*
*
* IDENTIFICATION
- * $PostgreSQL: pgsql/src/backend/optimizer/util/predtest.c,v 1.1 2005/06/10 22:25:36 tgl Exp $
+ * $PostgreSQL: pgsql/src/backend/optimizer/util/predtest.c,v 1.2 2005/07/23 21:05:47 tgl Exp $
*
*-------------------------------------------------------------------------
*/
static bool predicate_implied_by_recurse(Node *clause, Node *predicate);
+static bool predicate_refuted_by_recurse(Node *clause, Node *predicate);
static bool predicate_implied_by_simple_clause(Expr *predicate, Node *clause);
+static bool predicate_refuted_by_simple_clause(Expr *predicate, Node *clause);
+static bool btree_predicate_proof(Expr *predicate, Node *clause,
+ bool refute_it);
/*
* Recursively checks whether the clauses in restrictinfo_list imply
* that the given predicate is true.
*
- * The top-level List structure of each list corresponds to an AND list.
- * We assume that eval_const_expressions() has been applied and so there
- * are no un-flattened ANDs or ORs (e.g., no AND immediately within an AND,
- * including AND just below the top-level List structure).
- * If this is not true we might fail to prove an implication that is
- * valid, but no worse consequences will ensue.
+ * The top-level List structure of each list corresponds to an AND list.
+ * We assume that eval_const_expressions() has been applied and so there
+ * are no un-flattened ANDs or ORs (e.g., no AND immediately within an AND,
+ * including AND just below the top-level List structure).
+ * If this is not true we might fail to prove an implication that is
+ * valid, but no worse consequences will ensue.
+ *
+ * We assume the predicate has already been checked to contain only
+ * immutable functions and operators. (In current use this is true
+ * because the predicate is part of an index predicate that has passed
+ * CheckPredicate().) We dare not make deductions based on non-immutable
+ * functions, because they might change answers between the time we make
+ * the plan and the time we execute the plan.
*/
bool
predicate_implied_by(List *predicate_list, List *restrictinfo_list)
return true;
}
+/*
+ * predicate_refuted_by
+ * Recursively checks whether the clauses in restrictinfo_list refute
+ * the given predicate (that is, prove it false).
+ *
+ * This is NOT the same as !(predicate_implied_by), though it is similar
+ * in the technique and structure of the code.
+ *
+ * The top-level List structure of each list corresponds to an AND list.
+ * We assume that eval_const_expressions() has been applied and so there
+ * are no un-flattened ANDs or ORs (e.g., no AND immediately within an AND,
+ * including AND just below the top-level List structure).
+ * If this is not true we might fail to prove an implication that is
+ * valid, but no worse consequences will ensue.
+ *
+ * We assume the predicate has already been checked to contain only
+ * immutable functions and operators. We dare not make deductions based on
+ * non-immutable functions, because they might change answers between the
+ * time we make the plan and the time we execute the plan.
+ */
+bool
+predicate_refuted_by(List *predicate_list, List *restrictinfo_list)
+{
+ if (predicate_list == NIL)
+ return false; /* no predicate: no refutation is possible */
+ if (restrictinfo_list == NIL)
+ return false; /* no restriction: refutation must fail */
+
+ /*
+ * Unlike the implication case, predicate_refuted_by_recurse needs to
+ * be able to see the top-level AND structure on both sides --- otherwise
+ * it will fail to handle the case where one restriction clause is an OR
+ * that can refute the predicate AND as a whole, but not each predicate
+ * clause separately.
+ */
+ return predicate_refuted_by_recurse((Node *) restrictinfo_list,
+ (Node *) predicate_list);
+}
/*----------
* predicate_implied_by_recurse
}
}
+/*----------
+ * predicate_refuted_by_recurse
+ * Does the predicate refutation test for non-NULL restriction and
+ * predicate clauses.
+ *
+ * The logic followed here is ("R=>" means "refutes"):
+ * atom A R=> atom B iff: predicate_refuted_by_simple_clause says so
+ * atom A R=> AND-expr B iff: A R=> any of B's components
+ * atom A R=> OR-expr B iff: A R=> each of B's components
+ * AND-expr A R=> atom B iff: any of A's components R=> B
+ * AND-expr A R=> AND-expr B iff: A R=> any of B's components,
+ * *or* any of A's components R=> B
+ * AND-expr A R=> OR-expr B iff: A R=> each of B's components
+ * OR-expr A R=> atom B iff: each of A's components R=> B
+ * OR-expr A R=> AND-expr B iff: each of A's components R=> any of B's
+ * OR-expr A R=> OR-expr B iff: A R=> each of B's components
+ *
+ * Other comments are as for predicate_implied_by_recurse(), except that
+ * we have to handle a top-level AND list on both sides.
+ *----------
+ */
+static bool
+predicate_refuted_by_recurse(Node *clause, Node *predicate)
+{
+ ListCell *item;
+
+ Assert(clause != NULL);
+ /* skip through RestrictInfo */
+ if (IsA(clause, RestrictInfo))
+ {
+ clause = (Node *) ((RestrictInfo *) clause)->clause;
+ Assert(clause != NULL);
+ Assert(!IsA(clause, RestrictInfo));
+ }
+ Assert(predicate != NULL);
+
+ /*
+ * Since a restriction List clause is handled the same as an AND clause,
+ * we can avoid duplicate code like this:
+ */
+ if (and_clause(clause))
+ clause = (Node *) ((BoolExpr *) clause)->args;
+
+ /* Ditto for predicate AND-clause and List */
+ if (and_clause(predicate))
+ predicate = (Node *) ((BoolExpr *) predicate)->args;
+
+ if (IsA(clause, List))
+ {
+ if (IsA(predicate, List))
+ {
+ /* AND-clause R=> AND-clause if A refutes any of B's items */
+ /* Needed to handle (x AND y) R=> ((!x OR !y) AND z) */
+ foreach(item, (List *) predicate)
+ {
+ if (predicate_refuted_by_recurse(clause, lfirst(item)))
+ return true;
+ }
+ /* Also check if any of A's items refutes B */
+ /* Needed to handle ((x OR y) AND z) R=> (!x AND !y) */
+ foreach(item, (List *) clause)
+ {
+ if (predicate_refuted_by_recurse(lfirst(item), predicate))
+ return true;
+ }
+ return false;
+ }
+ else if (or_clause(predicate))
+ {
+ /* AND-clause R=> OR-clause if A refutes each of B's items */
+ foreach(item, ((BoolExpr *) predicate)->args)
+ {
+ if (!predicate_refuted_by_recurse(clause, lfirst(item)))
+ return false;
+ }
+ return true;
+ }
+ else
+ {
+ /* AND-clause R=> atom if any of A's items refutes B */
+ foreach(item, (List *) clause)
+ {
+ if (predicate_refuted_by_recurse(lfirst(item), predicate))
+ return true;
+ }
+ return false;
+ }
+ }
+ else if (or_clause(clause))
+ {
+ if (or_clause(predicate))
+ {
+ /* OR-clause R=> OR-clause if A refutes each of B's items */
+ foreach(item, ((BoolExpr *) predicate)->args)
+ {
+ if (!predicate_refuted_by_recurse(clause, lfirst(item)))
+ return false;
+ }
+ return true;
+ }
+ else if (IsA(predicate, List))
+ {
+ /*
+ * OR-clause R=> AND-clause if each of A's items refutes any of
+ * B's items.
+ */
+ foreach(item, ((BoolExpr *) clause)->args)
+ {
+ Node *citem = lfirst(item);
+ ListCell *item2;
+
+ foreach(item2, (List *) predicate)
+ {
+ if (predicate_refuted_by_recurse(citem, lfirst(item2)))
+ break;
+ }
+ if (item2 == NULL)
+ return false; /* citem refutes nothing */
+ }
+ return true;
+ }
+ else
+ {
+ /* OR-clause R=> atom if each of A's items refutes B */
+ foreach(item, ((BoolExpr *) clause)->args)
+ {
+ if (!predicate_refuted_by_recurse(lfirst(item), predicate))
+ return false;
+ }
+ return true;
+ }
+ }
+ else
+ {
+ if (IsA(predicate, List))
+ {
+ /* atom R=> AND-clause if A refutes any of B's items */
+ foreach(item, (List *) predicate)
+ {
+ if (predicate_refuted_by_recurse(clause, lfirst(item)))
+ return true;
+ }
+ return false;
+ }
+ else if (or_clause(predicate))
+ {
+ /* atom R=> OR-clause if A refutes each of B's items */
+ foreach(item, ((BoolExpr *) predicate)->args)
+ {
+ if (!predicate_refuted_by_recurse(clause, lfirst(item)))
+ return false;
+ }
+ return true;
+ }
+ else
+ {
+ /* atom R=> atom is the base case */
+ return predicate_refuted_by_simple_clause((Expr *) predicate,
+ clause);
+ }
+ }
+}
+
+
+/*----------
+ * predicate_implied_by_simple_clause
+ * Does the predicate implication test for a "simple clause" predicate
+ * and a "simple clause" restriction.
+ *
+ * We return TRUE if able to prove the implication, FALSE if not.
+ *
+ * We have three strategies for determining whether one simple clause
+ * implies another:
+ *
+ * A simple and general way is to see if they are equal(); this works for any
+ * kind of expression. (Actually, there is an implied assumption that the
+ * functions in the expression are immutable, ie dependent only on their input
+ * arguments --- but this was checked for the predicate by the caller.)
+ *
+ * When the predicate is of the form "foo IS NOT NULL", we can conclude that
+ * the predicate is implied if the clause is a strict operator or function
+ * that has "foo" as an input. In this case the clause must yield NULL when
+ * "foo" is NULL, which we can take as equivalent to FALSE because we know
+ * we are within an AND/OR subtree of a WHERE clause. (Again, "foo" is
+ * already known immutable, so the clause will certainly always fail.)
+ *
+ * Finally, we may be able to deduce something using knowledge about btree
+ * operator classes; this is encapsulated in btree_predicate_proof().
+ *----------
+ */
+static bool
+predicate_implied_by_simple_clause(Expr *predicate, Node *clause)
+{
+ /* First try the equal() test */
+ if (equal((Node *) predicate, clause))
+ return true;
+
+ /* Next try the IS NOT NULL case */
+ if (predicate && IsA(predicate, NullTest) &&
+ ((NullTest *) predicate)->nulltesttype == IS_NOT_NULL)
+ {
+ Expr *nonnullarg = ((NullTest *) predicate)->arg;
+
+ if (is_opclause(clause) &&
+ list_member(((OpExpr *) clause)->args, nonnullarg) &&
+ op_strict(((OpExpr *) clause)->opno))
+ return true;
+ if (is_funcclause(clause) &&
+ list_member(((FuncExpr *) clause)->args, nonnullarg) &&
+ func_strict(((FuncExpr *) clause)->funcid))
+ return true;
+ return false; /* we can't succeed below... */
+ }
+
+ /* Else try btree operator knowledge */
+ return btree_predicate_proof(predicate, clause, false);
+}
+
+/*----------
+ * predicate_refuted_by_simple_clause
+ * Does the predicate refutation test for a "simple clause" predicate
+ * and a "simple clause" restriction.
+ *
+ * We return TRUE if able to prove the refutation, FALSE if not.
+ *
+ * Unlike the implication case, checking for equal() clauses isn't
+ * helpful. (XXX is it worth looking at "x vs NOT x" cases? Probably
+ * not seeing that canonicalization tries to get rid of NOTs.)
+ *
+ * When the predicate is of the form "foo IS NULL", we can conclude that
+ * the predicate is refuted if the clause is a strict operator or function
+ * that has "foo" as an input. See notes for implication case.
+ *
+ * Finally, we may be able to deduce something using knowledge about btree
+ * operator classes; this is encapsulated in btree_predicate_proof().
+ *----------
+ */
+static bool
+predicate_refuted_by_simple_clause(Expr *predicate, Node *clause)
+{
+ /* First try the IS NULL case */
+ if (predicate && IsA(predicate, NullTest) &&
+ ((NullTest *) predicate)->nulltesttype == IS_NULL)
+ {
+ Expr *isnullarg = ((NullTest *) predicate)->arg;
+
+ if (is_opclause(clause) &&
+ list_member(((OpExpr *) clause)->args, isnullarg) &&
+ op_strict(((OpExpr *) clause)->opno))
+ return true;
+ if (is_funcclause(clause) &&
+ list_member(((FuncExpr *) clause)->args, isnullarg) &&
+ func_strict(((FuncExpr *) clause)->funcid))
+ return true;
+ return false; /* we can't succeed below... */
+ }
+
+ /* Else try btree operator knowledge */
+ return btree_predicate_proof(predicate, clause, true);
+}
+
/*
- * Define an "operator implication table" for btree operators ("strategies").
+ * Define an "operator implication table" for btree operators ("strategies"),
+ * and a similar table for refutation.
*
* The strategy numbers defined by btree indexes (see access/skey.h) are:
* (1) < (2) <= (3) = (4) >= (5) >
* then the target expression must be true; if the test returns false, then
* the target expression may be false.
*
- * An entry where test_op == 0 means the implication cannot be determined,
- * i.e., this test should always be considered false.
+ * For example, if clause is "Quantity > 10" and pred is "Quantity > 5"
+ * then we test "5 <= 10" which evals to true, so clause implies pred.
+ *
+ * Similarly, the interpretation of a BT_refute_table entry is:
+ *
+ * If you know, for some ATTR, that "ATTR given_op CONST1" is true, and you
+ * want to determine whether "ATTR target_op CONST2" must be false, then
+ * you can use "CONST2 test_op CONST1" as a test. If this test returns true,
+ * then the target expression must be false; if the test returns false, then
+ * the target expression may be true.
+ *
+ * For example, if clause is "Quantity > 10" and pred is "Quantity < 5"
+ * then we test "5 <= 10" which evals to true, so clause refutes pred.
+ *
+ * An entry where test_op == 0 means the implication cannot be determined.
*/
#define BTLT BTLessStrategyNumber
#define BTGT BTGreaterStrategyNumber
#define BTNE 6
-static const StrategyNumber
- BT_implic_table[6][6] = {
+static const StrategyNumber BT_implic_table[6][6] = {
/*
* The target operator:
*
- * LT LE EQ GE GT NE
+ * LT LE EQ GE GT NE
*/
- {BTGE, BTGE, 0, 0, 0, BTGE}, /* LT */
- {BTGT, BTGE, 0, 0, 0, BTGT}, /* LE */
+ {BTGE, BTGE, 0 , 0 , 0 , BTGE}, /* LT */
+ {BTGT, BTGE, 0 , 0 , 0 , BTGT}, /* LE */
{BTGT, BTGE, BTEQ, BTLE, BTLT, BTNE}, /* EQ */
- {0, 0, 0, BTLE, BTLT, BTLT}, /* GE */
- {0, 0, 0, BTLE, BTLE, BTLE}, /* GT */
- {0, 0, 0, 0, 0, BTEQ} /* NE */
+ {0 , 0 , 0 , BTLE, BTLT, BTLT}, /* GE */
+ {0 , 0 , 0 , BTLE, BTLE, BTLE}, /* GT */
+ {0 , 0 , 0 , 0 , 0 , BTEQ} /* NE */
+};
+
+static const StrategyNumber BT_refute_table[6][6] = {
+/*
+ * The target operator:
+ *
+ * LT LE EQ GE GT NE
+ */
+ {0 , 0 , BTGE, BTGE, BTGE, 0 }, /* LT */
+ {0 , 0 , BTGT, BTGT, BTGE, 0 }, /* LE */
+ {BTLE, BTLT, BTNE, BTGT, BTGE, BTEQ}, /* EQ */
+ {BTLE, BTLT, BTLT, 0 , 0 , 0 }, /* GE */
+ {BTLE, BTLE, BTLE, 0 , 0 , 0 }, /* GT */
+ {0 , 0 , BTEQ, 0 , 0 , 0 } /* NE */
};
/*----------
- * predicate_implied_by_simple_clause
- * Does the predicate implication test for a "simple clause" predicate
- * and a "simple clause" restriction.
+ * btree_predicate_proof
+ * Does the predicate implication or refutation test for a "simple clause"
+ * predicate and a "simple clause" restriction, when both are simple
+ * operator clauses using related btree operators.
*
- * We have three strategies for determining whether one simple clause
- * implies another:
- *
- * A simple and general way is to see if they are equal(); this works for any
- * kind of expression. (Actually, there is an implied assumption that the
- * functions in the expression are immutable, ie dependent only on their input
- * arguments --- but this was checked for the predicate by CheckPredicate().)
+ * When refute_it == false, we want to prove the predicate true;
+ * when refute_it == true, we want to prove the predicate false.
+ * (There is enough common code to justify handling these two cases
+ * in one routine.) We return TRUE if able to make the proof, FALSE
+ * if not able to prove it.
*
- * When the predicate is of the form "foo IS NOT NULL", we can conclude that
- * the predicate is implied if the clause is a strict operator or function
- * that has "foo" as an input. In this case the clause must yield NULL when
- * "foo" is NULL, which we can take as equivalent to FALSE because we know
- * we are within an AND/OR subtree of a WHERE clause. (Again, "foo" is
- * already known immutable, so the clause will certainly always fail.)
- *
- * Our other way works only for binary boolean opclauses of the form
+ * What we look for here is binary boolean opclauses of the form
* "foo op constant", where "foo" is the same in both clauses. The operators
* and constants can be different but the operators must be in the same btree
- * operator class. We use the above operator implication table to be able to
+ * operator class. We use the above operator implication tables to
* derive implications between nonidentical clauses. (Note: "foo" is known
* immutable, and constants are surely immutable, but we have to check that
* the operators are too. As of 8.0 it's possible for opclasses to contain
* operators that are merely stable, and we dare not make deductions with
* these.)
- *
- * Eventually, rtree operators could also be handled by defining an
- * appropriate "RT_implic_table" array.
*----------
*/
static bool
-predicate_implied_by_simple_clause(Expr *predicate, Node *clause)
+btree_predicate_proof(Expr *predicate, Node *clause, bool refute_it)
{
Node *leftop,
*rightop;
EState *estate;
MemoryContext oldcontext;
- /* First try the equal() test */
- if (equal((Node *) predicate, clause))
- return true;
-
- /* Next try the IS NOT NULL case */
- if (predicate && IsA(predicate, NullTest) &&
- ((NullTest *) predicate)->nulltesttype == IS_NOT_NULL)
- {
- Expr *nonnullarg = ((NullTest *) predicate)->arg;
-
- if (is_opclause(clause) &&
- list_member(((OpExpr *) clause)->args, nonnullarg) &&
- op_strict(((OpExpr *) clause)->opno))
- return true;
- if (is_funcclause(clause) &&
- list_member(((FuncExpr *) clause)->args, nonnullarg) &&
- func_strict(((FuncExpr *) clause)->funcid))
- return true;
- return false; /* we can't succeed below... */
- }
-
/*
- * Can't do anything more unless they are both binary opclauses with a
+ * Both expressions must be binary opclauses with a
* Const on one side, and identical subexpressions on the other sides.
* Note we don't have to think about binary relabeling of the Const
* node, since that would have been folded right into the Const.
/*
* Look up the "test" strategy number in the implication table
*/
- test_strategy = BT_implic_table[clause_strategy - 1][pred_strategy - 1];
+ if (refute_it)
+ test_strategy = BT_refute_table[clause_strategy - 1][pred_strategy - 1];
+ else
+ test_strategy = BT_implic_table[clause_strategy - 1][pred_strategy - 1];
+
if (test_strategy == 0)
{
/* Can't determine implication using this interpretation */
* Last check: test_op must be immutable.
*
* Note that we require only the test_op to be immutable, not the
- * original clause_op. (pred_op must be immutable, else it
- * would not be allowed in an index predicate.) Essentially
- * we are assuming that the opclass is consistent even if it
- * contains operators that are merely stable.
- *
- * XXX the above reasoning doesn't hold anymore if this routine
- * is used to prove things that are not index predicates ...
+ * original clause_op. (pred_op is assumed to have been checked
+ * immutable by the caller.) Essentially we are assuming that
+ * the opclass is consistent even if it contains operators that
+ * are merely stable.
*/
if (op_volatile(test_op) == PROVOLATILE_IMMUTABLE)
{
if (isNull)
{
- /* Treat a null result as false ... but it's a tad fishy ... */
+ /* Treat a null result as non-proof ... but it's a tad fishy ... */
elog(DEBUG2, "null predicate test result");
return false;
}
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