, ec->ec_members)
    {
        EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);
        List       *vars = pull_var_clause((Node *) cur_em->em_expr,
                                           PVC_RECURSE_AGGREGATES |
                                           PVC_RECURSE_WINDOWFUNCS |
                                           PVC_INCLUDE_PLACEHOLDERS);

        add_vars_to_targetlist(root, vars, ec->ec_relids, false);
        list_free(vars);
    }
}

/*
 * generate_base_implied_equalities cleanup after failure
 *
 * What we must do here is push any zero- or one-relation source RestrictInfos
 * of the EC back into the main restrictinfo datastructures.  Multi-relation
 * clauses will be regurgitated later by generate_join_implied_equalities().
 * (We do it this way to maintain continuity with the case that ec_broken
 * becomes set only after we've gone up a join level or two.)  However, for
 * an EC that contains constants, we can adopt a simpler strategy and just
 * throw back all the source RestrictInfos immediately; that works because
 * we know that such an EC can't become broken later.  (This rule justifies
 * ignoring ec_has_const ECs in generate_join_implied_equalities, even when
 * they are broken.)
 */
static void
generate_base_implied_equalities_broken(PlannerInfo *root,
                                        EquivalenceClass *ec)
{
    ListCell   *lc;

    foreach(lc, ec->ec_sources)
    {
        RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(lc);

        if (ec->ec_has_const ||
            bms_membership(restrictinfo->required_relids) != BMS_MULTIPLE)
            distribute_restrictinfo_to_rels(root, restrictinfo);
    }
}


/*
 * generate_join_implied_equalities
 *    Generate any join clauses that we can deduce from equivalence classes.
 *
 * At a join node, we must enforce restriction clauses sufficient to ensure
 * that all equivalence-class members computable at that node are equal.
 * Since the set of clauses to enforce can vary depending on which subset
 * relations are the inputs, we have to compute this afresh for each join
 * relation pair.  Hence a fresh List of RestrictInfo nodes is built and
 * passed back on each call.
 *
 * In addition to its use at join nodes, this can be applied to generate
 * eclass-based join clauses for use in a parameterized scan of a base rel.
 * The reason for the asymmetry of specifying the inner rel as a RelOptInfo
 * and the outer rel by Relids is that this usage occurs before we have
 * built any join RelOptInfos.
 *
 * An annoying special case for parameterized scans is that the inner rel can
 * be an appendrel child (an "other rel").  In this case we must generate
 * appropriate clauses using child EC members.  add_child_rel_equivalences
 * must already have been done for the child rel.
 *
 * The results are sufficient for use in merge, hash, and plain nestloop join
 * methods.  We do not worry here about selecting clauses that are optimal
 * for use in a parameterized indexscan.  indxpath.c makes its own selections
 * of clauses to use, and if the ones we pick here are redundant with those,
 * the extras will be eliminated at createplan time, using the parent_ec
 * markers that we provide (see is_redundant_derived_clause()).
 *
 * Because the same join clauses are likely to be needed multiple times as
 * we consider different join paths, we avoid generating multiple copies:
 * whenever we select a particular pair of EquivalenceMembers to join,
 * we check to see if the pair matches any original clause (in ec_sources)
 * or previously-built clause (in ec_derives).  This saves memory and allows
 * re-use of information cached in RestrictInfos.
 *
 * join_relids should always equal bms_union(outer_relids, inner_rel->relids).
 * We could simplify this function's API by computing it internally, but in
 * most current uses, the caller has the value at hand anyway.
 */
List *
generate_join_implied_equalities(PlannerInfo *root,
                                 Relids join_relids,
                                 Relids outer_relids,
                                 RelOptInfo *inner_rel)
{
    return generate_join_implied_equalities_for_ecs(root,
                                                    root->eq_classes,
                                                    join_relids,
                                                    outer_relids,
                                                    inner_rel);
}

/*
 * generate_join_implied_equalities_for_ecs
 *    As above, but consider only the listed ECs.
 */
List *
generate_join_implied_equalities_for_ecs(PlannerInfo *root,
                                         List *eclasses,
                                         Relids join_relids,
                                         Relids outer_relids,
                                         RelOptInfo *inner_rel)
{
    List       *result = NIL;
    Relids      inner_relids = inner_rel->relids;
    Relids      nominal_inner_relids;
    Relids      nominal_join_relids;
    ListCell   *lc;

    /* If inner rel is a child, extra setup work is needed */
    if (IS_OTHER_REL(inner_rel))
    {
        Assert(!bms_is_empty(inner_rel->top_parent_relids));

        /* Fetch relid set for the topmost parent rel */
        nominal_inner_relids = inner_rel->top_parent_relids;
        /* ECs will be marked with the parent's relid, not the child's */
        nominal_join_relids = bms_union(outer_relids, nominal_inner_relids);
    }
    else
    {
        nominal_inner_relids = inner_relids;
        nominal_join_relids = join_relids;
    }

    foreach(lc, eclasses)
    {
        EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc);
        List       *sublist = NIL;

        /* ECs containing consts do not need any further enforcement */
        if (ec->ec_has_const)
            continue;

        /* Single-member ECs won't generate any deductions */
        if (list_length(ec->ec_members) <= 1)
            continue;

        /* We can quickly ignore any that don't overlap the join, too */
        if (!bms_overlap(ec->ec_relids, nominal_join_relids))
            continue;

        if (!ec->ec_broken)
            sublist = generate_join_implied_equalities_normal(root,
                                                              ec,
                                                              join_relids,
                                                              outer_relids,
                                                              inner_relids);

        /* Recover if we failed to generate required derived clauses */
        if (ec->ec_broken)
            sublist = generate_join_implied_equalities_broken(root,
                                                              ec,
                                                              nominal_join_relids,
                                                              outer_relids,
                                                              nominal_inner_relids,
                                                              inner_rel);

        result = list_concat(result, sublist);
    }

    return result;
}

/*
 * generate_join_implied_equalities for a still-valid EC
 */
static List *
generate_join_implied_equalities_normal(PlannerInfo *root,
                                        EquivalenceClass *ec,
                                        Relids join_relids,
                                        Relids outer_relids,
                                        Relids inner_relids)
{
    List       *result = NIL;
    List       *new_members = NIL;
    List       *outer_members = NIL;
    List       *inner_members = NIL;
    ListCell   *lc1;

    /*
     * First, scan the EC to identify member values that are computable at the
     * outer rel, at the inner rel, or at this relation but not in either
     * input rel.  The outer-rel members should already be enforced equal,
     * likewise for the inner-rel members.  We'll need to create clauses to
     * enforce that any newly computable members are all equal to each other
     * as well as to at least one input member, plus enforce at least one
     * outer-rel member equal to at least one inner-rel member.
     */
    foreach(lc1, ec->ec_members)
    {
        EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc1);

        /*
         * We don't need to check explicitly for child EC members.  This test
         * against join_relids will cause them to be ignored except when
         * considering a child inner rel, which is what we want.
         */
        if (!bms_is_subset(cur_em->em_relids, join_relids))
            continue;           /* not computable yet, or wrong child */

        if (bms_is_subset(cur_em->em_relids, outer_relids))
            outer_members = lappend(outer_members, cur_em);
        else if (bms_is_subset(cur_em->em_relids, inner_relids))
            inner_members = lappend(inner_members, cur_em);
        else
            new_members = lappend(new_members, cur_em);
    }

    /*
     * First, select the joinclause if needed.  We can equate any one outer
     * member to any one inner member, but we have to find a datatype
     * combination for which an opfamily member operator exists.  If we have
     * choices, we prefer simple Var members (possibly with RelabelType) since
     * these are (a) cheapest to compute at runtime and (b) most likely to
     * have useful statistics. Also, prefer operators that are also
     * hashjoinable.
     */
    if (outer_members && inner_members)
    {
        EquivalenceMember *best_outer_em = NULL;
        EquivalenceMember *best_inner_em = NULL;
        Oid         best_eq_op = InvalidOid;
        int         best_score = -1;
        RestrictInfo *rinfo;

        foreach(lc1, outer_members)
        {
            EquivalenceMember *outer_em = (EquivalenceMember *) lfirst(lc1);
            ListCell   *lc2;

            foreach(lc2, inner_members)
            {
                EquivalenceMember *inner_em = (EquivalenceMember *) lfirst(lc2);
                Oid         eq_op;
                int         score;

                eq_op = select_equality_operator(ec,
                                                 outer_em->em_datatype,
                                                 inner_em->em_datatype);
                if (!OidIsValid(eq_op))
                    continue;
                score = 0;
                if (IsA(outer_em->em_expr, Var) ||
                    (IsA(outer_em->em_expr, RelabelType) &&
                     IsA(((RelabelType *) outer_em->em_expr)->arg, Var)))
                    score++;
                if (IsA(inner_em->em_expr, Var) ||
                    (IsA(inner_em->em_expr, RelabelType) &&
                     IsA(((RelabelType *) inner_em->em_expr)->arg, Var)))
                    score++;
                if (op_hashjoinable(eq_op,
                                    exprType((Node *) outer_em->em_expr)))
                    score++;
                if (score > best_score)
                {
                    best_outer_em = outer_em;
                    best_inner_em = inner_em;
                    best_eq_op = eq_op;
                    best_score = score;
                    if (best_score == 3)
                        break;  /* no need to look further */
                }
            }
            if (best_score == 3)
                break;          /* no need to look further */
        }
        if (best_score < 0)
        {
            /* failed... */
            ec->ec_broken = true;
            return NIL;
        }

        /*
         * Create clause, setting parent_ec to mark it as redundant with other
         * joinclauses
         */
        rinfo = create_join_clause(root, ec, best_eq_op,
                                   best_outer_em, best_inner_em,
                                   ec);

        result = lappend(result, rinfo);
    }

    /*
     * Now deal with building restrictions for any expressions that involve
     * Vars from both sides of the join.  We have to equate all of these to
     * each other as well as to at least one old member (if any).
     *
     * XXX as in generate_base_implied_equalities_no_const, we could be a lot
     * smarter here to avoid unnecessary failures in cross-type situations.
     * For now, use the same left-to-right method used there.
     */
    if (new_members)
    {
        List       *old_members = list_concat(outer_members, inner_members);
        EquivalenceMember *prev_em = NULL;
        RestrictInfo *rinfo;

        /* For now, arbitrarily take the first old_member as the one to use */
        if (old_members)
            new_members = lappend(new_members, linitial(old_members));

        foreach(lc1, new_members)
        {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc1);

            if (prev_em != NULL)
            {
                Oid         eq_op;

                eq_op = select_equality_operator(ec,
                                                 prev_em->em_datatype,
                                                 cur_em->em_datatype);
                if (!OidIsValid(eq_op))
                {
                    /* failed... */
                    ec->ec_broken = true;
                    return NIL;
                }
                /* do NOT set parent_ec, this qual is not redundant! */
                rinfo = create_join_clause(root, ec, eq_op,
                                           prev_em, cur_em,
                                           NULL);

                result = lappend(result, rinfo);
            }
            prev_em = cur_em;
        }
    }

    return result;
}

/*
 * generate_join_implied_equalities cleanup after failure
 *
 * Return any original RestrictInfos that are enforceable at this join.
 *
 * In the case of a child inner relation, we have to translate the
 * original RestrictInfos from parent to child Vars.
 */
static List *
generate_join_implied_equalities_broken(PlannerInfo *root,
                                        EquivalenceClass *ec,
                                        Relids nominal_join_relids,
                                        Relids outer_relids,
                                        Relids nominal_inner_relids,
                                        RelOptInfo *inner_rel)
{
    List       *result = NIL;
    ListCell   *lc;

    foreach(lc, ec->ec_sources)
    {
        RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(lc);
        Relids      clause_relids = restrictinfo->required_relids;

        if (bms_is_subset(clause_relids, nominal_join_relids) &&
            !bms_is_subset(clause_relids, outer_relids) &&
            !bms_is_subset(clause_relids, nominal_inner_relids))
            result = lappend(result, restrictinfo);
    }

    /*
     * If we have to translate, just brute-force apply adjust_appendrel_attrs
     * to all the RestrictInfos at once.  This will result in returning
     * RestrictInfos that are not listed in ec_derives, but there shouldn't be
     * any duplication, and it's a sufficiently narrow corner case that we
     * shouldn't sweat too much over it anyway.
     *
     * Since inner_rel might be an indirect descendant of the baserel
     * mentioned in the ec_sources clauses, we have to be prepared to apply
     * multiple levels of Var translation.
     */
    if (IS_OTHER_REL(inner_rel) && result != NIL)
        result = (List *) adjust_appendrel_attrs_multilevel(root,
                                                            (Node *) result,
                                                            inner_rel->relids,
                                                            inner_rel->top_parent_relids);

    return result;
}


/*
 * select_equality_operator
 *    Select a suitable equality operator for comparing two EC members
 *
 * Returns InvalidOid if no operator can be found for this datatype combination
 */
static Oid
select_equality_operator(EquivalenceClass *ec, Oid lefttype, Oid righttype)
{
    ListCell   *lc;

    foreach(lc, ec->ec_opfamilies)
    {
        Oid         opfamily = lfirst_oid(lc);
        Oid         opno;

        opno = get_opfamily_member(opfamily, lefttype, righttype,
                                   BTEqualStrategyNumber);
        if (!OidIsValid(opno))
            continue;
        /* If no barrier quals in query, don't worry about leaky operators */
        if (ec->ec_max_security == 0)
            return opno;
        /* Otherwise, insist that selected operators be leakproof */
        if (get_func_leakproof(get_opcode(opno)))
            return opno;
    }
    return InvalidOid;
}


/*
 * create_join_clause
 *    Find or make a RestrictInfo comparing the two given EC members
 *    with the given operator.
 *
 * parent_ec is either equal to ec (if the clause is a potentially-redundant
 * join clause) or NULL (if not).  We have to treat this as part of the
 * match requirements --- it's possible that a clause comparing the same two
 * EMs is a join clause in one join path and a restriction clause in another.
 */
static RestrictInfo *
create_join_clause(PlannerInfo *root,
                   EquivalenceClass *ec, Oid opno,
                   EquivalenceMember *leftem,
                   EquivalenceMember *rightem,
                   EquivalenceClass *parent_ec)
{
    RestrictInfo *rinfo;
    ListCell   *lc;
    MemoryContext oldcontext;

    /*
     * Search to see if we already built a RestrictInfo for this pair of
     * EquivalenceMembers.  We can use either original source clauses or
     * previously-derived clauses.  The check on opno is probably redundant,
     * but be safe ...
     */
    foreach(lc, ec->ec_sources)
    {
        rinfo = (RestrictInfo *) lfirst(lc);
        if (rinfo->left_em == leftem &&
            rinfo->right_em == rightem &&
            rinfo->parent_ec == parent_ec &&
            opno == ((OpExpr *) rinfo->clause)->opno)
            return rinfo;
    }

    foreach(lc, ec->ec_derives)
    {
        rinfo = (RestrictInfo *) lfirst(lc);
        if (rinfo->left_em == leftem &&
            rinfo->right_em == rightem &&
            rinfo->parent_ec == parent_ec &&
            opno == ((OpExpr *) rinfo->clause)->opno)
            return rinfo;
    }

    /*
     * Not there, so build it, in planner context so we can re-use it. (Not
     * important in normal planning, but definitely so in GEQO.)
     */
    oldcontext = MemoryContextSwitchTo(root->planner_cxt);

    rinfo = build_implied_join_equality(opno,
                                        ec->ec_collation,
                                        leftem->em_expr,
                                        rightem->em_expr,
                                        bms_union(leftem->em_relids,
                                                  rightem->em_relids),
                                        bms_union(leftem->em_nullable_relids,
                                                  rightem->em_nullable_relids),
                                        ec->ec_min_security);

    /* Mark the clause as redundant, or not */
    rinfo->parent_ec = parent_ec;

    /*
     * We know the correct values for left_ec/right_ec, ie this particular EC,
     * so we can just set them directly instead of forcing another lookup.
     */
    rinfo->left_ec = ec;
    rinfo->right_ec = ec;

    /* Mark it as usable with these EMs */
    rinfo->left_em = leftem;
    rinfo->right_em = rightem;
    /* and save it for possible re-use */
    ec->ec_derives = lappend(ec->ec_derives, rinfo);

    MemoryContextSwitchTo(oldcontext);

    return rinfo;
}


/*
 * reconsider_outer_join_clauses
 *    Re-examine any outer-join clauses that were set aside by
 *    distribute_qual_to_rels(), and see if we can derive any
 *    EquivalenceClasses from them.  Then, if they were not made
 *    redundant, push them out into the regular join-clause lists.
 *
 * When we have mergejoinable clauses A = B that are outer-join clauses,
 * we can't blindly combine them with other clauses A = C to deduce B = C,
 * since in fact the "equality" A = B won't necessarily hold above the
 * outer join (one of the variables might be NULL instead).  Nonetheless
 * there are cases where we can add qual clauses using transitivity.
 *
 * One case that we look for here is an outer-join clause OUTERVAR = INNERVAR
 * for which there is also an equivalence clause OUTERVAR = CONSTANT.
 * It is safe and useful to push a clause INNERVAR = CONSTANT into the
 * evaluation of the inner (nullable) relation, because any inner rows not
 * meeting this condition will not contribute to the outer-join result anyway.
 * (Any outer rows they could join to will be eliminated by the pushed-down
 * equivalence clause.)
 *
 * Note that the above rule does not work for full outer joins; nor is it
 * very interesting to consider cases where the generated equivalence clause
 * would involve relations outside the outer join, since such clauses couldn't
 * be pushed into the inner side's scan anyway.  So the restriction to
 * outervar = pseudoconstant is not really giving up anything.
 *
 * For full-join cases, we can only do something useful if it's a FULL JOIN
 * USING and a merged column has an equivalence MERGEDVAR = CONSTANT.
 * By the time it gets here, the merged column will look like
 *      COALESCE(LEFTVAR, RIGHTVAR)
 * and we will have a full-join clause LEFTVAR = RIGHTVAR that we can match
 * the COALESCE expression to. In this situation we can push LEFTVAR = CONSTANT
 * and RIGHTVAR = CONSTANT into the input relations, since any rows not
 * meeting these conditions cannot contribute to the join result.
 *
 * Again, there isn't any traction to be gained by trying to deal with
 * clauses comparing a mergedvar to a non-pseudoconstant.  So we can make
 * use of the EquivalenceClasses to search for matching variables that were
 * equivalenced to constants.  The interesting outer-join clauses were
 * accumulated for us by distribute_qual_to_rels.
 *
 * When we find one of these cases, we implement the changes we want by
 * generating a new equivalence clause INNERVAR = CONSTANT (or LEFTVAR, etc)
 * and pushing it into the EquivalenceClass structures.  This is because we
 * may already know that INNERVAR is equivalenced to some other var(s), and
 * we'd like the constant to propagate to them too.  Note that it would be
 * unsafe to merge any existing EC for INNERVAR with the OUTERVAR's EC ---
 * that could result in propagating constant restrictions from
 * INNERVAR to OUTERVAR, which would be very wrong.
 *
 * It's possible that the INNERVAR is also an OUTERVAR for some other
 * outer-join clause, in which case the process can be repeated.  So we repeat
 * looping over the lists of clauses until no further deductions can be made.
 * Whenever we do make a deduction, we remove the generating clause from the
 * lists, since we don't want to make the same deduction twice.
 *
 * If we don't find any match for a set-aside outer join clause, we must
 * throw it back into the regular joinclause processing by passing it to
 * distribute_restrictinfo_to_rels().  If we do generate a derived clause,
 * however, the outer-join clause is redundant.  We still throw it back,
 * because otherwise the join will be seen as a clauseless join and avoided
 * during join order searching; but we mark it as redundant to keep from
 * messing up the joinrel's size estimate.  (This behavior means that the
 * API for this routine is uselessly complex: we could have just put all
 * the clauses into the regular processing initially.  We keep it because
 * someday we might want to do something else, such as inserting "dummy"
 * joinclauses instead of real ones.)
 *
 * Outer join clauses that are marked outerjoin_delayed are special: this
 * condition means that one or both VARs might go to null due to a lower
 * outer join.  We can still push a constant through the clause, but only
 * if its operator is strict; and we *have to* throw the clause back into
 * regular joinclause processing.  By keeping the strict join clause,
 * we ensure that any null-extended rows that are mistakenly generated due
 * to suppressing rows not matching the constant will be rejected at the
 * upper outer join.  (This doesn't work for full-join clauses.)
 */
void
reconsider_outer_join_clauses(PlannerInfo *root)
{
    bool        found;
    ListCell   *cell;
    ListCell   *prev;
    ListCell   *next;

    /* Outer loop repeats until we find no more deductions */
    do
    {
        found = false;

        /* Process the LEFT JOIN clauses */
        prev = NULL;
        for (cell = list_head(root->left_join_clauses); cell; cell = next)
        {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

            next = lnext(cell);
            if (reconsider_outer_join_clause(root, rinfo, true))
            {
                found = true;
                /* remove it from the list */
                root->left_join_clauses =
                    list_delete_cell(root->left_join_clauses, cell, prev);
                /* we throw it back anyway (see notes above) */
                /* but the thrown-back clause has no extra selectivity */
                rinfo->norm_selec = 2.0;
                rinfo->outer_selec = 1.0;
                distribute_restrictinfo_to_rels(root, rinfo);
            }
            else
                prev = cell;
        }

        /* Process the RIGHT JOIN clauses */
        prev = NULL;
        for (cell = list_head(root->right_join_clauses); cell; cell = next)
        {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

            next = lnext(cell);
            if (reconsider_outer_join_clause(root, rinfo, false))
            {
                found = true;
                /* remove it from the list */
                root->right_join_clauses =
                    list_delete_cell(root->right_join_clauses, cell, prev);
                /* we throw it back anyway (see notes above) */
                /* but the thrown-back clause has no extra selectivity */
                rinfo->norm_selec = 2.0;
                rinfo->outer_selec = 1.0;
                distribute_restrictinfo_to_rels(root, rinfo);
            }
            else
                prev = cell;
        }

        /* Process the FULL JOIN clauses */
        prev = NULL;
        for (cell = list_head(root->full_join_clauses); cell; cell = next)
        {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

            next = lnext(cell);
            if (reconsider_full_join_clause(root, rinfo))
            {
                found = true;
                /* remove it from the list */
                root->full_join_clauses =
                    list_delete_cell(root->full_join_clauses, cell, prev);
                /* we throw it back anyway (see notes above) */
                /* but the thrown-back clause has no extra selectivity */
                rinfo->norm_selec = 2.0;
                rinfo->outer_selec = 1.0;
                distribute_restrictinfo_to_rels(root, rinfo);
            }
            else
                prev = cell;
        }
    } while (found);

    /* Now, any remaining clauses have to be thrown back */
    foreach(cell, root->left_join_clauses)
    {
        RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

        distribute_restrictinfo_to_rels(root, rinfo);
    }
    foreach(cell, root->right_join_clauses)
    {
        RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

        distribute_restrictinfo_to_rels(root, rinfo);
    }
    foreach(cell, root->full_join_clauses)
    {
        RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

        distribute_restrictinfo_to_rels(root, rinfo);
    }
}

/*
 * reconsider_outer_join_clauses for a single LEFT/RIGHT JOIN clause
 *
 * Returns TRUE if we were able to propagate a constant through the clause.
 */
static bool
reconsider_outer_join_clause(PlannerInfo *root, RestrictInfo *rinfo,
                             bool outer_on_left)
{
    Expr       *outervar,
               *innervar;
    Oid         opno,
                collation,
                left_type,
                right_type,
                inner_datatype;
    Relids      inner_relids,
                inner_nullable_relids;
    ListCell   *lc1;

    Assert(is_opclause(rinfo->clause));
    opno = ((OpExpr *) rinfo->clause)->opno;
    collation = ((OpExpr *) rinfo->clause)->inputcollid;

    /* If clause is outerjoin_delayed, operator must be strict */
    if (rinfo->outerjoin_delayed && !op_strict(opno))
        return false;

    /* Extract needed info from the clause */
    op_input_types(opno, &left_type, &right_type);
    if (outer_on_left)
    {
        outervar = (Expr *) get_leftop(rinfo->clause);
        innervar = (Expr *) get_rightop(rinfo->clause);
        inner_datatype = right_type;
        inner_relids = rinfo->right_relids;
    }
    else
    {
        outervar = (Expr *) get_rightop(rinfo->clause);
        innervar = (Expr *) get_leftop(rinfo->clause);
        inner_datatype = left_type;
        inner_relids = rinfo->left_relids;
    }
    inner_nullable_relids = bms_intersect(inner_relids,
                                          rinfo->nullable_relids);

    /* Scan EquivalenceClasses for a match to outervar */
    foreach(lc1, root->eq_classes)
    {
        EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
        bool        match;
        ListCell   *lc2;

        /* Ignore EC unless it contains pseudoconstants */
        if (!cur_ec->ec_has_const)
            continue;
        /* Never match to a volatile EC */
        if (cur_ec->ec_has_volatile)
            continue;
        /* It has to match the outer-join clause as to semantics, too */
        if (collation != cur_ec->ec_collation)
            continue;
        if (!equal(rinfo->mergeopfamilies, cur_ec->ec_opfamilies))
            continue;
        /* Does it contain a match to outervar? */
        match = false;
        foreach(lc2, cur_ec->ec_members)
        {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

            Assert(!cur_em->em_is_child);   /* no children yet */
            if (equal(outervar, cur_em->em_expr))
            {
                match = true;
                break;
            }
        }
        if (!match)
            continue;           /* no match, so ignore this EC */

        /*
         * Yes it does!  Try to generate a clause INNERVAR = CONSTANT for each
         * CONSTANT in the EC.  Note that we must succeed with at least one
         * constant before we can decide to throw away the outer-join clause.
         */
        match = false;
        foreach(lc2, cur_ec->ec_members)
        {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);
            Oid         eq_op;
            RestrictInfo *newrinfo;

            if (!cur_em->em_is_const)
                continue;       /* ignore non-const members */
            eq_op = select_equality_operator(cur_ec,
                                             inner_datatype,
                                             cur_em->em_datatype);
            if (!OidIsValid(eq_op))
                continue;       /* can't generate equality */
            newrinfo = build_implied_join_equality(eq_op,
                                                   cur_ec->ec_collation,
                                                   innervar,
                                                   cur_em->em_expr,
                                                   bms_copy(inner_relids),
                                                   bms_copy(inner_nullable_relids),
                                                   cur_ec->ec_min_security);
            if (process_equivalence(root, newrinfo, true))
                match = true;
        }

        /*
         * If we were able to equate INNERVAR to any constant, report success.
         * Otherwise, fall out of the search loop, since we know the OUTERVAR
         * appears in at most one EC.
         */
        if (match)
            return true;
        else
            break;
    }

    return false;               /* failed to make any deduction */
}

/*
 * reconsider_outer_join_clauses for a single FULL JOIN clause
 *
 * Returns TRUE if we were able to propagate a constant through the clause.
 */
static bool
reconsider_full_join_clause(PlannerInfo *root, RestrictInfo *rinfo)
{
    Expr       *leftvar;
    Expr       *rightvar;
    Oid         opno,
                collation,
                left_type,
                right_type;
    Relids      left_relids,
                right_relids,
                left_nullable_relids,
                right_nullable_relids;
    ListCell   *lc1;

    /* Can't use an outerjoin_delayed clause here */
    if (rinfo->outerjoin_delayed)
        return false;

    /* Extract needed info from the clause */
    Assert(is_opclause(rinfo->clause));
    opno = ((OpExpr *) rinfo->clause)->opno;
    collation = ((OpExpr *) rinfo->clause)->inputcollid;
    op_input_types(opno, &left_type, &right_type);
    leftvar = (Expr *) get_leftop(rinfo->clause);
    rightvar = (Expr *) get_rightop(rinfo->clause);
    left_relids = rinfo->left_relids;
    right_relids = rinfo->right_relids;
    left_nullable_relids = bms_intersect(left_relids,
                                         rinfo->nullable_relids);
    right_nullable_relids = bms_intersect(right_relids,
                                          rinfo->nullable_relids);

    foreach(lc1, root->eq_classes)
    {
        EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
        EquivalenceMember *coal_em = NULL;
        bool        match;
        bool        matchleft;
        bool        matchright;
        ListCell   *lc2;

        /* Ignore EC unless it contains pseudoconstants */
        if (!cur_ec->ec_has_const)
            continue;
        /* Never match to a volatile EC */
        if (cur_ec->ec_has_volatile)
            continue;
        /* It has to match the outer-join clause as to semantics, too */
        if (collation != cur_ec->ec_collation)
            continue;
        if (!equal(rinfo->mergeopfamilies, cur_ec->ec_opfamilies))
            continue;

        /*
         * Does it contain a COALESCE(leftvar, rightvar) construct?
         *
         * We can assume the COALESCE() inputs are in the same order as the
         * join clause, since both were automatically generated in the cases
         * we care about.
         *
         * XXX currently this may fail to match in cross-type cases because
         * the COALESCE will contain typecast operations while the join clause
         * may not (if there is a cross-type mergejoin operator available for
         * the two column types). Is it OK to strip implicit coercions from
         * the COALESCE arguments?
         */
        match = false;
        foreach(lc2, cur_ec->ec_members)
        {
            coal_em = (EquivalenceMember *) lfirst(lc2);
            Assert(!coal_em->em_is_child);  /* no children yet */
            if (IsA(coal_em->em_expr, CoalesceExpr))
            {
                CoalesceExpr *cexpr = (CoalesceExpr *) coal_em->em_expr;
                Node       *cfirst;
                Node       *csecond;

                if (list_length(cexpr->args) != 2)
                    continue;
                cfirst = (Node *) linitial(cexpr->args);
                csecond = (Node *) lsecond(cexpr->args);

                if (equal(leftvar, cfirst) && equal(rightvar, csecond))
                {
                    match = true;
                    break;
                }
            }
        }
        if (!match)
            continue;           /* no match, so ignore this EC */

        /*
         * Yes it does!  Try to generate clauses LEFTVAR = CONSTANT and
         * RIGHTVAR = CONSTANT for each CONSTANT in the EC.  Note that we must
         * succeed with at least one constant for each var before we can
         * decide to throw away the outer-join clause.
         */
        matchleft = matchright = false;
        foreach(lc2, cur_ec->ec_members)
        {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);
            Oid         eq_op;
            RestrictInfo *newrinfo;

            if (!cur_em->em_is_const)
                continue;       /* ignore non-const members */
            eq_op = select_equality_operator(cur_ec,
                                             left_type,
                                             cur_em->em_datatype);
            if (OidIsValid(eq_op))
            {
                newrinfo = build_implied_join_equality(eq_op,
                                                       cur_ec->ec_collation,
                                                       leftvar,
                                                       cur_em->em_expr,
                                                       bms_copy(left_relids),
                                                       bms_copy(left_nullable_relids),
                                                       cur_ec->ec_min_security);
                if (process_equivalence(root, newrinfo, true))
                    matchleft = true;
            }
            eq_op = select_equality_operator(cur_ec,
                                             right_type,
                                             cur_em->em_datatype);
            if (OidIsValid(eq_op))
            {
                newrinfo = build_implied_join_equality(eq_op,
                                                       cur_ec->ec_collation,
                                                       rightvar,
                                                       cur_em->em_expr,
                                                       bms_copy(right_relids),
                                                       bms_copy(right_nullable_relids),
                                                       cur_ec->ec_min_security);
                if (process_equivalence(root, newrinfo, true))
                    matchright = true;
            }
        }

        /*
         * If we were able to equate both vars to constants, we're done, and
         * we can throw away the full-join clause as redundant.  Moreover, we
         * can remove the COALESCE entry from the EC, since the added
         * restrictions ensure it will always have the expected value. (We
         * don't bother trying to update ec_relids or ec_sources.)
         */
        if (matchleft && matchright)
        {
            cur_ec->ec_members = list_delete_ptr(cur_ec->ec_members, coal_em);
            return true;
        }

        /*
         * Otherwise, fall out of the search loop, since we know the COALESCE
         * appears in at most one EC (XXX might stop being true if we allow
         * stripping of coercions above?)
         */
        break;
    }

    return false;               /* failed to make any deduction */
}


/*
 * exprs_known_equal
 *    Detect whether two expressions are known equal due to equivalence
 *    relationships.
 *
 * Actually, this only shows that the expressions are equal according
 * to some opfamily's notion of equality --- but we only use it for
 * selectivity estimation, so a fuzzy idea of equality is OK.
 *
 * Note: does not bother to check for "equal(item1, item2)"; caller must
 * check that case if it's possible to pass identical items.
 */
bool
exprs_known_equal(PlannerInfo *root, Node *item1, Node *item2)
{
    ListCell   *lc1;

    foreach(lc1, root->eq_classes)
    {
        EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc1);
        bool        item1member = false;
        bool        item2member = false;
        ListCell   *lc2;

        /* Never match to a volatile EC */
        if (ec->ec_has_volatile)
            continue;

        foreach(lc2, ec->ec_members)
        {
            EquivalenceMember *em = (EquivalenceMember *) lfirst(lc2);

            if (em->em_is_child)
                continue;       /* ignore children here */
            if (equal(item1, em->em_expr))
                item1member = true;
            else if (equal(item2, em->em_expr))
                item2member = true;
            /* Exit as soon as equality is proven */
            if (item1member && item2member)
                return true;
        }
    }
    return false;
}


/*
 * match_eclasses_to_foreign_key_col
 *    See whether a foreign key column match is proven by any eclass.
 *
 * If the referenced and referencing Vars of the fkey's colno'th column are
 * known equal due to any eclass, return that eclass; otherwise return NULL.
 * (In principle there might be more than one matching eclass if multiple
 * collations are involved, but since collation doesn't matter for equality,
 * we ignore that fine point here.)  This is much like exprs_known_equal,
 * except that we insist on the comparison operator matching the eclass, so
 * that the result is definite not approximate.
 */
EquivalenceClass *
match_eclasses_to_foreign_key_col(PlannerInfo *root,
                                  ForeignKeyOptInfo *fkinfo,
                                  int colno)
{
    Index       var1varno = fkinfo->con_relid;
    AttrNumber  var1attno = fkinfo->conkey[colno];
    Index       var2varno = fkinfo->ref_relid;
    AttrNumber  var2attno = fkinfo->confkey[colno];
    Oid         eqop = fkinfo->conpfeqop[colno];
    List       *opfamilies = NIL;   /* compute only if needed */
    ListCell   *lc1;

    foreach(lc1, root->eq_classes)
    {
        EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc1);
        bool        item1member = false;
        bool        item2member = false;
        ListCell   *lc2;

        /* Never match to a volatile EC */
        if (ec->ec_has_volatile)
            continue;
        /* Note: it seems okay to match to "broken" eclasses here */

        foreach(lc2, ec->ec_members)
        {
            EquivalenceMember *em = (EquivalenceMember *) lfirst(lc2);
            Var        *var;

            if (em->em_is_child)
                continue;       /* ignore children here */

            /* EM must be a Var, possibly with RelabelType */
            var = (Var *) em->em_expr;
            while (var && IsA(var, RelabelType))
                var = (Var *) ((RelabelType *) var)->arg;
            if (!(var && IsA(var, Var)))
                continue;

            /* Match? */
            if (var->varno == var1varno && var->varattno == var1attno)
                item1member = true;
            else if (var->varno == var2varno && var->varattno == var2attno)
                item2member = true;

            /* Have we found both PK and FK column in this EC? */
            if (item1member && item2member)
            {
                /*
                 * Succeed if eqop matches EC's opfamilies.  We could test
                 * this before scanning the members, but it's probably cheaper
                 * to test for member matches first.
                 */
                if (opfamilies == NIL)  /* compute if we didn't already */
                    opfamilies = get_mergejoin_opfamilies(eqop);
                if (equal(opfamilies, ec->ec_opfamilies))
                    return ec;
                /* Otherwise, done with this EC, move on to the next */
                break;
            }
        }
    }
    return NULL;
}


/*
 * add_child_rel_equivalences
 *    Search for EC members that reference the parent_rel, and
 *    add transformed members referencing the child_rel.
 *
 * Note that this function won't be called at all unless we have at least some
 * reason to believe that the EC members it generates will be useful.
 *
 * parent_rel and child_rel could be derived from appinfo, but since the
 * caller has already computed them, we might as well just pass them in.
 */
void
add_child_rel_equivalences(PlannerInfo *root,
                           AppendRelInfo *appinfo,
                           RelOptInfo *parent_rel,
                           RelOptInfo *child_rel)
{
    ListCell   *lc1;

    foreach(lc1, root->eq_classes)
    {
        EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
        ListCell   *lc2;

        /*
         * If this EC contains a volatile expression, then generating child
         * EMs would be downright dangerous, so skip it.  We rely on a
         * volatile EC having only one EM.
         */
        if (cur_ec->ec_has_volatile)
            continue;

        /*
         * No point in searching if parent rel not mentioned in eclass; but we
         * can't tell that for sure if parent rel is itself a child.
         */
        if (parent_rel->reloptkind == RELOPT_BASEREL &&
            !bms_is_subset(parent_rel->relids, cur_ec->ec_relids))
            continue;

        foreach(lc2, cur_ec->ec_members)
        {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

            if (cur_em->em_is_const)
                continue;       /* ignore consts here */

            /* Does it reference parent_rel? */
            if (bms_overlap(cur_em->em_relids, parent_rel->relids))
            {
                /* Yes, generate transformed child version */
                Expr       *child_expr;
                Relids      new_relids;
                Relids      new_nullable_relids;

                child_expr = (Expr *)
                    adjust_appendrel_attrs(root,
                                           (Node *) cur_em->em_expr,
                                           1, &appinfo);

                /*
                 * Transform em_relids to match.  Note we do *not* do
                 * pull_varnos(child_expr) here, as for example the
                 * transformation might have substituted a constant, but we
                 * don't want the child member to be marked as constant.
                 */
                new_relids = bms_difference(cur_em->em_relids,
                                            parent_rel->relids);
                new_relids = bms_add_members(new_relids, child_rel->relids);

                /*
                 * And likewise for nullable_relids.  Note this code assumes
                 * parent and child relids are singletons.
                 */
                new_nullable_relids = cur_em->em_nullable_relids;
                if (bms_overlap(new_nullable_relids, parent_rel->relids))
                {
                    new_nullable_relids = bms_difference(new_nullable_relids,
                                                         parent_rel->relids);
                    new_nullable_relids = bms_add_members(new_nullable_relids,
                                                          child_rel->relids);
                }

                (void) add_eq_member(cur_ec, child_expr,
                                     new_relids, new_nullable_relids,
                                     true, cur_em->em_datatype);
            }
        }
    }
}


/*
 * generate_implied_equalities_for_column
 *    Create EC-derived joinclauses usable with a specific column.
 *
 * This is used by indxpath.c to extract potentially indexable joinclauses
 * from ECs, and can be used by foreign data wrappers for similar purposes.
 * We assume that only expressions in Vars of a single table are of interest,
 * but the caller provides a callback function to identify exactly which
 * such expressions it would like to know about.
 *
 * We assume that any given table/index column could appear in only one EC.
 * (This should be true in all but the most pathological cases, and if it
 * isn't, we stop on the first match anyway.)  Therefore, what we return
 * is a redundant list of clauses equating the table/index column to each of
 * the other-relation values it is known to be equal to.  Any one of
 * these clauses can be used to create a parameterized path, and there
 * is no value in using more than one.  (But it *is* worthwhile to create
 * a separate parameterized path for each one, since that leads to different
 * join orders.)
 *
 * The caller can pass a Relids set of rels we aren't interested in joining
 * to, so as to save the work of creating useless clauses.
 */
List *
generate_implied_equalities_for_column(PlannerInfo *root,
                                       RelOptInfo *rel,
                                       ec_matches_callback_type callback,
                                       void *callback_arg,
                                       Relids prohibited_rels)
{
    List       *result = NIL;
    bool        is_child_rel = (rel->reloptkind == RELOPT_OTHER_MEMBER_REL);
    Relids      parent_relids;
    ListCell   *lc1;

    /* Indexes are available only on base or "other" member relations. */
    Assert(IS_SIMPLE_REL(rel));

    /* If it's a child rel, we'll need to know what its parent(s) are */
    if (is_child_rel)
        parent_relids = find_childrel_parents(root, rel);
    else
        parent_relids = NULL;   /* not used, but keep compiler quiet */

    foreach(lc1, root->eq_classes)
    {
        EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
        EquivalenceMember *cur_em;
        ListCell   *lc2;

        /*
         * Won't generate joinclauses if const or single-member (the latter
         * test covers the volatile case too)
         */
        if (cur_ec->ec_has_const || list_length(cur_ec->ec_members) <= 1)
            continue;

        /*
         * No point in searching if rel not mentioned in eclass (but we can't
         * tell that for a child rel).
         */
        if (!is_child_rel &&
            !bms_is_subset(rel->relids, cur_ec->ec_relids))
            continue;

        /*
         * Scan members, looking for a match to the target column.  Note that
         * child EC members are considered, but only when they belong to the
         * target relation.  (Unlike regular members, the same expression
         * could be a child member of more than one EC.  Therefore, it's
         * potentially order-dependent which EC a child relation's target
         * column gets matched to.  This is annoying but it only happens in
         * corner cases, so for now we live with just reporting the first
         * match.  See also get_eclass_for_sort_expr.)
         */
        cur_em = NULL;
        foreach(lc2, cur_ec->ec_members)
        {
            cur_em = (EquivalenceMember *) lfirst(lc2);
            if (bms_equal(cur_em->em_relids, rel->relids) &&
                callback(root, rel, cur_ec, cur_em, callback_arg))
                break;
            cur_em = NULL;
        }

        if (!cur_em)
            continue;

        /*
         * Found our match.  Scan the other EC members and attempt to generate
         * joinclauses.
         */
        foreach(lc2, cur_ec->ec_members)
        {
            EquivalenceMember *other_em = (EquivalenceMember *) lfirst(lc2);
            Oid         eq_op;
            RestrictInfo *rinfo;

            if (other_em->em_is_child)
                continue;       /* ignore children here */

            /* Make sure it'll be a join to a different rel */
            if (other_em == cur_em ||
                bms_overlap(other_em->em_relids, rel->relids))
                continue;

            /* Forget it if caller doesn't want joins to this rel */
            if (bms_overlap(other_em->em_relids, prohibited_rels))
                continue;

            /*
             * Also, if this is a child rel, avoid generating a useless join
             * to its parent rel(s).
             */
            if (is_child_rel &&
                bms_overlap(parent_relids, other_em->em_relids))
                continue;

            eq_op = select_equality_operator(cur_ec,
                                             cur_em->em_datatype,
                                             other_em->em_datatype);
            if (!OidIsValid(eq_op))
                continue;

            /* set parent_ec to mark as redundant with other joinclauses */
            rinfo = create_join_clause(root, cur_ec, eq_op,
                                       cur_em, other_em,
                                       cur_ec);

            result = lappend(result, rinfo);
        }

        /*
         * If somehow we failed to create any join clauses, we might as well
         * keep scanning the ECs for another match.  But if we did make any,
         * we're done, because we don't want to return non-redundant clauses.
         */
        if (result)
            break;
    }

    return result;
}

/*
 * have_relevant_eclass_joinclause
 *      Detect whether there is an EquivalenceClass that could produce
 *      a joinclause involving the two given relations.
 *
 * This is essentially a very cut-down version of
 * generate_join_implied_equalities().  Note it's OK to occasionally say "yes"
 * incorrectly.  Hence we don't bother with details like whether the lack of a
 * cross-type operator might prevent the clause from actually being generated.
 */
bool
have_relevant_eclass_joinclause(PlannerInfo *root,
                                RelOptInfo *rel1, RelOptInfo *rel2)
{
    ListCell   *lc1;

    foreach(lc1, root->eq_classes)
    {
        EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc1);

        /*
         * Won't generate joinclauses if single-member (this test covers the
         * volatile case too)
         */
        if (list_length(ec->ec_members) <= 1)
            continue;

        /*
         * We do not need to examine the individual members of the EC, because
         * all that we care about is whether each rel overlaps the relids of
         * at least one member, and a test on ec_relids is sufficient to prove
         * that.  (As with have_relevant_joinclause(), it is not necessary
         * that the EC be able to form a joinclause relating exactly the two
         * given rels, only that it be able to form a joinclause mentioning
         * both, and this will surely be true if both of them overlap
         * ec_relids.)
         *
         * Note we don't test ec_broken; if we did, we'd need a separate code
         * path to look through ec_sources.  Checking the membership anyway is
         * OK as a possibly-overoptimistic heuristic.
         *
         * We don't test ec_has_const either, even though a const eclass won't
         * generate real join clauses.  This is because if we had "WHERE a.x =
         * b.y and a.x = 42", it is worth considering a join between a and b,
         * since the join result is likely to be small even though it'll end
         * up being an unqualified nestloop.
         */
        if (bms_overlap(rel1->relids, ec->ec_relids) &&
            bms_overlap(rel2->relids, ec->ec_relids))
            return true;
    }

    return false;
}


/*
 * has_relevant_eclass_joinclause
 *      Detect whether there is an EquivalenceClass that could produce
 *      a joinclause involving the given relation and anything else.
 *
 * This is the same as have_relevant_eclass_joinclause with the other rel
 * implicitly defined as "everything else in the query".
 */
bool
has_relevant_eclass_joinclause(PlannerInfo *root, RelOptInfo *rel1)
{
    ListCell   *lc1;

    foreach(lc1, root->eq_classes)
    {
        EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc1);

        /*
         * Won't generate joinclauses if single-member (this test covers the
         * volatile case too)
         */
        if (list_length(ec->ec_members) <= 1)
            continue;

        /*
         * Per the comment in have_relevant_eclass_joinclause, it's sufficient
         * to find an EC that mentions both this rel and some other rel.
         */
        if (bms_overlap(rel1->relids, ec->ec_relids) &&
            !bms_is_subset(ec->ec_relids, rel1->relids))
            return true;
    }

    return false;
}


/*
 * eclass_useful_for_merging
 *    Detect whether the EC could produce any mergejoinable join clauses
 *    against the specified relation.
 *
 * This is just a heuristic test and doesn't have to be exact; it's better
 * to say "yes" incorrectly than "no".  Hence we don't bother with details
 * like whether the lack of a cross-type operator might prevent the clause
 * from actually being generated.
 */
bool
eclass_useful_for_merging(PlannerInfo *root,
                          EquivalenceClass *eclass,
                          RelOptInfo *rel)
{
    Relids      relids;
    ListCell   *lc;

    Assert(!eclass->ec_merged);

    /*
     * Won't generate joinclauses if const or single-member (the latter test
     * covers the volatile case too)
     */
    if (eclass->ec_has_const || list_length(eclass->ec_members) <= 1)
        return false;

    /*
     * Note we don't test ec_broken; if we did, we'd need a separate code path
     * to look through ec_sources.  Checking the members anyway is OK as a
     * possibly-overoptimistic heuristic.
     */

    /* If specified rel is a child, we must consider the topmost parent rel */
    if (IS_OTHER_REL(rel))
    {
        Assert(!bms_is_empty(rel->top_parent_relids));
        relids = rel->top_parent_relids;
    }
    else
        relids = rel->relids;

    /* If rel already includes all members of eclass, no point in searching */
    if (bms_is_subset(eclass->ec_relids, relids))
        return false;

    /* To join, we need a member not in the given rel */
    foreach(lc, eclass->ec_members)
    {
        EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);

        if (cur_em->em_is_child)
            continue;           /* ignore children here */

        if (!bms_overlap(cur_em->em_relids, relids))
            return true;
    }

    return false;
}


/*
 * is_redundant_derived_clause
 *      Test whether rinfo is derived from same EC as any clause in clauselist;
 *      if so, it can be presumed to represent a condition that's redundant
 *      with that member of the list.
 */
bool
is_redundant_derived_clause(RestrictInfo *rinfo, List *clauselist)
{
    EquivalenceClass *parent_ec = rinfo->parent_ec;
    ListCell   *lc;

    /* Fail if it's not a potentially-redundant clause from some EC */
    if (parent_ec == NULL)
        return false;

    foreach(lc, clauselist)
    {
        RestrictInfo *otherrinfo = (RestrictInfo *) lfirst(lc);

        if (otherrinfo->parent_ec == parent_ec)
            return true;
    }

    return false;
}