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Diffstat (limited to 'src/backend/optimizer/util/predtest.c')
| -rw-r--r-- | src/backend/optimizer/util/predtest.c | 2224 |
1 files changed, 2224 insertions, 0 deletions
diff --git a/src/backend/optimizer/util/predtest.c b/src/backend/optimizer/util/predtest.c new file mode 100644 index 0000000..182d5b1 --- /dev/null +++ b/src/backend/optimizer/util/predtest.c @@ -0,0 +1,2224 @@ +/*------------------------------------------------------------------------- + * + * predtest.c + * Routines to attempt to prove logical implications between predicate + * expressions. + * + * Portions Copyright (c) 1996-2022, PostgreSQL Global Development Group + * Portions Copyright (c) 1994, Regents of the University of California + * + * + * IDENTIFICATION + * src/backend/optimizer/util/predtest.c + * + *------------------------------------------------------------------------- + */ +#include "postgres.h" + +#include "catalog/pg_proc.h" +#include "catalog/pg_type.h" +#include "executor/executor.h" +#include "miscadmin.h" +#include "nodes/makefuncs.h" +#include "nodes/nodeFuncs.h" +#include "nodes/pathnodes.h" +#include "optimizer/optimizer.h" +#include "utils/array.h" +#include "utils/inval.h" +#include "utils/lsyscache.h" +#include "utils/syscache.h" + + +/* + * Proof attempts involving large arrays in ScalarArrayOpExpr nodes are + * likely to require O(N^2) time, and more often than not fail anyway. + * So we set an arbitrary limit on the number of array elements that + * we will allow to be treated as an AND or OR clause. + * XXX is it worth exposing this as a GUC knob? + */ +#define MAX_SAOP_ARRAY_SIZE 100 + +/* + * To avoid redundant coding in predicate_implied_by_recurse and + * predicate_refuted_by_recurse, we need to abstract out the notion of + * iterating over the components of an expression that is logically an AND + * or OR structure. There are multiple sorts of expression nodes that can + * be treated as ANDs or ORs, and we don't want to code each one separately. + * Hence, these types and support routines. + */ +typedef enum +{ + CLASS_ATOM, /* expression that's not AND or OR */ + CLASS_AND, /* expression with AND semantics */ + CLASS_OR /* expression with OR semantics */ +} PredClass; + +typedef struct PredIterInfoData *PredIterInfo; + +typedef struct PredIterInfoData +{ + /* node-type-specific iteration state */ + void *state; + List *state_list; + /* initialize to do the iteration */ + void (*startup_fn) (Node *clause, PredIterInfo info); + /* next-component iteration function */ + Node *(*next_fn) (PredIterInfo info); + /* release resources when done with iteration */ + void (*cleanup_fn) (PredIterInfo info); +} PredIterInfoData; + +#define iterate_begin(item, clause, info) \ + do { \ + Node *item; \ + (info).startup_fn((clause), &(info)); \ + while ((item = (info).next_fn(&(info))) != NULL) + +#define iterate_end(info) \ + (info).cleanup_fn(&(info)); \ + } while (0) + + +static bool predicate_implied_by_recurse(Node *clause, Node *predicate, + bool weak); +static bool predicate_refuted_by_recurse(Node *clause, Node *predicate, + bool weak); +static PredClass predicate_classify(Node *clause, PredIterInfo info); +static void list_startup_fn(Node *clause, PredIterInfo info); +static Node *list_next_fn(PredIterInfo info); +static void list_cleanup_fn(PredIterInfo info); +static void boolexpr_startup_fn(Node *clause, PredIterInfo info); +static void arrayconst_startup_fn(Node *clause, PredIterInfo info); +static Node *arrayconst_next_fn(PredIterInfo info); +static void arrayconst_cleanup_fn(PredIterInfo info); +static void arrayexpr_startup_fn(Node *clause, PredIterInfo info); +static Node *arrayexpr_next_fn(PredIterInfo info); +static void arrayexpr_cleanup_fn(PredIterInfo info); +static bool predicate_implied_by_simple_clause(Expr *predicate, Node *clause, + bool weak); +static bool predicate_refuted_by_simple_clause(Expr *predicate, Node *clause, + bool weak); +static Node *extract_not_arg(Node *clause); +static Node *extract_strong_not_arg(Node *clause); +static bool clause_is_strict_for(Node *clause, Node *subexpr, bool allow_false); +static bool operator_predicate_proof(Expr *predicate, Node *clause, + bool refute_it, bool weak); +static bool operator_same_subexprs_proof(Oid pred_op, Oid clause_op, + bool refute_it); +static bool operator_same_subexprs_lookup(Oid pred_op, Oid clause_op, + bool refute_it); +static Oid get_btree_test_op(Oid pred_op, Oid clause_op, bool refute_it); +static void InvalidateOprProofCacheCallBack(Datum arg, int cacheid, uint32 hashvalue); + + +/* + * predicate_implied_by + * Recursively checks whether the clauses in clause_list imply that the + * given predicate is true. + * + * We support two definitions of implication: + * + * "Strong" implication: A implies B means that truth of A implies truth of B. + * We use this to prove that a row satisfying one WHERE clause or index + * predicate must satisfy another one. + * + * "Weak" implication: A implies B means that non-falsity of A implies + * non-falsity of B ("non-false" means "either true or NULL"). We use this to + * prove that a row satisfying one CHECK constraint must satisfy another one. + * + * Strong implication can also be used to prove that a WHERE clause implies a + * CHECK constraint, although it will fail to prove a few cases where we could + * safely conclude that the implication holds. There's no support for proving + * the converse case, since only a few kinds of CHECK constraint would allow + * deducing anything. + * + * 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 many current uses this is known + * true because the predicate is part of an index predicate that has passed + * CheckPredicate(); otherwise, the caller must check it.) 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. + * Immutability of functions in the clause_list is checked here, if necessary. + */ +bool +predicate_implied_by(List *predicate_list, List *clause_list, + bool weak) +{ + Node *p, + *c; + + if (predicate_list == NIL) + return true; /* no predicate: implication is vacuous */ + if (clause_list == NIL) + return false; /* no restriction: implication must fail */ + + /* + * If either input is a single-element list, replace it with its lone + * member; this avoids one useless level of AND-recursion. We only need + * to worry about this at top level, since eval_const_expressions should + * have gotten rid of any trivial ANDs or ORs below that. + */ + if (list_length(predicate_list) == 1) + p = (Node *) linitial(predicate_list); + else + p = (Node *) predicate_list; + if (list_length(clause_list) == 1) + c = (Node *) linitial(clause_list); + else + c = (Node *) clause_list; + + /* And away we go ... */ + return predicate_implied_by_recurse(c, p, weak); +} + +/* + * predicate_refuted_by + * Recursively checks whether the clauses in clause_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. + * + * We support two definitions of refutation: + * + * "Strong" refutation: A refutes B means truth of A implies falsity of B. + * We use this to disprove a CHECK constraint given a WHERE clause, i.e., + * prove that any row satisfying the WHERE clause would violate the CHECK + * constraint. (Observe we must prove B yields false, not just not-true.) + * + * "Weak" refutation: A refutes B means truth of A implies non-truth of B + * (i.e., B must yield false or NULL). We use this to detect mutually + * contradictory WHERE clauses. + * + * Weak refutation can be proven in some cases where strong refutation doesn't + * hold, so it's useful to use it when possible. We don't currently have + * support for disproving one CHECK constraint based on another one, nor for + * disproving WHERE based on CHECK. (As with implication, the last case + * doesn't seem very practical. CHECK-vs-CHECK might be useful, but isn't + * currently needed anywhere.) + * + * 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. + * Immutability of functions in the clause_list is checked here, if necessary. + */ +bool +predicate_refuted_by(List *predicate_list, List *clause_list, + bool weak) +{ + Node *p, + *c; + + if (predicate_list == NIL) + return false; /* no predicate: no refutation is possible */ + if (clause_list == NIL) + return false; /* no restriction: refutation must fail */ + + /* + * If either input is a single-element list, replace it with its lone + * member; this avoids one useless level of AND-recursion. We only need + * to worry about this at top level, since eval_const_expressions should + * have gotten rid of any trivial ANDs or ORs below that. + */ + if (list_length(predicate_list) == 1) + p = (Node *) linitial(predicate_list); + else + p = (Node *) predicate_list; + if (list_length(clause_list) == 1) + c = (Node *) linitial(clause_list); + else + c = (Node *) clause_list; + + /* And away we go ... */ + return predicate_refuted_by_recurse(c, p, weak); +} + +/*---------- + * predicate_implied_by_recurse + * Does the predicate implication test for non-NULL restriction and + * predicate clauses. + * + * The logic followed here is ("=>" means "implies"): + * atom A => atom B iff: predicate_implied_by_simple_clause says so + * atom A => AND-expr B iff: A => each of B's components + * atom A => OR-expr B iff: A => any of B's components + * AND-expr A => atom B iff: any of A's components => B + * AND-expr A => AND-expr B iff: A => each of B's components + * AND-expr A => OR-expr B iff: A => any of B's components, + * *or* any of A's components => B + * OR-expr A => atom B iff: each of A's components => B + * OR-expr A => AND-expr B iff: A => each of B's components + * OR-expr A => OR-expr B iff: each of A's components => any of B's + * + * An "atom" is anything other than an AND or OR node. Notice that we don't + * have any special logic to handle NOT nodes; these should have been pushed + * down or eliminated where feasible during eval_const_expressions(). + * + * All of these rules apply equally to strong or weak implication. + * + * We can't recursively expand either side first, but have to interleave + * the expansions per the above rules, to be sure we handle all of these + * examples: + * (x OR y) => (x OR y OR z) + * (x AND y AND z) => (x AND y) + * (x AND y) => ((x AND y) OR z) + * ((x OR y) AND z) => (x OR y) + * This is still not an exhaustive test, but it handles most normal cases + * under the assumption that both inputs have been AND/OR flattened. + * + * We have to be prepared to handle RestrictInfo nodes in the restrictinfo + * tree, though not in the predicate tree. + *---------- + */ +static bool +predicate_implied_by_recurse(Node *clause, Node *predicate, + bool weak) +{ + PredIterInfoData clause_info; + PredIterInfoData pred_info; + PredClass pclass; + bool result; + + /* skip through RestrictInfo */ + Assert(clause != NULL); + if (IsA(clause, RestrictInfo)) + clause = (Node *) ((RestrictInfo *) clause)->clause; + + pclass = predicate_classify(predicate, &pred_info); + + switch (predicate_classify(clause, &clause_info)) + { + case CLASS_AND: + switch (pclass) + { + case CLASS_AND: + + /* + * AND-clause => AND-clause if A implies each of B's items + */ + result = true; + iterate_begin(pitem, predicate, pred_info) + { + if (!predicate_implied_by_recurse(clause, pitem, + weak)) + { + result = false; + break; + } + } + iterate_end(pred_info); + return result; + + case CLASS_OR: + + /* + * AND-clause => OR-clause if A implies any of B's items + * + * Needed to handle (x AND y) => ((x AND y) OR z) + */ + result = false; + iterate_begin(pitem, predicate, pred_info) + { + if (predicate_implied_by_recurse(clause, pitem, + weak)) + { + result = true; + break; + } + } + iterate_end(pred_info); + if (result) + return result; + + /* + * Also check if any of A's items implies B + * + * Needed to handle ((x OR y) AND z) => (x OR y) + */ + iterate_begin(citem, clause, clause_info) + { + if (predicate_implied_by_recurse(citem, predicate, + weak)) + { + result = true; + break; + } + } + iterate_end(clause_info); + return result; + + case CLASS_ATOM: + + /* + * AND-clause => atom if any of A's items implies B + */ + result = false; + iterate_begin(citem, clause, clause_info) + { + if (predicate_implied_by_recurse(citem, predicate, + weak)) + { + result = true; + break; + } + } + iterate_end(clause_info); + return result; + } + break; + + case CLASS_OR: + switch (pclass) + { + case CLASS_OR: + + /* + * OR-clause => OR-clause if each of A's items implies any + * of B's items. Messy but can't do it any more simply. + */ + result = true; + iterate_begin(citem, clause, clause_info) + { + bool presult = false; + + iterate_begin(pitem, predicate, pred_info) + { + if (predicate_implied_by_recurse(citem, pitem, + weak)) + { + presult = true; + break; + } + } + iterate_end(pred_info); + if (!presult) + { + result = false; /* doesn't imply any of B's */ + break; + } + } + iterate_end(clause_info); + return result; + + case CLASS_AND: + case CLASS_ATOM: + + /* + * OR-clause => AND-clause if each of A's items implies B + * + * OR-clause => atom if each of A's items implies B + */ + result = true; + iterate_begin(citem, clause, clause_info) + { + if (!predicate_implied_by_recurse(citem, predicate, + weak)) + { + result = false; + break; + } + } + iterate_end(clause_info); + return result; + } + break; + + case CLASS_ATOM: + switch (pclass) + { + case CLASS_AND: + + /* + * atom => AND-clause if A implies each of B's items + */ + result = true; + iterate_begin(pitem, predicate, pred_info) + { + if (!predicate_implied_by_recurse(clause, pitem, + weak)) + { + result = false; + break; + } + } + iterate_end(pred_info); + return result; + + case CLASS_OR: + + /* + * atom => OR-clause if A implies any of B's items + */ + result = false; + iterate_begin(pitem, predicate, pred_info) + { + if (predicate_implied_by_recurse(clause, pitem, + weak)) + { + result = true; + break; + } + } + iterate_end(pred_info); + return result; + + case CLASS_ATOM: + + /* + * atom => atom is the base case + */ + return + predicate_implied_by_simple_clause((Expr *) predicate, + clause, + weak); + } + break; + } + + /* can't get here */ + elog(ERROR, "predicate_classify returned a bogus value"); + return false; +} + +/*---------- + * 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 + * + * All of the above rules apply equally to strong or weak refutation. + * + * In addition, if the predicate is a NOT-clause then we can use + * A R=> NOT B if: A => B + * This works for several different SQL constructs that assert the non-truth + * of their argument, ie NOT, IS FALSE, IS NOT TRUE, IS UNKNOWN, although some + * of them require that we prove strong implication. Likewise, we can use + * NOT A R=> B if: B => A + * but here we must be careful about strong vs. weak refutation and make + * the appropriate type of implication proof (weak or strong respectively). + * + * Other comments are as for predicate_implied_by_recurse(). + *---------- + */ +static bool +predicate_refuted_by_recurse(Node *clause, Node *predicate, + bool weak) +{ + PredIterInfoData clause_info; + PredIterInfoData pred_info; + PredClass pclass; + Node *not_arg; + bool result; + + /* skip through RestrictInfo */ + Assert(clause != NULL); + if (IsA(clause, RestrictInfo)) + clause = (Node *) ((RestrictInfo *) clause)->clause; + + pclass = predicate_classify(predicate, &pred_info); + + switch (predicate_classify(clause, &clause_info)) + { + case CLASS_AND: + switch (pclass) + { + case CLASS_AND: + + /* + * 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) + */ + result = false; + iterate_begin(pitem, predicate, pred_info) + { + if (predicate_refuted_by_recurse(clause, pitem, + weak)) + { + result = true; + break; + } + } + iterate_end(pred_info); + if (result) + return result; + + /* + * Also check if any of A's items refutes B + * + * Needed to handle ((x OR y) AND z) R=> (!x AND !y) + */ + iterate_begin(citem, clause, clause_info) + { + if (predicate_refuted_by_recurse(citem, predicate, + weak)) + { + result = true; + break; + } + } + iterate_end(clause_info); + return result; + + case CLASS_OR: + + /* + * AND-clause R=> OR-clause if A refutes each of B's items + */ + result = true; + iterate_begin(pitem, predicate, pred_info) + { + if (!predicate_refuted_by_recurse(clause, pitem, + weak)) + { + result = false; + break; + } + } + iterate_end(pred_info); + return result; + + case CLASS_ATOM: + + /* + * If B is a NOT-type clause, A R=> B if A => B's arg + * + * Since, for either type of refutation, we are starting + * with the premise that A is true, we can use a strong + * implication test in all cases. That proves B's arg is + * true, which is more than we need for weak refutation if + * B is a simple NOT, but it allows not worrying about + * exactly which kind of negation clause we have. + */ + not_arg = extract_not_arg(predicate); + if (not_arg && + predicate_implied_by_recurse(clause, not_arg, + false)) + return true; + + /* + * AND-clause R=> atom if any of A's items refutes B + */ + result = false; + iterate_begin(citem, clause, clause_info) + { + if (predicate_refuted_by_recurse(citem, predicate, + weak)) + { + result = true; + break; + } + } + iterate_end(clause_info); + return result; + } + break; + + case CLASS_OR: + switch (pclass) + { + case CLASS_OR: + + /* + * OR-clause R=> OR-clause if A refutes each of B's items + */ + result = true; + iterate_begin(pitem, predicate, pred_info) + { + if (!predicate_refuted_by_recurse(clause, pitem, + weak)) + { + result = false; + break; + } + } + iterate_end(pred_info); + return result; + + case CLASS_AND: + + /* + * OR-clause R=> AND-clause if each of A's items refutes + * any of B's items. + */ + result = true; + iterate_begin(citem, clause, clause_info) + { + bool presult = false; + + iterate_begin(pitem, predicate, pred_info) + { + if (predicate_refuted_by_recurse(citem, pitem, + weak)) + { + presult = true; + break; + } + } + iterate_end(pred_info); + if (!presult) + { + result = false; /* citem refutes nothing */ + break; + } + } + iterate_end(clause_info); + return result; + + case CLASS_ATOM: + + /* + * If B is a NOT-type clause, A R=> B if A => B's arg + * + * Same logic as for the AND-clause case above. + */ + not_arg = extract_not_arg(predicate); + if (not_arg && + predicate_implied_by_recurse(clause, not_arg, + false)) + return true; + + /* + * OR-clause R=> atom if each of A's items refutes B + */ + result = true; + iterate_begin(citem, clause, clause_info) + { + if (!predicate_refuted_by_recurse(citem, predicate, + weak)) + { + result = false; + break; + } + } + iterate_end(clause_info); + return result; + } + break; + + case CLASS_ATOM: + + /* + * If A is a strong NOT-clause, A R=> B if B => A's arg + * + * Since A is strong, we may assume A's arg is false (not just + * not-true). If B weakly implies A's arg, then B can be neither + * true nor null, so that strong refutation is proven. If B + * strongly implies A's arg, then B cannot be true, so that weak + * refutation is proven. + */ + not_arg = extract_strong_not_arg(clause); + if (not_arg && + predicate_implied_by_recurse(predicate, not_arg, + !weak)) + return true; + + switch (pclass) + { + case CLASS_AND: + + /* + * atom R=> AND-clause if A refutes any of B's items + */ + result = false; + iterate_begin(pitem, predicate, pred_info) + { + if (predicate_refuted_by_recurse(clause, pitem, + weak)) + { + result = true; + break; + } + } + iterate_end(pred_info); + return result; + + case CLASS_OR: + + /* + * atom R=> OR-clause if A refutes each of B's items + */ + result = true; + iterate_begin(pitem, predicate, pred_info) + { + if (!predicate_refuted_by_recurse(clause, pitem, + weak)) + { + result = false; + break; + } + } + iterate_end(pred_info); + return result; + + case CLASS_ATOM: + + /* + * If B is a NOT-type clause, A R=> B if A => B's arg + * + * Same logic as for the AND-clause case above. + */ + not_arg = extract_not_arg(predicate); + if (not_arg && + predicate_implied_by_recurse(clause, not_arg, + false)) + return true; + + /* + * atom R=> atom is the base case + */ + return + predicate_refuted_by_simple_clause((Expr *) predicate, + clause, + weak); + } + break; + } + + /* can't get here */ + elog(ERROR, "predicate_classify returned a bogus value"); + return false; +} + + +/* + * predicate_classify + * Classify an expression node as AND-type, OR-type, or neither (an atom). + * + * If the expression is classified as AND- or OR-type, then *info is filled + * in with the functions needed to iterate over its components. + * + * This function also implements enforcement of MAX_SAOP_ARRAY_SIZE: if a + * ScalarArrayOpExpr's array has too many elements, we just classify it as an + * atom. (This will result in its being passed as-is to the simple_clause + * functions, many of which will fail to prove anything about it.) Note that we + * cannot just stop after considering MAX_SAOP_ARRAY_SIZE elements; in general + * that would result in wrong proofs, rather than failing to prove anything. + */ +static PredClass +predicate_classify(Node *clause, PredIterInfo info) +{ + /* Caller should not pass us NULL, nor a RestrictInfo clause */ + Assert(clause != NULL); + Assert(!IsA(clause, RestrictInfo)); + + /* + * If we see a List, assume it's an implicit-AND list; this is the correct + * semantics for lists of RestrictInfo nodes. + */ + if (IsA(clause, List)) + { + info->startup_fn = list_startup_fn; + info->next_fn = list_next_fn; + info->cleanup_fn = list_cleanup_fn; + return CLASS_AND; + } + + /* Handle normal AND and OR boolean clauses */ + if (is_andclause(clause)) + { + info->startup_fn = boolexpr_startup_fn; + info->next_fn = list_next_fn; + info->cleanup_fn = list_cleanup_fn; + return CLASS_AND; + } + if (is_orclause(clause)) + { + info->startup_fn = boolexpr_startup_fn; + info->next_fn = list_next_fn; + info->cleanup_fn = list_cleanup_fn; + return CLASS_OR; + } + + /* Handle ScalarArrayOpExpr */ + if (IsA(clause, ScalarArrayOpExpr)) + { + ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause; + Node *arraynode = (Node *) lsecond(saop->args); + + /* + * We can break this down into an AND or OR structure, but only if we + * know how to iterate through expressions for the array's elements. + * We can do that if the array operand is a non-null constant or a + * simple ArrayExpr. + */ + if (arraynode && IsA(arraynode, Const) && + !((Const *) arraynode)->constisnull) + { + ArrayType *arrayval; + int nelems; + + arrayval = DatumGetArrayTypeP(((Const *) arraynode)->constvalue); + nelems = ArrayGetNItems(ARR_NDIM(arrayval), ARR_DIMS(arrayval)); + if (nelems <= MAX_SAOP_ARRAY_SIZE) + { + info->startup_fn = arrayconst_startup_fn; + info->next_fn = arrayconst_next_fn; + info->cleanup_fn = arrayconst_cleanup_fn; + return saop->useOr ? CLASS_OR : CLASS_AND; + } + } + else if (arraynode && IsA(arraynode, ArrayExpr) && + !((ArrayExpr *) arraynode)->multidims && + list_length(((ArrayExpr *) arraynode)->elements) <= MAX_SAOP_ARRAY_SIZE) + { + info->startup_fn = arrayexpr_startup_fn; + info->next_fn = arrayexpr_next_fn; + info->cleanup_fn = arrayexpr_cleanup_fn; + return saop->useOr ? CLASS_OR : CLASS_AND; + } + } + + /* None of the above, so it's an atom */ + return CLASS_ATOM; +} + +/* + * PredIterInfo routines for iterating over regular Lists. The iteration + * state variable is the next ListCell to visit. + */ +static void +list_startup_fn(Node *clause, PredIterInfo info) +{ + info->state_list = (List *) clause; + info->state = (void *) list_head(info->state_list); +} + +static Node * +list_next_fn(PredIterInfo info) +{ + ListCell *l = (ListCell *) info->state; + Node *n; + + if (l == NULL) + return NULL; + n = lfirst(l); + info->state = (void *) lnext(info->state_list, l); + return n; +} + +static void +list_cleanup_fn(PredIterInfo info) +{ + /* Nothing to clean up */ +} + +/* + * BoolExpr needs its own startup function, but can use list_next_fn and + * list_cleanup_fn. + */ +static void +boolexpr_startup_fn(Node *clause, PredIterInfo info) +{ + info->state_list = ((BoolExpr *) clause)->args; + info->state = (void *) list_head(info->state_list); +} + +/* + * PredIterInfo routines for iterating over a ScalarArrayOpExpr with a + * constant array operand. + */ +typedef struct +{ + OpExpr opexpr; + Const constexpr; + int next_elem; + int num_elems; + Datum *elem_values; + bool *elem_nulls; +} ArrayConstIterState; + +static void +arrayconst_startup_fn(Node *clause, PredIterInfo info) +{ + ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause; + ArrayConstIterState *state; + Const *arrayconst; + ArrayType *arrayval; + int16 elmlen; + bool elmbyval; + char elmalign; + + /* Create working state struct */ + state = (ArrayConstIterState *) palloc(sizeof(ArrayConstIterState)); + info->state = (void *) state; + + /* Deconstruct the array literal */ + arrayconst = (Const *) lsecond(saop->args); + arrayval = DatumGetArrayTypeP(arrayconst->constvalue); + get_typlenbyvalalign(ARR_ELEMTYPE(arrayval), + &elmlen, &elmbyval, &elmalign); + deconstruct_array(arrayval, + ARR_ELEMTYPE(arrayval), + elmlen, elmbyval, elmalign, + &state->elem_values, &state->elem_nulls, + &state->num_elems); + + /* Set up a dummy OpExpr to return as the per-item node */ + state->opexpr.xpr.type = T_OpExpr; + state->opexpr.opno = saop->opno; + state->opexpr.opfuncid = saop->opfuncid; + state->opexpr.opresulttype = BOOLOID; + state->opexpr.opretset = false; + state->opexpr.opcollid = InvalidOid; + state->opexpr.inputcollid = saop->inputcollid; + state->opexpr.args = list_copy(saop->args); + + /* Set up a dummy Const node to hold the per-element values */ + state->constexpr.xpr.type = T_Const; + state->constexpr.consttype = ARR_ELEMTYPE(arrayval); + state->constexpr.consttypmod = -1; + state->constexpr.constcollid = arrayconst->constcollid; + state->constexpr.constlen = elmlen; + state->constexpr.constbyval = elmbyval; + lsecond(state->opexpr.args) = &state->constexpr; + + /* Initialize iteration state */ + state->next_elem = 0; +} + +static Node * +arrayconst_next_fn(PredIterInfo info) +{ + ArrayConstIterState *state = (ArrayConstIterState *) info->state; + + if (state->next_elem >= state->num_elems) + return NULL; + state->constexpr.constvalue = state->elem_values[state->next_elem]; + state->constexpr.constisnull = state->elem_nulls[state->next_elem]; + state->next_elem++; + return (Node *) &(state->opexpr); +} + +static void +arrayconst_cleanup_fn(PredIterInfo info) +{ + ArrayConstIterState *state = (ArrayConstIterState *) info->state; + + pfree(state->elem_values); + pfree(state->elem_nulls); + list_free(state->opexpr.args); + pfree(state); +} + +/* + * PredIterInfo routines for iterating over a ScalarArrayOpExpr with a + * one-dimensional ArrayExpr array operand. + */ +typedef struct +{ + OpExpr opexpr; + ListCell *next; +} ArrayExprIterState; + +static void +arrayexpr_startup_fn(Node *clause, PredIterInfo info) +{ + ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause; + ArrayExprIterState *state; + ArrayExpr *arrayexpr; + + /* Create working state struct */ + state = (ArrayExprIterState *) palloc(sizeof(ArrayExprIterState)); + info->state = (void *) state; + + /* Set up a dummy OpExpr to return as the per-item node */ + state->opexpr.xpr.type = T_OpExpr; + state->opexpr.opno = saop->opno; + state->opexpr.opfuncid = saop->opfuncid; + state->opexpr.opresulttype = BOOLOID; + state->opexpr.opretset = false; + state->opexpr.opcollid = InvalidOid; + state->opexpr.inputcollid = saop->inputcollid; + state->opexpr.args = list_copy(saop->args); + + /* Initialize iteration variable to first member of ArrayExpr */ + arrayexpr = (ArrayExpr *) lsecond(saop->args); + info->state_list = arrayexpr->elements; + state->next = list_head(arrayexpr->elements); +} + +static Node * +arrayexpr_next_fn(PredIterInfo info) +{ + ArrayExprIterState *state = (ArrayExprIterState *) info->state; + + if (state->next == NULL) + return NULL; + lsecond(state->opexpr.args) = lfirst(state->next); + state->next = lnext(info->state_list, state->next); + return (Node *) &(state->opexpr); +} + +static void +arrayexpr_cleanup_fn(PredIterInfo info) +{ + ArrayExprIterState *state = (ArrayExprIterState *) info->state; + + list_free(state->opexpr.args); + pfree(state); +} + + +/*---------- + * 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, and for either implication definition. (Actually, + * there is an implied assumption that the functions in the expression are + * immutable --- but this was checked for the predicate by the caller.) + * + * If the predicate is of the form "foo IS NOT NULL", and we are considering + * strong implication, we can conclude that the predicate is implied if the + * clause is strict for "foo", i.e., it must yield false or NULL when "foo" + * is NULL. In that case truth of the clause ensures that "foo" isn't NULL. + * (Again, this is a safe conclusion because "foo" must be immutable.) + * This doesn't work for weak implication, though. + * + * Finally, if both clauses are binary operator expressions, we may be able + * to prove something using the system's knowledge about operators; those + * proof rules are encapsulated in operator_predicate_proof(). + *---------- + */ +static bool +predicate_implied_by_simple_clause(Expr *predicate, Node *clause, + bool weak) +{ + /* Allow interrupting long proof attempts */ + CHECK_FOR_INTERRUPTS(); + + /* First try the equal() test */ + if (equal((Node *) predicate, clause)) + return true; + + /* Next try the IS NOT NULL case */ + if (!weak && + predicate && IsA(predicate, NullTest)) + { + NullTest *ntest = (NullTest *) predicate; + + /* row IS NOT NULL does not act in the simple way we have in mind */ + if (ntest->nulltesttype == IS_NOT_NULL && + !ntest->argisrow) + { + /* strictness of clause for foo implies foo IS NOT NULL */ + if (clause_is_strict_for(clause, (Node *) ntest->arg, true)) + return true; + } + return false; /* we can't succeed below... */ + } + + /* Else try operator-related knowledge */ + return operator_predicate_proof(predicate, clause, false, weak); +} + +/*---------- + * 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. + * But relation_excluded_by_constraints() checks for self-contradictions in a + * list of clauses, so that we may get here with predicate and clause being + * actually pointer-equal, and that is worth eliminating quickly. + * + * When the predicate is of the form "foo IS NULL", we can conclude that + * the predicate is refuted if the clause is strict for "foo" (see notes for + * implication case), or is "foo IS NOT NULL". That works for either strong + * or weak refutation. + * + * A clause "foo IS NULL" refutes a predicate "foo IS NOT NULL" in all cases. + * If we are considering weak refutation, it also refutes a predicate that + * is strict for "foo", since then the predicate must yield false or NULL + * (and since "foo" appears in the predicate, it's known immutable). + * + * (The main motivation for covering these IS [NOT] NULL cases is to support + * using IS NULL/IS NOT NULL as partition-defining constraints.) + * + * Finally, if both clauses are binary operator expressions, we may be able + * to prove something using the system's knowledge about operators; those + * proof rules are encapsulated in operator_predicate_proof(). + *---------- + */ +static bool +predicate_refuted_by_simple_clause(Expr *predicate, Node *clause, + bool weak) +{ + /* Allow interrupting long proof attempts */ + CHECK_FOR_INTERRUPTS(); + + /* A simple clause can't refute itself */ + /* Worth checking because of relation_excluded_by_constraints() */ + if ((Node *) predicate == clause) + return false; + + /* Try the predicate-IS-NULL case */ + if (predicate && IsA(predicate, NullTest) && + ((NullTest *) predicate)->nulltesttype == IS_NULL) + { + Expr *isnullarg = ((NullTest *) predicate)->arg; + + /* row IS NULL does not act in the simple way we have in mind */ + if (((NullTest *) predicate)->argisrow) + return false; + + /* strictness of clause for foo refutes foo IS NULL */ + if (clause_is_strict_for(clause, (Node *) isnullarg, true)) + return true; + + /* foo IS NOT NULL refutes foo IS NULL */ + if (clause && IsA(clause, NullTest) && + ((NullTest *) clause)->nulltesttype == IS_NOT_NULL && + !((NullTest *) clause)->argisrow && + equal(((NullTest *) clause)->arg, isnullarg)) + return true; + + return false; /* we can't succeed below... */ + } + + /* Try the clause-IS-NULL case */ + if (clause && IsA(clause, NullTest) && + ((NullTest *) clause)->nulltesttype == IS_NULL) + { + Expr *isnullarg = ((NullTest *) clause)->arg; + + /* row IS NULL does not act in the simple way we have in mind */ + if (((NullTest *) clause)->argisrow) + return false; + + /* foo IS NULL refutes foo IS NOT NULL */ + if (predicate && IsA(predicate, NullTest) && + ((NullTest *) predicate)->nulltesttype == IS_NOT_NULL && + !((NullTest *) predicate)->argisrow && + equal(((NullTest *) predicate)->arg, isnullarg)) + return true; + + /* foo IS NULL weakly refutes any predicate that is strict for foo */ + if (weak && + clause_is_strict_for((Node *) predicate, (Node *) isnullarg, true)) + return true; + + return false; /* we can't succeed below... */ + } + + /* Else try operator-related knowledge */ + return operator_predicate_proof(predicate, clause, true, weak); +} + + +/* + * If clause asserts the non-truth of a subclause, return that subclause; + * otherwise return NULL. + */ +static Node * +extract_not_arg(Node *clause) +{ + if (clause == NULL) + return NULL; + if (IsA(clause, BoolExpr)) + { + BoolExpr *bexpr = (BoolExpr *) clause; + + if (bexpr->boolop == NOT_EXPR) + return (Node *) linitial(bexpr->args); + } + else if (IsA(clause, BooleanTest)) + { + BooleanTest *btest = (BooleanTest *) clause; + + if (btest->booltesttype == IS_NOT_TRUE || + btest->booltesttype == IS_FALSE || + btest->booltesttype == IS_UNKNOWN) + return (Node *) btest->arg; + } + return NULL; +} + +/* + * If clause asserts the falsity of a subclause, return that subclause; + * otherwise return NULL. + */ +static Node * +extract_strong_not_arg(Node *clause) +{ + if (clause == NULL) + return NULL; + if (IsA(clause, BoolExpr)) + { + BoolExpr *bexpr = (BoolExpr *) clause; + + if (bexpr->boolop == NOT_EXPR) + return (Node *) linitial(bexpr->args); + } + else if (IsA(clause, BooleanTest)) + { + BooleanTest *btest = (BooleanTest *) clause; + + if (btest->booltesttype == IS_FALSE) + return (Node *) btest->arg; + } + return NULL; +} + + +/* + * Can we prove that "clause" returns NULL (or FALSE) if "subexpr" is + * assumed to yield NULL? + * + * In most places in the planner, "strictness" refers to a guarantee that + * an expression yields NULL output for a NULL input, and that's mostly what + * we're looking for here. However, at top level where the clause is known + * to yield boolean, it may be sufficient to prove that it cannot return TRUE + * when "subexpr" is NULL. The caller should pass allow_false = true when + * this weaker property is acceptable. (When this function recurses + * internally, we pass down allow_false = false since we need to prove actual + * nullness of the subexpression.) + * + * We assume that the caller checked that least one of the input expressions + * is immutable. All of the proof rules here involve matching "subexpr" to + * some portion of "clause", so that this allows assuming that "subexpr" is + * immutable without a separate check. + * + * The base case is that clause and subexpr are equal(). + * + * We can also report success if the subexpr appears as a subexpression + * of "clause" in a place where it'd force nullness of the overall result. + */ +static bool +clause_is_strict_for(Node *clause, Node *subexpr, bool allow_false) +{ + ListCell *lc; + + /* safety checks */ + if (clause == NULL || subexpr == NULL) + return false; + + /* + * Look through any RelabelType nodes, so that we can match, say, + * varcharcol with lower(varcharcol::text). (In general we could recurse + * through any nullness-preserving, immutable operation.) We should not + * see stacked RelabelTypes here. + */ + if (IsA(clause, RelabelType)) + clause = (Node *) ((RelabelType *) clause)->arg; + if (IsA(subexpr, RelabelType)) + subexpr = (Node *) ((RelabelType *) subexpr)->arg; + + /* Base case */ + if (equal(clause, subexpr)) + return true; + + /* + * If we have a strict operator or function, a NULL result is guaranteed + * if any input is forced NULL by subexpr. This is OK even if the op or + * func isn't immutable, since it won't even be called on NULL input. + */ + if (is_opclause(clause) && + op_strict(((OpExpr *) clause)->opno)) + { + foreach(lc, ((OpExpr *) clause)->args) + { + if (clause_is_strict_for((Node *) lfirst(lc), subexpr, false)) + return true; + } + return false; + } + if (is_funcclause(clause) && + func_strict(((FuncExpr *) clause)->funcid)) + { + foreach(lc, ((FuncExpr *) clause)->args) + { + if (clause_is_strict_for((Node *) lfirst(lc), subexpr, false)) + return true; + } + return false; + } + + /* + * CoerceViaIO is strict (whether or not the I/O functions it calls are). + * Likewise, ArrayCoerceExpr is strict for its array argument (regardless + * of what the per-element expression is), ConvertRowtypeExpr is strict at + * the row level, and CoerceToDomain is strict too. These are worth + * checking mainly because it saves us having to explain to users why some + * type coercions are known strict and others aren't. + */ + if (IsA(clause, CoerceViaIO)) + return clause_is_strict_for((Node *) ((CoerceViaIO *) clause)->arg, + subexpr, false); + if (IsA(clause, ArrayCoerceExpr)) + return clause_is_strict_for((Node *) ((ArrayCoerceExpr *) clause)->arg, + subexpr, false); + if (IsA(clause, ConvertRowtypeExpr)) + return clause_is_strict_for((Node *) ((ConvertRowtypeExpr *) clause)->arg, + subexpr, false); + if (IsA(clause, CoerceToDomain)) + return clause_is_strict_for((Node *) ((CoerceToDomain *) clause)->arg, + subexpr, false); + + /* + * ScalarArrayOpExpr is a special case. Note that we'd only reach here + * with a ScalarArrayOpExpr clause if we failed to deconstruct it into an + * AND or OR tree, as for example if it has too many array elements. + */ + if (IsA(clause, ScalarArrayOpExpr)) + { + ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause; + Node *scalarnode = (Node *) linitial(saop->args); + Node *arraynode = (Node *) lsecond(saop->args); + + /* + * If we can prove the scalar input to be null, and the operator is + * strict, then the SAOP result has to be null --- unless the array is + * empty. For an empty array, we'd get either false (for ANY) or true + * (for ALL). So if allow_false = true then the proof succeeds anyway + * for the ANY case; otherwise we can only make the proof if we can + * prove the array non-empty. + */ + if (clause_is_strict_for(scalarnode, subexpr, false) && + op_strict(saop->opno)) + { + int nelems = 0; + + if (allow_false && saop->useOr) + return true; /* can succeed even if array is empty */ + + if (arraynode && IsA(arraynode, Const)) + { + Const *arrayconst = (Const *) arraynode; + ArrayType *arrval; + + /* + * If array is constant NULL then we can succeed, as in the + * case below. + */ + if (arrayconst->constisnull) + return true; + + /* Otherwise, we can compute the number of elements. */ + arrval = DatumGetArrayTypeP(arrayconst->constvalue); + nelems = ArrayGetNItems(ARR_NDIM(arrval), ARR_DIMS(arrval)); + } + else if (arraynode && IsA(arraynode, ArrayExpr) && + !((ArrayExpr *) arraynode)->multidims) + { + /* + * We can also reliably count the number of array elements if + * the input is a non-multidim ARRAY[] expression. + */ + nelems = list_length(((ArrayExpr *) arraynode)->elements); + } + + /* Proof succeeds if array is definitely non-empty */ + if (nelems > 0) + return true; + } + + /* + * If we can prove the array input to be null, the proof succeeds in + * all cases, since ScalarArrayOpExpr will always return NULL for a + * NULL array. Otherwise, we're done here. + */ + return clause_is_strict_for(arraynode, subexpr, false); + } + + /* + * When recursing into an expression, we might find a NULL constant. + * That's certainly NULL, whether it matches subexpr or not. + */ + if (IsA(clause, Const)) + return ((Const *) clause)->constisnull; + + return false; +} + + +/* + * Define "operator implication tables" for btree operators ("strategies"), + * and similar tables for refutation. + * + * The strategy numbers defined by btree indexes (see access/stratnum.h) are: + * 1 < 2 <= 3 = 4 >= 5 > + * and in addition we use 6 to represent <>. <> is not a btree-indexable + * operator, but we assume here that if an equality operator of a btree + * opfamily has a negator operator, the negator behaves as <> for the opfamily. + * (This convention is also known to get_op_btree_interpretation().) + * + * BT_implies_table[] and BT_refutes_table[] are used for cases where we have + * two identical subexpressions and we want to know whether one operator + * expression implies or refutes the other. That is, if the "clause" is + * EXPR1 clause_op EXPR2 and the "predicate" is EXPR1 pred_op EXPR2 for the + * same two (immutable) subexpressions: + * BT_implies_table[clause_op-1][pred_op-1] + * is true if the clause implies the predicate + * BT_refutes_table[clause_op-1][pred_op-1] + * is true if the clause refutes the predicate + * where clause_op and pred_op are strategy numbers (from 1 to 6) in the + * same btree opfamily. For example, "x < y" implies "x <= y" and refutes + * "x > y". + * + * BT_implic_table[] and BT_refute_table[] are used where we have two + * constants that we need to compare. The interpretation of: + * + * test_op = BT_implic_table[clause_op-1][pred_op-1] + * + * where test_op, clause_op and pred_op are strategy numbers (from 1 to 6) + * of btree operators, is as follows: + * + * If you know, for some EXPR, that "EXPR clause_op CONST1" is true, and you + * want to determine whether "EXPR pred_op CONST2" must also be true, then + * you can use "CONST2 test_op CONST1" as a test. If this test returns true, + * then the predicate expression must be true; if the test returns false, + * then the predicate expression may be 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 EXPR, that "EXPR clause_op CONST1" is true, and you + * want to determine whether "EXPR pred_op CONST2" must be false, then + * you can use "CONST2 test_op CONST1" as a test. If this test returns true, + * then the predicate expression must be false; if the test returns false, + * then the predicate 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 BTLE BTLessEqualStrategyNumber +#define BTEQ BTEqualStrategyNumber +#define BTGE BTGreaterEqualStrategyNumber +#define BTGT BTGreaterStrategyNumber +#define BTNE ROWCOMPARE_NE + +/* We use "none" for 0/false to make the tables align nicely */ +#define none 0 + +static const bool BT_implies_table[6][6] = { +/* + * The predicate operator: + * LT LE EQ GE GT NE + */ + {true, true, none, none, none, true}, /* LT */ + {none, true, none, none, none, none}, /* LE */ + {none, true, true, true, none, none}, /* EQ */ + {none, none, none, true, none, none}, /* GE */ + {none, none, none, true, true, true}, /* GT */ + {none, none, none, none, none, true} /* NE */ +}; + +static const bool BT_refutes_table[6][6] = { +/* + * The predicate operator: + * LT LE EQ GE GT NE + */ + {none, none, true, true, true, none}, /* LT */ + {none, none, none, none, true, none}, /* LE */ + {true, none, none, none, true, true}, /* EQ */ + {true, none, none, none, none, none}, /* GE */ + {true, true, true, none, none, none}, /* GT */ + {none, none, true, none, none, none} /* NE */ +}; + +static const StrategyNumber BT_implic_table[6][6] = { +/* + * The predicate operator: + * LT LE EQ GE GT NE + */ + {BTGE, BTGE, none, none, none, BTGE}, /* LT */ + {BTGT, BTGE, none, none, none, BTGT}, /* LE */ + {BTGT, BTGE, BTEQ, BTLE, BTLT, BTNE}, /* EQ */ + {none, none, none, BTLE, BTLT, BTLT}, /* GE */ + {none, none, none, BTLE, BTLE, BTLE}, /* GT */ + {none, none, none, none, none, BTEQ} /* NE */ +}; + +static const StrategyNumber BT_refute_table[6][6] = { +/* + * The predicate operator: + * LT LE EQ GE GT NE + */ + {none, none, BTGE, BTGE, BTGE, none}, /* LT */ + {none, none, BTGT, BTGT, BTGE, none}, /* LE */ + {BTLE, BTLT, BTNE, BTGT, BTGE, BTEQ}, /* EQ */ + {BTLE, BTLT, BTLT, none, none, none}, /* GE */ + {BTLE, BTLE, BTLE, none, none, none}, /* GT */ + {none, none, BTEQ, none, none, none} /* NE */ +}; + + +/* + * operator_predicate_proof + * Does the predicate implication or refutation test for a "simple clause" + * predicate and a "simple clause" restriction, when both are operator + * clauses using related operators and identical input expressions. + * + * 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. + * + * We mostly need not distinguish strong vs. weak implication/refutation here. + * This depends on the assumption that a pair of related operators (i.e., + * commutators, negators, or btree opfamily siblings) will not return one NULL + * and one non-NULL result for the same inputs. Then, for the proof types + * where we start with an assumption of truth of the clause, the predicate + * operator could not return NULL either, so it doesn't matter whether we are + * trying to make a strong or weak proof. For weak implication, it could be + * that the clause operator returned NULL, but then the predicate operator + * would as well, so that the weak implication still holds. This argument + * doesn't apply in the case where we are considering two different constant + * values, since then the operators aren't being given identical inputs. But + * we only support that for btree operators, for which we can assume that all + * non-null inputs result in non-null outputs, so that it doesn't matter which + * two non-null constants we consider. If either constant is NULL, we have + * to think harder, but sometimes the proof still works, as explained below. + * + * We can make proofs involving several expression forms (here "foo" and "bar" + * represent subexpressions that are identical according to equal()): + * "foo op1 bar" refutes "foo op2 bar" if op1 is op2's negator + * "foo op1 bar" implies "bar op2 foo" if op1 is op2's commutator + * "foo op1 bar" refutes "bar op2 foo" if op1 is negator of op2's commutator + * "foo op1 bar" can imply/refute "foo op2 bar" based on btree semantics + * "foo op1 bar" can imply/refute "bar op2 foo" based on btree semantics + * "foo op1 const1" can imply/refute "foo op2 const2" based on btree semantics + * + * For the last three cases, op1 and op2 have to be members of the same btree + * operator family. When both subexpressions are identical, the idea is that, + * for instance, x < y implies x <= y, independently of exactly what x and y + * are. If we have two different constants compared to the same expression + * foo, we have to execute a comparison between the two constant values + * in order to determine the result; for instance, foo < c1 implies foo < c2 + * if c1 <= c2. We assume it's safe to compare the constants at plan time + * if the comparison operator is immutable. + * + * Note: all the operators and subexpressions have to be immutable for the + * proof to be safe. We assume the predicate expression is entirely immutable, + * so no explicit check on the subexpressions is needed here, but in some + * cases we need an extra check of operator immutability. In particular, + * btree opfamilies can contain cross-type operators that are merely stable, + * and we dare not make deductions with those. + */ +static bool +operator_predicate_proof(Expr *predicate, Node *clause, + bool refute_it, bool weak) +{ + OpExpr *pred_opexpr, + *clause_opexpr; + Oid pred_collation, + clause_collation; + Oid pred_op, + clause_op, + test_op; + Node *pred_leftop, + *pred_rightop, + *clause_leftop, + *clause_rightop; + Const *pred_const, + *clause_const; + Expr *test_expr; + ExprState *test_exprstate; + Datum test_result; + bool isNull; + EState *estate; + MemoryContext oldcontext; + + /* + * Both expressions must be binary opclauses, else we can't do anything. + * + * Note: in future we might extend this logic to other operator-based + * constructs such as DistinctExpr. But the planner isn't very smart + * about DistinctExpr in general, and this probably isn't the first place + * to fix if you want to improve that. + */ + if (!is_opclause(predicate)) + return false; + pred_opexpr = (OpExpr *) predicate; + if (list_length(pred_opexpr->args) != 2) + return false; + if (!is_opclause(clause)) + return false; + clause_opexpr = (OpExpr *) clause; + if (list_length(clause_opexpr->args) != 2) + return false; + + /* + * If they're marked with different collations then we can't do anything. + * This is a cheap test so let's get it out of the way early. + */ + pred_collation = pred_opexpr->inputcollid; + clause_collation = clause_opexpr->inputcollid; + if (pred_collation != clause_collation) + return false; + + /* Grab the operator OIDs now too. We may commute these below. */ + pred_op = pred_opexpr->opno; + clause_op = clause_opexpr->opno; + + /* + * We have to match up at least one pair of input expressions. + */ + pred_leftop = (Node *) linitial(pred_opexpr->args); + pred_rightop = (Node *) lsecond(pred_opexpr->args); + clause_leftop = (Node *) linitial(clause_opexpr->args); + clause_rightop = (Node *) lsecond(clause_opexpr->args); + + if (equal(pred_leftop, clause_leftop)) + { + if (equal(pred_rightop, clause_rightop)) + { + /* We have x op1 y and x op2 y */ + return operator_same_subexprs_proof(pred_op, clause_op, refute_it); + } + else + { + /* Fail unless rightops are both Consts */ + if (pred_rightop == NULL || !IsA(pred_rightop, Const)) + return false; + pred_const = (Const *) pred_rightop; + if (clause_rightop == NULL || !IsA(clause_rightop, Const)) + return false; + clause_const = (Const *) clause_rightop; + } + } + else if (equal(pred_rightop, clause_rightop)) + { + /* Fail unless leftops are both Consts */ + if (pred_leftop == NULL || !IsA(pred_leftop, Const)) + return false; + pred_const = (Const *) pred_leftop; + if (clause_leftop == NULL || !IsA(clause_leftop, Const)) + return false; + clause_const = (Const *) clause_leftop; + /* Commute both operators so we can assume Consts are on the right */ + pred_op = get_commutator(pred_op); + if (!OidIsValid(pred_op)) + return false; + clause_op = get_commutator(clause_op); + if (!OidIsValid(clause_op)) + return false; + } + else if (equal(pred_leftop, clause_rightop)) + { + if (equal(pred_rightop, clause_leftop)) + { + /* We have x op1 y and y op2 x */ + /* Commute pred_op that we can treat this like a straight match */ + pred_op = get_commutator(pred_op); + if (!OidIsValid(pred_op)) + return false; + return operator_same_subexprs_proof(pred_op, clause_op, refute_it); + } + else + { + /* Fail unless pred_rightop/clause_leftop are both Consts */ + if (pred_rightop == NULL || !IsA(pred_rightop, Const)) + return false; + pred_const = (Const *) pred_rightop; + if (clause_leftop == NULL || !IsA(clause_leftop, Const)) + return false; + clause_const = (Const *) clause_leftop; + /* Commute clause_op so we can assume Consts are on the right */ + clause_op = get_commutator(clause_op); + if (!OidIsValid(clause_op)) + return false; + } + } + else if (equal(pred_rightop, clause_leftop)) + { + /* Fail unless pred_leftop/clause_rightop are both Consts */ + if (pred_leftop == NULL || !IsA(pred_leftop, Const)) + return false; + pred_const = (Const *) pred_leftop; + if (clause_rightop == NULL || !IsA(clause_rightop, Const)) + return false; + clause_const = (Const *) clause_rightop; + /* Commute pred_op so we can assume Consts are on the right */ + pred_op = get_commutator(pred_op); + if (!OidIsValid(pred_op)) + return false; + } + else + { + /* Failed to match up any of the subexpressions, so we lose */ + return false; + } + + /* + * We have two identical subexpressions, and two other subexpressions that + * are not identical but are both Consts; and we have commuted the + * operators if necessary so that the Consts are on the right. We'll need + * to compare the Consts' values. If either is NULL, we can't do that, so + * usually the proof fails ... but in some cases we can claim success. + */ + if (clause_const->constisnull) + { + /* If clause_op isn't strict, we can't prove anything */ + if (!op_strict(clause_op)) + return false; + + /* + * At this point we know that the clause returns NULL. For proof + * types that assume truth of the clause, this means the proof is + * vacuously true (a/k/a "false implies anything"). That's all proof + * types except weak implication. + */ + if (!(weak && !refute_it)) + return true; + + /* + * For weak implication, it's still possible for the proof to succeed, + * if the predicate can also be proven NULL. In that case we've got + * NULL => NULL which is valid for this proof type. + */ + if (pred_const->constisnull && op_strict(pred_op)) + return true; + /* Else the proof fails */ + return false; + } + if (pred_const->constisnull) + { + /* + * If the pred_op is strict, we know the predicate yields NULL, which + * means the proof succeeds for either weak implication or weak + * refutation. + */ + if (weak && op_strict(pred_op)) + return true; + /* Else the proof fails */ + return false; + } + + /* + * Lookup the constant-comparison operator using the system catalogs and + * the operator implication tables. + */ + test_op = get_btree_test_op(pred_op, clause_op, refute_it); + + if (!OidIsValid(test_op)) + { + /* couldn't find a suitable comparison operator */ + return false; + } + + /* + * Evaluate the test. For this we need an EState. + */ + estate = CreateExecutorState(); + + /* We can use the estate's working context to avoid memory leaks. */ + oldcontext = MemoryContextSwitchTo(estate->es_query_cxt); + + /* Build expression tree */ + test_expr = make_opclause(test_op, + BOOLOID, + false, + (Expr *) pred_const, + (Expr *) clause_const, + InvalidOid, + pred_collation); + + /* Fill in opfuncids */ + fix_opfuncids((Node *) test_expr); + + /* Prepare it for execution */ + test_exprstate = ExecInitExpr(test_expr, NULL); + + /* And execute it. */ + test_result = ExecEvalExprSwitchContext(test_exprstate, + GetPerTupleExprContext(estate), + &isNull); + + /* Get back to outer memory context */ + MemoryContextSwitchTo(oldcontext); + + /* Release all the junk we just created */ + FreeExecutorState(estate); + + if (isNull) + { + /* Treat a null result as non-proof ... but it's a tad fishy ... */ + elog(DEBUG2, "null predicate test result"); + return false; + } + return DatumGetBool(test_result); +} + + +/* + * operator_same_subexprs_proof + * Assuming that EXPR1 clause_op EXPR2 is true, try to prove or refute + * EXPR1 pred_op EXPR2. + * + * Return true if able to make the proof, false if not able to prove it. + */ +static bool +operator_same_subexprs_proof(Oid pred_op, Oid clause_op, bool refute_it) +{ + /* + * A simple and general rule is that the predicate is proven if clause_op + * and pred_op are the same, or refuted if they are each other's negators. + * We need not check immutability since the pred_op is already known + * immutable. (Actually, by this point we may have the commutator of a + * known-immutable pred_op, but that should certainly be immutable too. + * Likewise we don't worry whether the pred_op's negator is immutable.) + * + * Note: the "same" case won't get here if we actually had EXPR1 clause_op + * EXPR2 and EXPR1 pred_op EXPR2, because the overall-expression-equality + * test in predicate_implied_by_simple_clause would have caught it. But + * we can see the same operator after having commuted the pred_op. + */ + if (refute_it) + { + if (get_negator(pred_op) == clause_op) + return true; + } + else + { + if (pred_op == clause_op) + return true; + } + + /* + * Otherwise, see if we can determine the implication by finding the + * operators' relationship via some btree opfamily. + */ + return operator_same_subexprs_lookup(pred_op, clause_op, refute_it); +} + + +/* + * We use a lookaside table to cache the result of btree proof operator + * lookups, since the actual lookup is pretty expensive and doesn't change + * for any given pair of operators (at least as long as pg_amop doesn't + * change). A single hash entry stores both implication and refutation + * results for a given pair of operators; but note we may have determined + * only one of those sets of results as yet. + */ +typedef struct OprProofCacheKey +{ + Oid pred_op; /* predicate operator */ + Oid clause_op; /* clause operator */ +} OprProofCacheKey; + +typedef struct OprProofCacheEntry +{ + /* the hash lookup key MUST BE FIRST */ + OprProofCacheKey key; + + bool have_implic; /* do we know the implication result? */ + bool have_refute; /* do we know the refutation result? */ + bool same_subexprs_implies; /* X clause_op Y implies X pred_op Y? */ + bool same_subexprs_refutes; /* X clause_op Y refutes X pred_op Y? */ + Oid implic_test_op; /* OID of the test operator, or 0 if none */ + Oid refute_test_op; /* OID of the test operator, or 0 if none */ +} OprProofCacheEntry; + +static HTAB *OprProofCacheHash = NULL; + + +/* + * lookup_proof_cache + * Get, and fill in if necessary, the appropriate cache entry. + */ +static OprProofCacheEntry * +lookup_proof_cache(Oid pred_op, Oid clause_op, bool refute_it) +{ + OprProofCacheKey key; + OprProofCacheEntry *cache_entry; + bool cfound; + bool same_subexprs = false; + Oid test_op = InvalidOid; + bool found = false; + List *pred_op_infos, + *clause_op_infos; + ListCell *lcp, + *lcc; + + /* + * Find or make a cache entry for this pair of operators. + */ + if (OprProofCacheHash == NULL) + { + /* First time through: initialize the hash table */ + HASHCTL ctl; + + ctl.keysize = sizeof(OprProofCacheKey); + ctl.entrysize = sizeof(OprProofCacheEntry); + OprProofCacheHash = hash_create("Btree proof lookup cache", 256, + &ctl, HASH_ELEM | HASH_BLOBS); + + /* Arrange to flush cache on pg_amop changes */ + CacheRegisterSyscacheCallback(AMOPOPID, + InvalidateOprProofCacheCallBack, + (Datum) 0); + } + + key.pred_op = pred_op; + key.clause_op = clause_op; + cache_entry = (OprProofCacheEntry *) hash_search(OprProofCacheHash, + (void *) &key, + HASH_ENTER, &cfound); + if (!cfound) + { + /* new cache entry, set it invalid */ + cache_entry->have_implic = false; + cache_entry->have_refute = false; + } + else + { + /* pre-existing cache entry, see if we know the answer yet */ + if (refute_it ? cache_entry->have_refute : cache_entry->have_implic) + return cache_entry; + } + + /* + * Try to find a btree opfamily containing the given operators. + * + * We must find a btree opfamily that contains both operators, else the + * implication can't be determined. Also, the opfamily must contain a + * suitable test operator taking the operators' righthand datatypes. + * + * If there are multiple matching opfamilies, assume we can use any one to + * determine the logical relationship of the two operators and the correct + * corresponding test operator. This should work for any logically + * consistent opfamilies. + * + * Note that we can determine the operators' relationship for + * same-subexprs cases even from an opfamily that lacks a usable test + * operator. This can happen in cases with incomplete sets of cross-type + * comparison operators. + */ + clause_op_infos = get_op_btree_interpretation(clause_op); + if (clause_op_infos) + pred_op_infos = get_op_btree_interpretation(pred_op); + else /* no point in looking */ + pred_op_infos = NIL; + + foreach(lcp, pred_op_infos) + { + OpBtreeInterpretation *pred_op_info = lfirst(lcp); + Oid opfamily_id = pred_op_info->opfamily_id; + + foreach(lcc, clause_op_infos) + { + OpBtreeInterpretation *clause_op_info = lfirst(lcc); + StrategyNumber pred_strategy, + clause_strategy, + test_strategy; + + /* Must find them in same opfamily */ + if (opfamily_id != clause_op_info->opfamily_id) + continue; + /* Lefttypes should match */ + Assert(clause_op_info->oplefttype == pred_op_info->oplefttype); + + pred_strategy = pred_op_info->strategy; + clause_strategy = clause_op_info->strategy; + + /* + * Check to see if we can make a proof for same-subexpressions + * cases based on the operators' relationship in this opfamily. + */ + if (refute_it) + same_subexprs |= BT_refutes_table[clause_strategy - 1][pred_strategy - 1]; + else + same_subexprs |= BT_implies_table[clause_strategy - 1][pred_strategy - 1]; + + /* + * Look up the "test" strategy number in the implication table + */ + 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 */ + continue; + } + + /* + * See if opfamily has an operator for the test strategy and the + * datatypes. + */ + if (test_strategy == BTNE) + { + test_op = get_opfamily_member(opfamily_id, + pred_op_info->oprighttype, + clause_op_info->oprighttype, + BTEqualStrategyNumber); + if (OidIsValid(test_op)) + test_op = get_negator(test_op); + } + else + { + test_op = get_opfamily_member(opfamily_id, + pred_op_info->oprighttype, + clause_op_info->oprighttype, + test_strategy); + } + + if (!OidIsValid(test_op)) + continue; + + /* + * 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 is assumed to have been checked + * immutable by the caller.) Essentially we are assuming that the + * opfamily is consistent even if it contains operators that are + * merely stable. + */ + if (op_volatile(test_op) == PROVOLATILE_IMMUTABLE) + { + found = true; + break; + } + } + + if (found) + break; + } + + list_free_deep(pred_op_infos); + list_free_deep(clause_op_infos); + + if (!found) + { + /* couldn't find a suitable comparison operator */ + test_op = InvalidOid; + } + + /* + * If we think we were able to prove something about same-subexpressions + * cases, check to make sure the clause_op is immutable before believing + * it completely. (Usually, the clause_op would be immutable if the + * pred_op is, but it's not entirely clear that this must be true in all + * cases, so let's check.) + */ + if (same_subexprs && + op_volatile(clause_op) != PROVOLATILE_IMMUTABLE) + same_subexprs = false; + + /* Cache the results, whether positive or negative */ + if (refute_it) + { + cache_entry->refute_test_op = test_op; + cache_entry->same_subexprs_refutes = same_subexprs; + cache_entry->have_refute = true; + } + else + { + cache_entry->implic_test_op = test_op; + cache_entry->same_subexprs_implies = same_subexprs; + cache_entry->have_implic = true; + } + + return cache_entry; +} + +/* + * operator_same_subexprs_lookup + * Convenience subroutine to look up the cached answer for + * same-subexpressions cases. + */ +static bool +operator_same_subexprs_lookup(Oid pred_op, Oid clause_op, bool refute_it) +{ + OprProofCacheEntry *cache_entry; + + cache_entry = lookup_proof_cache(pred_op, clause_op, refute_it); + if (refute_it) + return cache_entry->same_subexprs_refutes; + else + return cache_entry->same_subexprs_implies; +} + +/* + * get_btree_test_op + * Identify the comparison operator needed for a btree-operator + * proof or refutation involving comparison of constants. + * + * Given the truth of a clause "var clause_op const1", we are attempting to + * prove or refute a predicate "var pred_op const2". The identities of the + * two operators are sufficient to determine the operator (if any) to compare + * const2 to const1 with. + * + * Returns the OID of the operator to use, or InvalidOid if no proof is + * possible. + */ +static Oid +get_btree_test_op(Oid pred_op, Oid clause_op, bool refute_it) +{ + OprProofCacheEntry *cache_entry; + + cache_entry = lookup_proof_cache(pred_op, clause_op, refute_it); + if (refute_it) + return cache_entry->refute_test_op; + else + return cache_entry->implic_test_op; +} + + +/* + * Callback for pg_amop inval events + */ +static void +InvalidateOprProofCacheCallBack(Datum arg, int cacheid, uint32 hashvalue) +{ + HASH_SEQ_STATUS status; + OprProofCacheEntry *hentry; + + Assert(OprProofCacheHash != NULL); + + /* Currently we just reset all entries; hard to be smarter ... */ + hash_seq_init(&status, OprProofCacheHash); + + while ((hentry = (OprProofCacheEntry *) hash_seq_search(&status)) != NULL) + { + hentry->have_implic = false; + hentry->have_refute = false; + } +} |