Line data Source code
1 : /*-------------------------------------------------------------------------
2 : *
3 : * predtest.c
4 : * Routines to attempt to prove logical implications between predicate
5 : * expressions.
6 : *
7 : * Portions Copyright (c) 1996-2024, PostgreSQL Global Development Group
8 : * Portions Copyright (c) 1994, Regents of the University of California
9 : *
10 : *
11 : * IDENTIFICATION
12 : * src/backend/optimizer/util/predtest.c
13 : *
14 : *-------------------------------------------------------------------------
15 : */
16 : #include "postgres.h"
17 :
18 : #include "catalog/pg_operator.h"
19 : #include "catalog/pg_proc.h"
20 : #include "catalog/pg_type.h"
21 : #include "executor/executor.h"
22 : #include "miscadmin.h"
23 : #include "nodes/makefuncs.h"
24 : #include "nodes/nodeFuncs.h"
25 : #include "nodes/pathnodes.h"
26 : #include "optimizer/optimizer.h"
27 : #include "utils/array.h"
28 : #include "utils/inval.h"
29 : #include "utils/lsyscache.h"
30 : #include "utils/syscache.h"
31 :
32 :
33 : /*
34 : * Proof attempts involving large arrays in ScalarArrayOpExpr nodes are
35 : * likely to require O(N^2) time, and more often than not fail anyway.
36 : * So we set an arbitrary limit on the number of array elements that
37 : * we will allow to be treated as an AND or OR clause.
38 : * XXX is it worth exposing this as a GUC knob?
39 : */
40 : #define MAX_SAOP_ARRAY_SIZE 100
41 :
42 : /*
43 : * To avoid redundant coding in predicate_implied_by_recurse and
44 : * predicate_refuted_by_recurse, we need to abstract out the notion of
45 : * iterating over the components of an expression that is logically an AND
46 : * or OR structure. There are multiple sorts of expression nodes that can
47 : * be treated as ANDs or ORs, and we don't want to code each one separately.
48 : * Hence, these types and support routines.
49 : */
50 : typedef enum
51 : {
52 : CLASS_ATOM, /* expression that's not AND or OR */
53 : CLASS_AND, /* expression with AND semantics */
54 : CLASS_OR, /* expression with OR semantics */
55 : } PredClass;
56 :
57 : typedef struct PredIterInfoData *PredIterInfo;
58 :
59 : typedef struct PredIterInfoData
60 : {
61 : /* node-type-specific iteration state */
62 : void *state;
63 : List *state_list;
64 : /* initialize to do the iteration */
65 : void (*startup_fn) (Node *clause, PredIterInfo info);
66 : /* next-component iteration function */
67 : Node *(*next_fn) (PredIterInfo info);
68 : /* release resources when done with iteration */
69 : void (*cleanup_fn) (PredIterInfo info);
70 : } PredIterInfoData;
71 :
72 : #define iterate_begin(item, clause, info) \
73 : do { \
74 : Node *item; \
75 : (info).startup_fn((clause), &(info)); \
76 : while ((item = (info).next_fn(&(info))) != NULL)
77 :
78 : #define iterate_end(info) \
79 : (info).cleanup_fn(&(info)); \
80 : } while (0)
81 :
82 :
83 : static bool predicate_implied_by_recurse(Node *clause, Node *predicate,
84 : bool weak);
85 : static bool predicate_refuted_by_recurse(Node *clause, Node *predicate,
86 : bool weak);
87 : static PredClass predicate_classify(Node *clause, PredIterInfo info);
88 : static void list_startup_fn(Node *clause, PredIterInfo info);
89 : static Node *list_next_fn(PredIterInfo info);
90 : static void list_cleanup_fn(PredIterInfo info);
91 : static void boolexpr_startup_fn(Node *clause, PredIterInfo info);
92 : static void arrayconst_startup_fn(Node *clause, PredIterInfo info);
93 : static Node *arrayconst_next_fn(PredIterInfo info);
94 : static void arrayconst_cleanup_fn(PredIterInfo info);
95 : static void arrayexpr_startup_fn(Node *clause, PredIterInfo info);
96 : static Node *arrayexpr_next_fn(PredIterInfo info);
97 : static void arrayexpr_cleanup_fn(PredIterInfo info);
98 : static bool predicate_implied_by_simple_clause(Expr *predicate, Node *clause,
99 : bool weak);
100 : static bool predicate_refuted_by_simple_clause(Expr *predicate, Node *clause,
101 : bool weak);
102 : static Node *extract_not_arg(Node *clause);
103 : static Node *extract_strong_not_arg(Node *clause);
104 : static bool clause_is_strict_for(Node *clause, Node *subexpr, bool allow_false);
105 : static bool operator_predicate_proof(Expr *predicate, Node *clause,
106 : bool refute_it, bool weak);
107 : static bool operator_same_subexprs_proof(Oid pred_op, Oid clause_op,
108 : bool refute_it);
109 : static bool operator_same_subexprs_lookup(Oid pred_op, Oid clause_op,
110 : bool refute_it);
111 : static Oid get_btree_test_op(Oid pred_op, Oid clause_op, bool refute_it);
112 : static void InvalidateOprProofCacheCallBack(Datum arg, int cacheid, uint32 hashvalue);
113 :
114 :
115 : /*
116 : * predicate_implied_by
117 : * Recursively checks whether the clauses in clause_list imply that the
118 : * given predicate is true.
119 : *
120 : * We support two definitions of implication:
121 : *
122 : * "Strong" implication: A implies B means that truth of A implies truth of B.
123 : * We use this to prove that a row satisfying one WHERE clause or index
124 : * predicate must satisfy another one.
125 : *
126 : * "Weak" implication: A implies B means that non-falsity of A implies
127 : * non-falsity of B ("non-false" means "either true or NULL"). We use this to
128 : * prove that a row satisfying one CHECK constraint must satisfy another one.
129 : *
130 : * Strong implication can also be used to prove that a WHERE clause implies a
131 : * CHECK constraint, although it will fail to prove a few cases where we could
132 : * safely conclude that the implication holds. There's no support for proving
133 : * the converse case, since only a few kinds of CHECK constraint would allow
134 : * deducing anything.
135 : *
136 : * The top-level List structure of each list corresponds to an AND list.
137 : * We assume that eval_const_expressions() has been applied and so there
138 : * are no un-flattened ANDs or ORs (e.g., no AND immediately within an AND,
139 : * including AND just below the top-level List structure).
140 : * If this is not true we might fail to prove an implication that is
141 : * valid, but no worse consequences will ensue.
142 : *
143 : * We assume the predicate has already been checked to contain only
144 : * immutable functions and operators. (In many current uses this is known
145 : * true because the predicate is part of an index predicate that has passed
146 : * CheckPredicate(); otherwise, the caller must check it.) We dare not make
147 : * deductions based on non-immutable functions, because they might change
148 : * answers between the time we make the plan and the time we execute the plan.
149 : * Immutability of functions in the clause_list is checked here, if necessary.
150 : */
151 : bool
152 92534 : predicate_implied_by(List *predicate_list, List *clause_list,
153 : bool weak)
154 : {
155 : Node *p,
156 : *c;
157 :
158 92534 : if (predicate_list == NIL)
159 1104 : return true; /* no predicate: implication is vacuous */
160 91430 : if (clause_list == NIL)
161 4610 : return false; /* no restriction: implication must fail */
162 :
163 : /*
164 : * If either input is a single-element list, replace it with its lone
165 : * member; this avoids one useless level of AND-recursion. We only need
166 : * to worry about this at top level, since eval_const_expressions should
167 : * have gotten rid of any trivial ANDs or ORs below that.
168 : */
169 86820 : if (list_length(predicate_list) == 1)
170 86530 : p = (Node *) linitial(predicate_list);
171 : else
172 290 : p = (Node *) predicate_list;
173 86820 : if (list_length(clause_list) == 1)
174 77452 : c = (Node *) linitial(clause_list);
175 : else
176 9368 : c = (Node *) clause_list;
177 :
178 : /* And away we go ... */
179 86820 : return predicate_implied_by_recurse(c, p, weak);
180 : }
181 :
182 : /*
183 : * predicate_refuted_by
184 : * Recursively checks whether the clauses in clause_list refute the given
185 : * predicate (that is, prove it false).
186 : *
187 : * This is NOT the same as !(predicate_implied_by), though it is similar
188 : * in the technique and structure of the code.
189 : *
190 : * We support two definitions of refutation:
191 : *
192 : * "Strong" refutation: A refutes B means truth of A implies falsity of B.
193 : * We use this to disprove a CHECK constraint given a WHERE clause, i.e.,
194 : * prove that any row satisfying the WHERE clause would violate the CHECK
195 : * constraint. (Observe we must prove B yields false, not just not-true.)
196 : *
197 : * "Weak" refutation: A refutes B means truth of A implies non-truth of B
198 : * (i.e., B must yield false or NULL). We use this to detect mutually
199 : * contradictory WHERE clauses.
200 : *
201 : * Weak refutation can be proven in some cases where strong refutation doesn't
202 : * hold, so it's useful to use it when possible. We don't currently have
203 : * support for disproving one CHECK constraint based on another one, nor for
204 : * disproving WHERE based on CHECK. (As with implication, the last case
205 : * doesn't seem very practical. CHECK-vs-CHECK might be useful, but isn't
206 : * currently needed anywhere.)
207 : *
208 : * The top-level List structure of each list corresponds to an AND list.
209 : * We assume that eval_const_expressions() has been applied and so there
210 : * are no un-flattened ANDs or ORs (e.g., no AND immediately within an AND,
211 : * including AND just below the top-level List structure).
212 : * If this is not true we might fail to prove an implication that is
213 : * valid, but no worse consequences will ensue.
214 : *
215 : * We assume the predicate has already been checked to contain only
216 : * immutable functions and operators. We dare not make deductions based on
217 : * non-immutable functions, because they might change answers between the
218 : * time we make the plan and the time we execute the plan.
219 : * Immutability of functions in the clause_list is checked here, if necessary.
220 : */
221 : bool
222 48370 : predicate_refuted_by(List *predicate_list, List *clause_list,
223 : bool weak)
224 : {
225 : Node *p,
226 : *c;
227 :
228 48370 : if (predicate_list == NIL)
229 17636 : return false; /* no predicate: no refutation is possible */
230 30734 : if (clause_list == NIL)
231 0 : return false; /* no restriction: refutation must fail */
232 :
233 : /*
234 : * If either input is a single-element list, replace it with its lone
235 : * member; this avoids one useless level of AND-recursion. We only need
236 : * to worry about this at top level, since eval_const_expressions should
237 : * have gotten rid of any trivial ANDs or ORs below that.
238 : */
239 30734 : if (list_length(predicate_list) == 1)
240 23230 : p = (Node *) linitial(predicate_list);
241 : else
242 7504 : p = (Node *) predicate_list;
243 30734 : if (list_length(clause_list) == 1)
244 22840 : c = (Node *) linitial(clause_list);
245 : else
246 7894 : c = (Node *) clause_list;
247 :
248 : /* And away we go ... */
249 30734 : return predicate_refuted_by_recurse(c, p, weak);
250 : }
251 :
252 : /*----------
253 : * predicate_implied_by_recurse
254 : * Does the predicate implication test for non-NULL restriction and
255 : * predicate clauses.
256 : *
257 : * The logic followed here is ("=>" means "implies"):
258 : * atom A => atom B iff: predicate_implied_by_simple_clause says so
259 : * atom A => AND-expr B iff: A => each of B's components
260 : * atom A => OR-expr B iff: A => any of B's components
261 : * AND-expr A => atom B iff: any of A's components => B
262 : * AND-expr A => AND-expr B iff: A => each of B's components
263 : * AND-expr A => OR-expr B iff: A => any of B's components,
264 : * *or* any of A's components => B
265 : * OR-expr A => atom B iff: each of A's components => B
266 : * OR-expr A => AND-expr B iff: A => each of B's components
267 : * OR-expr A => OR-expr B iff: each of A's components => any of B's
268 : *
269 : * An "atom" is anything other than an AND or OR node. Notice that we don't
270 : * have any special logic to handle NOT nodes; these should have been pushed
271 : * down or eliminated where feasible during eval_const_expressions().
272 : *
273 : * All of these rules apply equally to strong or weak implication.
274 : *
275 : * We can't recursively expand either side first, but have to interleave
276 : * the expansions per the above rules, to be sure we handle all of these
277 : * examples:
278 : * (x OR y) => (x OR y OR z)
279 : * (x AND y AND z) => (x AND y)
280 : * (x AND y) => ((x AND y) OR z)
281 : * ((x OR y) AND z) => (x OR y)
282 : * This is still not an exhaustive test, but it handles most normal cases
283 : * under the assumption that both inputs have been AND/OR flattened.
284 : *
285 : * We have to be prepared to handle RestrictInfo nodes in the restrictinfo
286 : * tree, though not in the predicate tree.
287 : *----------
288 : */
289 : static bool
290 138228 : predicate_implied_by_recurse(Node *clause, Node *predicate,
291 : bool weak)
292 : {
293 : PredIterInfoData clause_info;
294 : PredIterInfoData pred_info;
295 : PredClass pclass;
296 : bool result;
297 :
298 : /* skip through RestrictInfo */
299 : Assert(clause != NULL);
300 138228 : if (IsA(clause, RestrictInfo))
301 3196 : clause = (Node *) ((RestrictInfo *) clause)->clause;
302 :
303 138228 : pclass = predicate_classify(predicate, &pred_info);
304 :
305 138228 : switch (predicate_classify(clause, &clause_info))
306 : {
307 12938 : case CLASS_AND:
308 : switch (pclass)
309 : {
310 508 : case CLASS_AND:
311 :
312 : /*
313 : * AND-clause => AND-clause if A implies each of B's items
314 : */
315 508 : result = true;
316 1002 : iterate_begin(pitem, predicate, pred_info)
317 : {
318 920 : if (!predicate_implied_by_recurse(clause, pitem,
319 : weak))
320 : {
321 426 : result = false;
322 426 : break;
323 : }
324 : }
325 508 : iterate_end(pred_info);
326 508 : return result;
327 :
328 752 : case CLASS_OR:
329 :
330 : /*
331 : * AND-clause => OR-clause if A implies any of B's items
332 : *
333 : * Needed to handle (x AND y) => ((x AND y) OR z)
334 : */
335 752 : result = false;
336 2584 : iterate_begin(pitem, predicate, pred_info)
337 : {
338 1884 : if (predicate_implied_by_recurse(clause, pitem,
339 : weak))
340 : {
341 52 : result = true;
342 52 : break;
343 : }
344 : }
345 752 : iterate_end(pred_info);
346 752 : if (result)
347 52 : return result;
348 :
349 : /*
350 : * Also check if any of A's items implies B
351 : *
352 : * Needed to handle ((x OR y) AND z) => (x OR y)
353 : */
354 2120 : iterate_begin(citem, clause, clause_info)
355 : {
356 1432 : if (predicate_implied_by_recurse(citem, predicate,
357 : weak))
358 : {
359 12 : result = true;
360 12 : break;
361 : }
362 : }
363 700 : iterate_end(clause_info);
364 700 : return result;
365 :
366 11678 : case CLASS_ATOM:
367 :
368 : /*
369 : * AND-clause => atom if any of A's items implies B
370 : */
371 11678 : result = false;
372 33878 : iterate_begin(citem, clause, clause_info)
373 : {
374 23548 : if (predicate_implied_by_recurse(citem, predicate,
375 : weak))
376 : {
377 1348 : result = true;
378 1348 : break;
379 : }
380 : }
381 11678 : iterate_end(clause_info);
382 11678 : return result;
383 : }
384 0 : break;
385 :
386 1404 : case CLASS_OR:
387 : switch (pclass)
388 : {
389 432 : case CLASS_OR:
390 :
391 : /*
392 : * OR-clause => OR-clause if each of A's items implies any
393 : * of B's items. Messy but can't do it any more simply.
394 : */
395 432 : result = true;
396 690 : iterate_begin(citem, clause, clause_info)
397 : {
398 580 : bool presult = false;
399 :
400 1492 : iterate_begin(pitem, predicate, pred_info)
401 : {
402 1170 : if (predicate_implied_by_recurse(citem, pitem,
403 : weak))
404 : {
405 258 : presult = true;
406 258 : break;
407 : }
408 : }
409 580 : iterate_end(pred_info);
410 580 : if (!presult)
411 : {
412 322 : result = false; /* doesn't imply any of B's */
413 322 : break;
414 : }
415 : }
416 432 : iterate_end(clause_info);
417 432 : return result;
418 :
419 972 : case CLASS_AND:
420 : case CLASS_ATOM:
421 :
422 : /*
423 : * OR-clause => AND-clause if each of A's items implies B
424 : *
425 : * OR-clause => atom if each of A's items implies B
426 : */
427 972 : result = true;
428 1212 : iterate_begin(citem, clause, clause_info)
429 : {
430 1160 : if (!predicate_implied_by_recurse(citem, predicate,
431 : weak))
432 : {
433 920 : result = false;
434 920 : break;
435 : }
436 : }
437 972 : iterate_end(clause_info);
438 972 : return result;
439 : }
440 0 : break;
441 :
442 123886 : case CLASS_ATOM:
443 : switch (pclass)
444 : {
445 1498 : case CLASS_AND:
446 :
447 : /*
448 : * atom => AND-clause if A implies each of B's items
449 : */
450 1498 : result = true;
451 1978 : iterate_begin(pitem, predicate, pred_info)
452 : {
453 1952 : if (!predicate_implied_by_recurse(clause, pitem,
454 : weak))
455 : {
456 1472 : result = false;
457 1472 : break;
458 : }
459 : }
460 1498 : iterate_end(pred_info);
461 1498 : return result;
462 :
463 6698 : case CLASS_OR:
464 :
465 : /*
466 : * atom => OR-clause if A implies any of B's items
467 : */
468 6698 : result = false;
469 24108 : iterate_begin(pitem, predicate, pred_info)
470 : {
471 17648 : if (predicate_implied_by_recurse(clause, pitem,
472 : weak))
473 : {
474 238 : result = true;
475 238 : break;
476 : }
477 : }
478 6698 : iterate_end(pred_info);
479 6698 : return result;
480 :
481 115690 : case CLASS_ATOM:
482 :
483 : /*
484 : * atom => atom is the base case
485 : */
486 : return
487 115690 : predicate_implied_by_simple_clause((Expr *) predicate,
488 : clause,
489 : weak);
490 : }
491 0 : break;
492 : }
493 :
494 : /* can't get here */
495 0 : elog(ERROR, "predicate_classify returned a bogus value");
496 : return false;
497 : }
498 :
499 : /*----------
500 : * predicate_refuted_by_recurse
501 : * Does the predicate refutation test for non-NULL restriction and
502 : * predicate clauses.
503 : *
504 : * The logic followed here is ("R=>" means "refutes"):
505 : * atom A R=> atom B iff: predicate_refuted_by_simple_clause says so
506 : * atom A R=> AND-expr B iff: A R=> any of B's components
507 : * atom A R=> OR-expr B iff: A R=> each of B's components
508 : * AND-expr A R=> atom B iff: any of A's components R=> B
509 : * AND-expr A R=> AND-expr B iff: A R=> any of B's components,
510 : * *or* any of A's components R=> B
511 : * AND-expr A R=> OR-expr B iff: A R=> each of B's components
512 : * OR-expr A R=> atom B iff: each of A's components R=> B
513 : * OR-expr A R=> AND-expr B iff: each of A's components R=> any of B's
514 : * OR-expr A R=> OR-expr B iff: A R=> each of B's components
515 : *
516 : * All of the above rules apply equally to strong or weak refutation.
517 : *
518 : * In addition, if the predicate is a NOT-clause then we can use
519 : * A R=> NOT B if: A => B
520 : * This works for several different SQL constructs that assert the non-truth
521 : * of their argument, ie NOT, IS FALSE, IS NOT TRUE, IS UNKNOWN, although some
522 : * of them require that we prove strong implication. Likewise, we can use
523 : * NOT A R=> B if: B => A
524 : * but here we must be careful about strong vs. weak refutation and make
525 : * the appropriate type of implication proof (weak or strong respectively).
526 : *
527 : * Other comments are as for predicate_implied_by_recurse().
528 : *----------
529 : */
530 : static bool
531 224528 : predicate_refuted_by_recurse(Node *clause, Node *predicate,
532 : bool weak)
533 : {
534 : PredIterInfoData clause_info;
535 : PredIterInfoData pred_info;
536 : PredClass pclass;
537 : Node *not_arg;
538 : bool result;
539 :
540 : /* skip through RestrictInfo */
541 : Assert(clause != NULL);
542 224528 : if (IsA(clause, RestrictInfo))
543 18566 : clause = (Node *) ((RestrictInfo *) clause)->clause;
544 :
545 224528 : pclass = predicate_classify(predicate, &pred_info);
546 :
547 224528 : switch (predicate_classify(clause, &clause_info))
548 : {
549 33848 : case CLASS_AND:
550 : switch (pclass)
551 : {
552 7774 : case CLASS_AND:
553 :
554 : /*
555 : * AND-clause R=> AND-clause if A refutes any of B's items
556 : *
557 : * Needed to handle (x AND y) R=> ((!x OR !y) AND z)
558 : */
559 7774 : result = false;
560 26946 : iterate_begin(pitem, predicate, pred_info)
561 : {
562 19284 : if (predicate_refuted_by_recurse(clause, pitem,
563 : weak))
564 : {
565 112 : result = true;
566 112 : break;
567 : }
568 : }
569 7774 : iterate_end(pred_info);
570 7774 : if (result)
571 112 : return result;
572 :
573 : /*
574 : * Also check if any of A's items refutes B
575 : *
576 : * Needed to handle ((x OR y) AND z) R=> (!x AND !y)
577 : */
578 27388 : iterate_begin(citem, clause, clause_info)
579 : {
580 19730 : if (predicate_refuted_by_recurse(citem, predicate,
581 : weak))
582 : {
583 4 : result = true;
584 4 : break;
585 : }
586 : }
587 7662 : iterate_end(clause_info);
588 7662 : return result;
589 :
590 3148 : case CLASS_OR:
591 :
592 : /*
593 : * AND-clause R=> OR-clause if A refutes each of B's items
594 : */
595 3148 : result = true;
596 4224 : iterate_begin(pitem, predicate, pred_info)
597 : {
598 4220 : if (!predicate_refuted_by_recurse(clause, pitem,
599 : weak))
600 : {
601 3144 : result = false;
602 3144 : break;
603 : }
604 : }
605 3148 : iterate_end(pred_info);
606 3148 : return result;
607 :
608 22926 : case CLASS_ATOM:
609 :
610 : /*
611 : * If B is a NOT-type clause, A R=> B if A => B's arg
612 : *
613 : * Since, for either type of refutation, we are starting
614 : * with the premise that A is true, we can use a strong
615 : * implication test in all cases. That proves B's arg is
616 : * true, which is more than we need for weak refutation if
617 : * B is a simple NOT, but it allows not worrying about
618 : * exactly which kind of negation clause we have.
619 : */
620 22926 : not_arg = extract_not_arg(predicate);
621 23124 : if (not_arg &&
622 198 : predicate_implied_by_recurse(clause, not_arg,
623 : false))
624 22 : return true;
625 :
626 : /*
627 : * AND-clause R=> atom if any of A's items refutes B
628 : */
629 22904 : result = false;
630 82780 : iterate_begin(citem, clause, clause_info)
631 : {
632 61194 : if (predicate_refuted_by_recurse(citem, predicate,
633 : weak))
634 : {
635 1318 : result = true;
636 1318 : break;
637 : }
638 : }
639 22904 : iterate_end(clause_info);
640 22904 : return result;
641 : }
642 0 : break;
643 :
644 13900 : case CLASS_OR:
645 : switch (pclass)
646 : {
647 1310 : case CLASS_OR:
648 :
649 : /*
650 : * OR-clause R=> OR-clause if A refutes each of B's items
651 : */
652 1310 : result = true;
653 1348 : iterate_begin(pitem, predicate, pred_info)
654 : {
655 1348 : if (!predicate_refuted_by_recurse(clause, pitem,
656 : weak))
657 : {
658 1310 : result = false;
659 1310 : break;
660 : }
661 : }
662 1310 : iterate_end(pred_info);
663 1310 : return result;
664 :
665 2940 : case CLASS_AND:
666 :
667 : /*
668 : * OR-clause R=> AND-clause if each of A's items refutes
669 : * any of B's items.
670 : */
671 2940 : result = true;
672 3488 : iterate_begin(citem, clause, clause_info)
673 : {
674 3448 : bool presult = false;
675 :
676 13350 : iterate_begin(pitem, predicate, pred_info)
677 : {
678 10450 : if (predicate_refuted_by_recurse(citem, pitem,
679 : weak))
680 : {
681 548 : presult = true;
682 548 : break;
683 : }
684 : }
685 3448 : iterate_end(pred_info);
686 3448 : if (!presult)
687 : {
688 2900 : result = false; /* citem refutes nothing */
689 2900 : break;
690 : }
691 : }
692 2940 : iterate_end(clause_info);
693 2940 : return result;
694 :
695 9650 : case CLASS_ATOM:
696 :
697 : /*
698 : * If B is a NOT-type clause, A R=> B if A => B's arg
699 : *
700 : * Same logic as for the AND-clause case above.
701 : */
702 9650 : not_arg = extract_not_arg(predicate);
703 9658 : if (not_arg &&
704 8 : predicate_implied_by_recurse(clause, not_arg,
705 : false))
706 0 : return true;
707 :
708 : /*
709 : * OR-clause R=> atom if each of A's items refutes B
710 : */
711 9650 : result = true;
712 10492 : iterate_begin(citem, clause, clause_info)
713 : {
714 10490 : if (!predicate_refuted_by_recurse(citem, predicate,
715 : weak))
716 : {
717 9648 : result = false;
718 9648 : break;
719 : }
720 : }
721 9650 : iterate_end(clause_info);
722 9650 : return result;
723 : }
724 0 : break;
725 :
726 176780 : case CLASS_ATOM:
727 :
728 : /*
729 : * If A is a strong NOT-clause, A R=> B if B => A's arg
730 : *
731 : * Since A is strong, we may assume A's arg is false (not just
732 : * not-true). If B weakly implies A's arg, then B can be neither
733 : * true nor null, so that strong refutation is proven. If B
734 : * strongly implies A's arg, then B cannot be true, so that weak
735 : * refutation is proven.
736 : */
737 176780 : not_arg = extract_strong_not_arg(clause);
738 177192 : if (not_arg &&
739 412 : predicate_implied_by_recurse(predicate, not_arg,
740 412 : !weak))
741 22 : return true;
742 :
743 : switch (pclass)
744 : {
745 19070 : case CLASS_AND:
746 :
747 : /*
748 : * atom R=> AND-clause if A refutes any of B's items
749 : */
750 19070 : result = false;
751 70780 : iterate_begin(pitem, predicate, pred_info)
752 : {
753 52000 : if (predicate_refuted_by_recurse(clause, pitem,
754 : weak))
755 : {
756 290 : result = true;
757 290 : break;
758 : }
759 : }
760 19070 : iterate_end(pred_info);
761 19070 : return result;
762 :
763 11790 : case CLASS_OR:
764 :
765 : /*
766 : * atom R=> OR-clause if A refutes each of B's items
767 : */
768 11790 : result = true;
769 15282 : iterate_begin(pitem, predicate, pred_info)
770 : {
771 15078 : if (!predicate_refuted_by_recurse(clause, pitem,
772 : weak))
773 : {
774 11586 : result = false;
775 11586 : break;
776 : }
777 : }
778 11790 : iterate_end(pred_info);
779 11790 : return result;
780 :
781 145898 : case CLASS_ATOM:
782 :
783 : /*
784 : * If B is a NOT-type clause, A R=> B if A => B's arg
785 : *
786 : * Same logic as for the AND-clause case above.
787 : */
788 145898 : not_arg = extract_not_arg(predicate);
789 146974 : if (not_arg &&
790 1076 : predicate_implied_by_recurse(clause, not_arg,
791 : false))
792 32 : return true;
793 :
794 : /*
795 : * atom R=> atom is the base case
796 : */
797 : return
798 145866 : predicate_refuted_by_simple_clause((Expr *) predicate,
799 : clause,
800 : weak);
801 : }
802 0 : break;
803 : }
804 :
805 : /* can't get here */
806 0 : elog(ERROR, "predicate_classify returned a bogus value");
807 : return false;
808 : }
809 :
810 :
811 : /*
812 : * predicate_classify
813 : * Classify an expression node as AND-type, OR-type, or neither (an atom).
814 : *
815 : * If the expression is classified as AND- or OR-type, then *info is filled
816 : * in with the functions needed to iterate over its components.
817 : *
818 : * This function also implements enforcement of MAX_SAOP_ARRAY_SIZE: if a
819 : * ScalarArrayOpExpr's array has too many elements, we just classify it as an
820 : * atom. (This will result in its being passed as-is to the simple_clause
821 : * functions, many of which will fail to prove anything about it.) Note that we
822 : * cannot just stop after considering MAX_SAOP_ARRAY_SIZE elements; in general
823 : * that would result in wrong proofs, rather than failing to prove anything.
824 : */
825 : static PredClass
826 725512 : predicate_classify(Node *clause, PredIterInfo info)
827 : {
828 : /* Caller should not pass us NULL, nor a RestrictInfo clause */
829 : Assert(clause != NULL);
830 : Assert(!IsA(clause, RestrictInfo));
831 :
832 : /*
833 : * If we see a List, assume it's an implicit-AND list; this is the correct
834 : * semantics for lists of RestrictInfo nodes.
835 : */
836 725512 : if (IsA(clause, List))
837 : {
838 65566 : info->startup_fn = list_startup_fn;
839 65566 : info->next_fn = list_next_fn;
840 65566 : info->cleanup_fn = list_cleanup_fn;
841 65566 : return CLASS_AND;
842 : }
843 :
844 : /* Handle normal AND and OR boolean clauses */
845 659946 : if (is_andclause(clause))
846 : {
847 11776 : info->startup_fn = boolexpr_startup_fn;
848 11776 : info->next_fn = list_next_fn;
849 11776 : info->cleanup_fn = list_cleanup_fn;
850 11776 : return CLASS_AND;
851 : }
852 648170 : if (is_orclause(clause))
853 : {
854 28728 : info->startup_fn = boolexpr_startup_fn;
855 28728 : info->next_fn = list_next_fn;
856 28728 : info->cleanup_fn = list_cleanup_fn;
857 28728 : return CLASS_OR;
858 : }
859 :
860 : /* Handle ScalarArrayOpExpr */
861 619442 : if (IsA(clause, ScalarArrayOpExpr))
862 : {
863 12156 : ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause;
864 12156 : Node *arraynode = (Node *) lsecond(saop->args);
865 :
866 : /*
867 : * We can break this down into an AND or OR structure, but only if we
868 : * know how to iterate through expressions for the array's elements.
869 : * We can do that if the array operand is a non-null constant or a
870 : * simple ArrayExpr.
871 : */
872 12156 : if (arraynode && IsA(arraynode, Const) &&
873 10774 : !((Const *) arraynode)->constisnull)
874 16 : {
875 : ArrayType *arrayval;
876 : int nelems;
877 :
878 10774 : arrayval = DatumGetArrayTypeP(((Const *) arraynode)->constvalue);
879 10774 : nelems = ArrayGetNItems(ARR_NDIM(arrayval), ARR_DIMS(arrayval));
880 10774 : if (nelems <= MAX_SAOP_ARRAY_SIZE)
881 : {
882 10758 : info->startup_fn = arrayconst_startup_fn;
883 10758 : info->next_fn = arrayconst_next_fn;
884 10758 : info->cleanup_fn = arrayconst_cleanup_fn;
885 10758 : return saop->useOr ? CLASS_OR : CLASS_AND;
886 : }
887 : }
888 1382 : else if (arraynode && IsA(arraynode, ArrayExpr) &&
889 2504 : !((ArrayExpr *) arraynode)->multidims &&
890 1252 : list_length(((ArrayExpr *) arraynode)->elements) <= MAX_SAOP_ARRAY_SIZE)
891 : {
892 1244 : info->startup_fn = arrayexpr_startup_fn;
893 1244 : info->next_fn = arrayexpr_next_fn;
894 1244 : info->cleanup_fn = arrayexpr_cleanup_fn;
895 1244 : return saop->useOr ? CLASS_OR : CLASS_AND;
896 : }
897 : }
898 :
899 : /* None of the above, so it's an atom */
900 607440 : return CLASS_ATOM;
901 : }
902 :
903 : /*
904 : * PredIterInfo routines for iterating over regular Lists. The iteration
905 : * state variable is the next ListCell to visit.
906 : */
907 : static void
908 62832 : list_startup_fn(Node *clause, PredIterInfo info)
909 : {
910 62832 : info->state_list = (List *) clause;
911 62832 : info->state = (void *) list_head(info->state_list);
912 62832 : }
913 :
914 : static Node *
915 296374 : list_next_fn(PredIterInfo info)
916 : {
917 296374 : ListCell *l = (ListCell *) info->state;
918 : Node *n;
919 :
920 296374 : if (l == NULL)
921 71736 : return NULL;
922 224638 : n = lfirst(l);
923 224638 : info->state = (void *) lnext(info->state_list, l);
924 224638 : return n;
925 : }
926 :
927 : static void
928 101906 : list_cleanup_fn(PredIterInfo info)
929 : {
930 : /* Nothing to clean up */
931 101906 : }
932 :
933 : /*
934 : * BoolExpr needs its own startup function, but can use list_next_fn and
935 : * list_cleanup_fn.
936 : */
937 : static void
938 39074 : boolexpr_startup_fn(Node *clause, PredIterInfo info)
939 : {
940 39074 : info->state_list = ((BoolExpr *) clause)->args;
941 39074 : info->state = (void *) list_head(info->state_list);
942 39074 : }
943 :
944 : /*
945 : * PredIterInfo routines for iterating over a ScalarArrayOpExpr with a
946 : * constant array operand.
947 : */
948 : typedef struct
949 : {
950 : OpExpr opexpr;
951 : Const const_expr;
952 : int next_elem;
953 : int num_elems;
954 : Datum *elem_values;
955 : bool *elem_nulls;
956 : } ArrayConstIterState;
957 :
958 : static void
959 10418 : arrayconst_startup_fn(Node *clause, PredIterInfo info)
960 : {
961 10418 : ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause;
962 : ArrayConstIterState *state;
963 : Const *arrayconst;
964 : ArrayType *arrayval;
965 : int16 elmlen;
966 : bool elmbyval;
967 : char elmalign;
968 :
969 : /* Create working state struct */
970 10418 : state = (ArrayConstIterState *) palloc(sizeof(ArrayConstIterState));
971 10418 : info->state = (void *) state;
972 :
973 : /* Deconstruct the array literal */
974 10418 : arrayconst = (Const *) lsecond(saop->args);
975 10418 : arrayval = DatumGetArrayTypeP(arrayconst->constvalue);
976 10418 : get_typlenbyvalalign(ARR_ELEMTYPE(arrayval),
977 : &elmlen, &elmbyval, &elmalign);
978 10418 : deconstruct_array(arrayval,
979 : ARR_ELEMTYPE(arrayval),
980 : elmlen, elmbyval, elmalign,
981 : &state->elem_values, &state->elem_nulls,
982 : &state->num_elems);
983 :
984 : /* Set up a dummy OpExpr to return as the per-item node */
985 10418 : state->opexpr.xpr.type = T_OpExpr;
986 10418 : state->opexpr.opno = saop->opno;
987 10418 : state->opexpr.opfuncid = saop->opfuncid;
988 10418 : state->opexpr.opresulttype = BOOLOID;
989 10418 : state->opexpr.opretset = false;
990 10418 : state->opexpr.opcollid = InvalidOid;
991 10418 : state->opexpr.inputcollid = saop->inputcollid;
992 10418 : state->opexpr.args = list_copy(saop->args);
993 :
994 : /* Set up a dummy Const node to hold the per-element values */
995 10418 : state->const_expr.xpr.type = T_Const;
996 10418 : state->const_expr.consttype = ARR_ELEMTYPE(arrayval);
997 10418 : state->const_expr.consttypmod = -1;
998 10418 : state->const_expr.constcollid = arrayconst->constcollid;
999 10418 : state->const_expr.constlen = elmlen;
1000 10418 : state->const_expr.constbyval = elmbyval;
1001 10418 : lsecond(state->opexpr.args) = &state->const_expr;
1002 :
1003 : /* Initialize iteration state */
1004 10418 : state->next_elem = 0;
1005 10418 : }
1006 :
1007 : static Node *
1008 27578 : arrayconst_next_fn(PredIterInfo info)
1009 : {
1010 27578 : ArrayConstIterState *state = (ArrayConstIterState *) info->state;
1011 :
1012 27578 : if (state->next_elem >= state->num_elems)
1013 5870 : return NULL;
1014 21708 : state->const_expr.constvalue = state->elem_values[state->next_elem];
1015 21708 : state->const_expr.constisnull = state->elem_nulls[state->next_elem];
1016 21708 : state->next_elem++;
1017 21708 : return (Node *) &(state->opexpr);
1018 : }
1019 :
1020 : static void
1021 10418 : arrayconst_cleanup_fn(PredIterInfo info)
1022 : {
1023 10418 : ArrayConstIterState *state = (ArrayConstIterState *) info->state;
1024 :
1025 10418 : pfree(state->elem_values);
1026 10418 : pfree(state->elem_nulls);
1027 10418 : list_free(state->opexpr.args);
1028 10418 : pfree(state);
1029 10418 : }
1030 :
1031 : /*
1032 : * PredIterInfo routines for iterating over a ScalarArrayOpExpr with a
1033 : * one-dimensional ArrayExpr array operand.
1034 : */
1035 : typedef struct
1036 : {
1037 : OpExpr opexpr;
1038 : ListCell *next;
1039 : } ArrayExprIterState;
1040 :
1041 : static void
1042 1190 : arrayexpr_startup_fn(Node *clause, PredIterInfo info)
1043 : {
1044 1190 : ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause;
1045 : ArrayExprIterState *state;
1046 : ArrayExpr *arrayexpr;
1047 :
1048 : /* Create working state struct */
1049 1190 : state = (ArrayExprIterState *) palloc(sizeof(ArrayExprIterState));
1050 1190 : info->state = (void *) state;
1051 :
1052 : /* Set up a dummy OpExpr to return as the per-item node */
1053 1190 : state->opexpr.xpr.type = T_OpExpr;
1054 1190 : state->opexpr.opno = saop->opno;
1055 1190 : state->opexpr.opfuncid = saop->opfuncid;
1056 1190 : state->opexpr.opresulttype = BOOLOID;
1057 1190 : state->opexpr.opretset = false;
1058 1190 : state->opexpr.opcollid = InvalidOid;
1059 1190 : state->opexpr.inputcollid = saop->inputcollid;
1060 1190 : state->opexpr.args = list_copy(saop->args);
1061 :
1062 : /* Initialize iteration variable to first member of ArrayExpr */
1063 1190 : arrayexpr = (ArrayExpr *) lsecond(saop->args);
1064 1190 : info->state_list = arrayexpr->elements;
1065 1190 : state->next = list_head(arrayexpr->elements);
1066 1190 : }
1067 :
1068 : static Node *
1069 1190 : arrayexpr_next_fn(PredIterInfo info)
1070 : {
1071 1190 : ArrayExprIterState *state = (ArrayExprIterState *) info->state;
1072 :
1073 1190 : if (state->next == NULL)
1074 0 : return NULL;
1075 1190 : lsecond(state->opexpr.args) = lfirst(state->next);
1076 1190 : state->next = lnext(info->state_list, state->next);
1077 1190 : return (Node *) &(state->opexpr);
1078 : }
1079 :
1080 : static void
1081 1190 : arrayexpr_cleanup_fn(PredIterInfo info)
1082 : {
1083 1190 : ArrayExprIterState *state = (ArrayExprIterState *) info->state;
1084 :
1085 1190 : list_free(state->opexpr.args);
1086 1190 : pfree(state);
1087 1190 : }
1088 :
1089 :
1090 : /*
1091 : * predicate_implied_by_simple_clause
1092 : * Does the predicate implication test for a "simple clause" predicate
1093 : * and a "simple clause" restriction.
1094 : *
1095 : * We return true if able to prove the implication, false if not.
1096 : */
1097 : static bool
1098 115690 : predicate_implied_by_simple_clause(Expr *predicate, Node *clause,
1099 : bool weak)
1100 : {
1101 : /* Allow interrupting long proof attempts */
1102 115690 : CHECK_FOR_INTERRUPTS();
1103 :
1104 : /*
1105 : * A simple and general rule is that a clause implies itself, hence we
1106 : * check if they are equal(); this works for any kind of expression, and
1107 : * for either implication definition. (Actually, there is an implied
1108 : * assumption that the functions in the expression are immutable --- but
1109 : * this was checked for the predicate by the caller.)
1110 : */
1111 115690 : if (equal((Node *) predicate, clause))
1112 2262 : return true;
1113 :
1114 : /* Next we have some clause-type-specific strategies */
1115 113428 : switch (nodeTag(clause))
1116 : {
1117 109838 : case T_OpExpr:
1118 : {
1119 109838 : OpExpr *op = (OpExpr *) clause;
1120 :
1121 : /*----------
1122 : * For boolean x, "x = TRUE" is equivalent to "x", likewise
1123 : * "x = FALSE" is equivalent to "NOT x". These can be worth
1124 : * checking because, while we preferentially simplify boolean
1125 : * comparisons down to "x" and "NOT x", the other form has to
1126 : * be dealt with anyway in the context of index conditions.
1127 : *
1128 : * We could likewise check whether the predicate is boolean
1129 : * equality to a constant; but there are no known use-cases
1130 : * for that at the moment, assuming that the predicate has
1131 : * been through constant-folding.
1132 : *----------
1133 : */
1134 109838 : if (op->opno == BooleanEqualOperator)
1135 : {
1136 : Node *rightop;
1137 :
1138 : Assert(list_length(op->args) == 2);
1139 152 : rightop = lsecond(op->args);
1140 : /* We might never see null Consts here, but better check */
1141 152 : if (rightop && IsA(rightop, Const) &&
1142 152 : !((Const *) rightop)->constisnull)
1143 : {
1144 152 : Node *leftop = linitial(op->args);
1145 :
1146 152 : if (DatumGetBool(((Const *) rightop)->constvalue))
1147 : {
1148 : /* X = true implies X */
1149 4 : if (equal(predicate, leftop))
1150 4 : return true;
1151 : }
1152 : else
1153 : {
1154 : /* X = false implies NOT X */
1155 296 : if (is_notclause(predicate) &&
1156 148 : equal(get_notclausearg(predicate), leftop))
1157 148 : return true;
1158 : }
1159 : }
1160 : }
1161 : }
1162 109686 : break;
1163 3590 : default:
1164 3590 : break;
1165 : }
1166 :
1167 : /* ... and some predicate-type-specific ones */
1168 113276 : switch (nodeTag(predicate))
1169 : {
1170 1150 : case T_NullTest:
1171 : {
1172 1150 : NullTest *predntest = (NullTest *) predicate;
1173 :
1174 1150 : switch (predntest->nulltesttype)
1175 : {
1176 590 : case IS_NOT_NULL:
1177 :
1178 : /*
1179 : * If the predicate is of the form "foo IS NOT NULL",
1180 : * and we are considering strong implication, we can
1181 : * conclude that the predicate is implied if the
1182 : * clause is strict for "foo", i.e., it must yield
1183 : * false or NULL when "foo" is NULL. In that case
1184 : * truth of the clause ensures that "foo" isn't NULL.
1185 : * (Again, this is a safe conclusion because "foo"
1186 : * must be immutable.) This doesn't work for weak
1187 : * implication, though. Also, "row IS NOT NULL" does
1188 : * not act in the simple way we have in mind.
1189 : */
1190 590 : if (!weak &&
1191 324 : !predntest->argisrow &&
1192 162 : clause_is_strict_for(clause,
1193 162 : (Node *) predntest->arg,
1194 : true))
1195 34 : return true;
1196 556 : break;
1197 560 : case IS_NULL:
1198 560 : break;
1199 : }
1200 1116 : }
1201 1116 : break;
1202 112126 : default:
1203 112126 : break;
1204 : }
1205 :
1206 : /*
1207 : * Finally, if both clauses are binary operator expressions, we may be
1208 : * able to prove something using the system's knowledge about operators;
1209 : * those proof rules are encapsulated in operator_predicate_proof().
1210 : */
1211 113242 : return operator_predicate_proof(predicate, clause, false, weak);
1212 : }
1213 :
1214 : /*
1215 : * predicate_refuted_by_simple_clause
1216 : * Does the predicate refutation test for a "simple clause" predicate
1217 : * and a "simple clause" restriction.
1218 : *
1219 : * We return true if able to prove the refutation, false if not.
1220 : *
1221 : * The main motivation for covering IS [NOT] NULL cases is to support using
1222 : * IS NULL/IS NOT NULL as partition-defining constraints.
1223 : */
1224 : static bool
1225 145866 : predicate_refuted_by_simple_clause(Expr *predicate, Node *clause,
1226 : bool weak)
1227 : {
1228 : /* Allow interrupting long proof attempts */
1229 145866 : CHECK_FOR_INTERRUPTS();
1230 :
1231 : /*
1232 : * A simple clause can't refute itself, so unlike the implication case,
1233 : * checking for equal() clauses isn't helpful.
1234 : *
1235 : * But relation_excluded_by_constraints() checks for self-contradictions
1236 : * in a list of clauses, so that we may get here with predicate and clause
1237 : * being actually pointer-equal, and that is worth eliminating quickly.
1238 : */
1239 145866 : if ((Node *) predicate == clause)
1240 45922 : return false;
1241 :
1242 : /* Next we have some clause-type-specific strategies */
1243 99944 : switch (nodeTag(clause))
1244 : {
1245 7156 : case T_NullTest:
1246 : {
1247 7156 : NullTest *clausentest = (NullTest *) clause;
1248 :
1249 : /* row IS NULL does not act in the simple way we have in mind */
1250 7156 : if (clausentest->argisrow)
1251 0 : return false;
1252 :
1253 7156 : switch (clausentest->nulltesttype)
1254 : {
1255 4230 : case IS_NULL:
1256 : {
1257 4230 : switch (nodeTag(predicate))
1258 : {
1259 1258 : case T_NullTest:
1260 : {
1261 1258 : NullTest *predntest = (NullTest *) predicate;
1262 :
1263 : /*
1264 : * row IS NULL does not act in the
1265 : * simple way we have in mind
1266 : */
1267 1258 : if (predntest->argisrow)
1268 0 : return false;
1269 :
1270 : /*
1271 : * foo IS NULL refutes foo IS NOT
1272 : * NULL, at least in the non-row case,
1273 : * for both strong and weak refutation
1274 : */
1275 1292 : if (predntest->nulltesttype == IS_NOT_NULL &&
1276 34 : equal(predntest->arg, clausentest->arg))
1277 4 : return true;
1278 : }
1279 1254 : break;
1280 2972 : default:
1281 2972 : break;
1282 : }
1283 :
1284 : /*
1285 : * foo IS NULL weakly refutes any predicate that
1286 : * is strict for foo, since then the predicate
1287 : * must yield false or NULL (and since foo appears
1288 : * in the predicate, it's known immutable).
1289 : */
1290 6780 : if (weak &&
1291 2554 : clause_is_strict_for((Node *) predicate,
1292 2554 : (Node *) clausentest->arg,
1293 : true))
1294 32 : return true;
1295 :
1296 4194 : return false; /* we can't succeed below... */
1297 : }
1298 : break;
1299 2926 : case IS_NOT_NULL:
1300 2926 : break;
1301 : }
1302 2926 : }
1303 2926 : break;
1304 92788 : default:
1305 92788 : break;
1306 : }
1307 :
1308 : /* ... and some predicate-type-specific ones */
1309 95714 : switch (nodeTag(predicate))
1310 : {
1311 27060 : case T_NullTest:
1312 : {
1313 27060 : NullTest *predntest = (NullTest *) predicate;
1314 :
1315 : /* row IS NULL does not act in the simple way we have in mind */
1316 27060 : if (predntest->argisrow)
1317 0 : return false;
1318 :
1319 27060 : switch (predntest->nulltesttype)
1320 : {
1321 3016 : case IS_NULL:
1322 : {
1323 3016 : switch (nodeTag(clause))
1324 : {
1325 16 : case T_NullTest:
1326 : {
1327 16 : NullTest *clausentest = (NullTest *) clause;
1328 :
1329 : /*
1330 : * row IS NULL does not act in the
1331 : * simple way we have in mind
1332 : */
1333 16 : if (clausentest->argisrow)
1334 0 : return false;
1335 :
1336 : /*
1337 : * foo IS NOT NULL refutes foo IS NULL
1338 : * for both strong and weak refutation
1339 : */
1340 32 : if (clausentest->nulltesttype == IS_NOT_NULL &&
1341 16 : equal(clausentest->arg, predntest->arg))
1342 16 : return true;
1343 : }
1344 0 : break;
1345 3000 : default:
1346 3000 : break;
1347 : }
1348 :
1349 : /*
1350 : * When the predicate is of the form "foo IS
1351 : * NULL", we can conclude that the predicate is
1352 : * refuted if the clause is strict for "foo" (see
1353 : * notes for implication case). That works for
1354 : * either strong or weak refutation.
1355 : */
1356 3000 : if (clause_is_strict_for(clause,
1357 3000 : (Node *) predntest->arg,
1358 : true))
1359 1644 : return true;
1360 : }
1361 1356 : break;
1362 24044 : case IS_NOT_NULL:
1363 24044 : break;
1364 : }
1365 :
1366 25400 : return false; /* we can't succeed below... */
1367 : }
1368 : break;
1369 68654 : default:
1370 68654 : break;
1371 : }
1372 :
1373 : /*
1374 : * Finally, if both clauses are binary operator expressions, we may be
1375 : * able to prove something using the system's knowledge about operators.
1376 : */
1377 68654 : return operator_predicate_proof(predicate, clause, true, weak);
1378 : }
1379 :
1380 :
1381 : /*
1382 : * If clause asserts the non-truth of a subclause, return that subclause;
1383 : * otherwise return NULL.
1384 : */
1385 : static Node *
1386 178474 : extract_not_arg(Node *clause)
1387 : {
1388 178474 : if (clause == NULL)
1389 0 : return NULL;
1390 178474 : if (IsA(clause, BoolExpr))
1391 : {
1392 456 : BoolExpr *bexpr = (BoolExpr *) clause;
1393 :
1394 456 : if (bexpr->boolop == NOT_EXPR)
1395 456 : return (Node *) linitial(bexpr->args);
1396 : }
1397 178018 : else if (IsA(clause, BooleanTest))
1398 : {
1399 1630 : BooleanTest *btest = (BooleanTest *) clause;
1400 :
1401 1630 : if (btest->booltesttype == IS_NOT_TRUE ||
1402 860 : btest->booltesttype == IS_FALSE ||
1403 856 : btest->booltesttype == IS_UNKNOWN)
1404 826 : return (Node *) btest->arg;
1405 : }
1406 177192 : return NULL;
1407 : }
1408 :
1409 : /*
1410 : * If clause asserts the falsity of a subclause, return that subclause;
1411 : * otherwise return NULL.
1412 : */
1413 : static Node *
1414 176780 : extract_strong_not_arg(Node *clause)
1415 : {
1416 176780 : if (clause == NULL)
1417 0 : return NULL;
1418 176780 : if (IsA(clause, BoolExpr))
1419 : {
1420 400 : BoolExpr *bexpr = (BoolExpr *) clause;
1421 :
1422 400 : if (bexpr->boolop == NOT_EXPR)
1423 400 : return (Node *) linitial(bexpr->args);
1424 : }
1425 176380 : else if (IsA(clause, BooleanTest))
1426 : {
1427 1556 : BooleanTest *btest = (BooleanTest *) clause;
1428 :
1429 1556 : if (btest->booltesttype == IS_FALSE)
1430 12 : return (Node *) btest->arg;
1431 : }
1432 176368 : return NULL;
1433 : }
1434 :
1435 :
1436 : /*
1437 : * Can we prove that "clause" returns NULL (or FALSE) if "subexpr" is
1438 : * assumed to yield NULL?
1439 : *
1440 : * In most places in the planner, "strictness" refers to a guarantee that
1441 : * an expression yields NULL output for a NULL input, and that's mostly what
1442 : * we're looking for here. However, at top level where the clause is known
1443 : * to yield boolean, it may be sufficient to prove that it cannot return TRUE
1444 : * when "subexpr" is NULL. The caller should pass allow_false = true when
1445 : * this weaker property is acceptable. (When this function recurses
1446 : * internally, we pass down allow_false = false since we need to prove actual
1447 : * nullness of the subexpression.)
1448 : *
1449 : * We assume that the caller checked that least one of the input expressions
1450 : * is immutable. All of the proof rules here involve matching "subexpr" to
1451 : * some portion of "clause", so that this allows assuming that "subexpr" is
1452 : * immutable without a separate check.
1453 : *
1454 : * The base case is that clause and subexpr are equal().
1455 : *
1456 : * We can also report success if the subexpr appears as a subexpression
1457 : * of "clause" in a place where it'd force nullness of the overall result.
1458 : */
1459 : static bool
1460 13076 : clause_is_strict_for(Node *clause, Node *subexpr, bool allow_false)
1461 : {
1462 : ListCell *lc;
1463 :
1464 : /* safety checks */
1465 13076 : if (clause == NULL || subexpr == NULL)
1466 0 : return false;
1467 :
1468 : /*
1469 : * Look through any RelabelType nodes, so that we can match, say,
1470 : * varcharcol with lower(varcharcol::text). (In general we could recurse
1471 : * through any nullness-preserving, immutable operation.) We should not
1472 : * see stacked RelabelTypes here.
1473 : */
1474 13076 : if (IsA(clause, RelabelType))
1475 26 : clause = (Node *) ((RelabelType *) clause)->arg;
1476 13076 : if (IsA(subexpr, RelabelType))
1477 0 : subexpr = (Node *) ((RelabelType *) subexpr)->arg;
1478 :
1479 : /* Base case */
1480 13076 : if (equal(clause, subexpr))
1481 1730 : return true;
1482 :
1483 : /*
1484 : * If we have a strict operator or function, a NULL result is guaranteed
1485 : * if any input is forced NULL by subexpr. This is OK even if the op or
1486 : * func isn't immutable, since it won't even be called on NULL input.
1487 : */
1488 15794 : if (is_opclause(clause) &&
1489 4448 : op_strict(((OpExpr *) clause)->opno))
1490 : {
1491 10022 : foreach(lc, ((OpExpr *) clause)->args)
1492 : {
1493 7238 : if (clause_is_strict_for((Node *) lfirst(lc), subexpr, false))
1494 1664 : return true;
1495 : }
1496 2784 : return false;
1497 : }
1498 6948 : if (is_funcclause(clause) &&
1499 50 : func_strict(((FuncExpr *) clause)->funcid))
1500 : {
1501 82 : foreach(lc, ((FuncExpr *) clause)->args)
1502 : {
1503 56 : if (clause_is_strict_for((Node *) lfirst(lc), subexpr, false))
1504 24 : return true;
1505 : }
1506 26 : return false;
1507 : }
1508 :
1509 : /*
1510 : * CoerceViaIO is strict (whether or not the I/O functions it calls are).
1511 : * Likewise, ArrayCoerceExpr is strict for its array argument (regardless
1512 : * of what the per-element expression is), ConvertRowtypeExpr is strict at
1513 : * the row level, and CoerceToDomain is strict too. These are worth
1514 : * checking mainly because it saves us having to explain to users why some
1515 : * type coercions are known strict and others aren't.
1516 : */
1517 6848 : if (IsA(clause, CoerceViaIO))
1518 0 : return clause_is_strict_for((Node *) ((CoerceViaIO *) clause)->arg,
1519 : subexpr, false);
1520 6848 : if (IsA(clause, ArrayCoerceExpr))
1521 0 : return clause_is_strict_for((Node *) ((ArrayCoerceExpr *) clause)->arg,
1522 : subexpr, false);
1523 6848 : if (IsA(clause, ConvertRowtypeExpr))
1524 0 : return clause_is_strict_for((Node *) ((ConvertRowtypeExpr *) clause)->arg,
1525 : subexpr, false);
1526 6848 : if (IsA(clause, CoerceToDomain))
1527 0 : return clause_is_strict_for((Node *) ((CoerceToDomain *) clause)->arg,
1528 : subexpr, false);
1529 :
1530 : /*
1531 : * ScalarArrayOpExpr is a special case. Note that we'd only reach here
1532 : * with a ScalarArrayOpExpr clause if we failed to deconstruct it into an
1533 : * AND or OR tree, as for example if it has too many array elements.
1534 : */
1535 6848 : if (IsA(clause, ScalarArrayOpExpr))
1536 : {
1537 44 : ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause;
1538 44 : Node *scalarnode = (Node *) linitial(saop->args);
1539 44 : Node *arraynode = (Node *) lsecond(saop->args);
1540 :
1541 : /*
1542 : * If we can prove the scalar input to be null, and the operator is
1543 : * strict, then the SAOP result has to be null --- unless the array is
1544 : * empty. For an empty array, we'd get either false (for ANY) or true
1545 : * (for ALL). So if allow_false = true then the proof succeeds anyway
1546 : * for the ANY case; otherwise we can only make the proof if we can
1547 : * prove the array non-empty.
1548 : */
1549 86 : if (clause_is_strict_for(scalarnode, subexpr, false) &&
1550 42 : op_strict(saop->opno))
1551 : {
1552 42 : int nelems = 0;
1553 :
1554 42 : if (allow_false && saop->useOr)
1555 14 : return true; /* can succeed even if array is empty */
1556 :
1557 28 : if (arraynode && IsA(arraynode, Const))
1558 6 : {
1559 6 : Const *arrayconst = (Const *) arraynode;
1560 : ArrayType *arrval;
1561 :
1562 : /*
1563 : * If array is constant NULL then we can succeed, as in the
1564 : * case below.
1565 : */
1566 6 : if (arrayconst->constisnull)
1567 0 : return true;
1568 :
1569 : /* Otherwise, we can compute the number of elements. */
1570 6 : arrval = DatumGetArrayTypeP(arrayconst->constvalue);
1571 6 : nelems = ArrayGetNItems(ARR_NDIM(arrval), ARR_DIMS(arrval));
1572 : }
1573 22 : else if (arraynode && IsA(arraynode, ArrayExpr) &&
1574 2 : !((ArrayExpr *) arraynode)->multidims)
1575 : {
1576 : /*
1577 : * We can also reliably count the number of array elements if
1578 : * the input is a non-multidim ARRAY[] expression.
1579 : */
1580 2 : nelems = list_length(((ArrayExpr *) arraynode)->elements);
1581 : }
1582 :
1583 : /* Proof succeeds if array is definitely non-empty */
1584 28 : if (nelems > 0)
1585 8 : return true;
1586 : }
1587 :
1588 : /*
1589 : * If we can prove the array input to be null, the proof succeeds in
1590 : * all cases, since ScalarArrayOpExpr will always return NULL for a
1591 : * NULL array. Otherwise, we're done here.
1592 : */
1593 22 : return clause_is_strict_for(arraynode, subexpr, false);
1594 : }
1595 :
1596 : /*
1597 : * When recursing into an expression, we might find a NULL constant.
1598 : * That's certainly NULL, whether it matches subexpr or not.
1599 : */
1600 6804 : if (IsA(clause, Const))
1601 2648 : return ((Const *) clause)->constisnull;
1602 :
1603 4156 : return false;
1604 : }
1605 :
1606 :
1607 : /*
1608 : * Define "operator implication tables" for btree operators ("strategies"),
1609 : * and similar tables for refutation.
1610 : *
1611 : * The strategy numbers defined by btree indexes (see access/stratnum.h) are:
1612 : * 1 < 2 <= 3 = 4 >= 5 >
1613 : * and in addition we use 6 to represent <>. <> is not a btree-indexable
1614 : * operator, but we assume here that if an equality operator of a btree
1615 : * opfamily has a negator operator, the negator behaves as <> for the opfamily.
1616 : * (This convention is also known to get_op_btree_interpretation().)
1617 : *
1618 : * BT_implies_table[] and BT_refutes_table[] are used for cases where we have
1619 : * two identical subexpressions and we want to know whether one operator
1620 : * expression implies or refutes the other. That is, if the "clause" is
1621 : * EXPR1 clause_op EXPR2 and the "predicate" is EXPR1 pred_op EXPR2 for the
1622 : * same two (immutable) subexpressions:
1623 : * BT_implies_table[clause_op-1][pred_op-1]
1624 : * is true if the clause implies the predicate
1625 : * BT_refutes_table[clause_op-1][pred_op-1]
1626 : * is true if the clause refutes the predicate
1627 : * where clause_op and pred_op are strategy numbers (from 1 to 6) in the
1628 : * same btree opfamily. For example, "x < y" implies "x <= y" and refutes
1629 : * "x > y".
1630 : *
1631 : * BT_implic_table[] and BT_refute_table[] are used where we have two
1632 : * constants that we need to compare. The interpretation of:
1633 : *
1634 : * test_op = BT_implic_table[clause_op-1][pred_op-1]
1635 : *
1636 : * where test_op, clause_op and pred_op are strategy numbers (from 1 to 6)
1637 : * of btree operators, is as follows:
1638 : *
1639 : * If you know, for some EXPR, that "EXPR clause_op CONST1" is true, and you
1640 : * want to determine whether "EXPR pred_op CONST2" must also be true, then
1641 : * you can use "CONST2 test_op CONST1" as a test. If this test returns true,
1642 : * then the predicate expression must be true; if the test returns false,
1643 : * then the predicate expression may be false.
1644 : *
1645 : * For example, if clause is "Quantity > 10" and pred is "Quantity > 5"
1646 : * then we test "5 <= 10" which evals to true, so clause implies pred.
1647 : *
1648 : * Similarly, the interpretation of a BT_refute_table entry is:
1649 : *
1650 : * If you know, for some EXPR, that "EXPR clause_op CONST1" is true, and you
1651 : * want to determine whether "EXPR pred_op CONST2" must be false, then
1652 : * you can use "CONST2 test_op CONST1" as a test. If this test returns true,
1653 : * then the predicate expression must be false; if the test returns false,
1654 : * then the predicate expression may be true.
1655 : *
1656 : * For example, if clause is "Quantity > 10" and pred is "Quantity < 5"
1657 : * then we test "5 <= 10" which evals to true, so clause refutes pred.
1658 : *
1659 : * An entry where test_op == 0 means the implication cannot be determined.
1660 : */
1661 :
1662 : #define BTLT BTLessStrategyNumber
1663 : #define BTLE BTLessEqualStrategyNumber
1664 : #define BTEQ BTEqualStrategyNumber
1665 : #define BTGE BTGreaterEqualStrategyNumber
1666 : #define BTGT BTGreaterStrategyNumber
1667 : #define BTNE ROWCOMPARE_NE
1668 :
1669 : /* We use "none" for 0/false to make the tables align nicely */
1670 : #define none 0
1671 :
1672 : static const bool BT_implies_table[6][6] = {
1673 : /*
1674 : * The predicate operator:
1675 : * LT LE EQ GE GT NE
1676 : */
1677 : {true, true, none, none, none, true}, /* LT */
1678 : {none, true, none, none, none, none}, /* LE */
1679 : {none, true, true, true, none, none}, /* EQ */
1680 : {none, none, none, true, none, none}, /* GE */
1681 : {none, none, none, true, true, true}, /* GT */
1682 : {none, none, none, none, none, true} /* NE */
1683 : };
1684 :
1685 : static const bool BT_refutes_table[6][6] = {
1686 : /*
1687 : * The predicate operator:
1688 : * LT LE EQ GE GT NE
1689 : */
1690 : {none, none, true, true, true, none}, /* LT */
1691 : {none, none, none, none, true, none}, /* LE */
1692 : {true, none, none, none, true, true}, /* EQ */
1693 : {true, none, none, none, none, none}, /* GE */
1694 : {true, true, true, none, none, none}, /* GT */
1695 : {none, none, true, none, none, none} /* NE */
1696 : };
1697 :
1698 : static const StrategyNumber BT_implic_table[6][6] = {
1699 : /*
1700 : * The predicate operator:
1701 : * LT LE EQ GE GT NE
1702 : */
1703 : {BTGE, BTGE, none, none, none, BTGE}, /* LT */
1704 : {BTGT, BTGE, none, none, none, BTGT}, /* LE */
1705 : {BTGT, BTGE, BTEQ, BTLE, BTLT, BTNE}, /* EQ */
1706 : {none, none, none, BTLE, BTLT, BTLT}, /* GE */
1707 : {none, none, none, BTLE, BTLE, BTLE}, /* GT */
1708 : {none, none, none, none, none, BTEQ} /* NE */
1709 : };
1710 :
1711 : static const StrategyNumber BT_refute_table[6][6] = {
1712 : /*
1713 : * The predicate operator:
1714 : * LT LE EQ GE GT NE
1715 : */
1716 : {none, none, BTGE, BTGE, BTGE, none}, /* LT */
1717 : {none, none, BTGT, BTGT, BTGE, none}, /* LE */
1718 : {BTLE, BTLT, BTNE, BTGT, BTGE, BTEQ}, /* EQ */
1719 : {BTLE, BTLT, BTLT, none, none, none}, /* GE */
1720 : {BTLE, BTLE, BTLE, none, none, none}, /* GT */
1721 : {none, none, BTEQ, none, none, none} /* NE */
1722 : };
1723 :
1724 :
1725 : /*
1726 : * operator_predicate_proof
1727 : * Does the predicate implication or refutation test for a "simple clause"
1728 : * predicate and a "simple clause" restriction, when both are operator
1729 : * clauses using related operators and identical input expressions.
1730 : *
1731 : * When refute_it == false, we want to prove the predicate true;
1732 : * when refute_it == true, we want to prove the predicate false.
1733 : * (There is enough common code to justify handling these two cases
1734 : * in one routine.) We return true if able to make the proof, false
1735 : * if not able to prove it.
1736 : *
1737 : * We mostly need not distinguish strong vs. weak implication/refutation here.
1738 : * This depends on the assumption that a pair of related operators (i.e.,
1739 : * commutators, negators, or btree opfamily siblings) will not return one NULL
1740 : * and one non-NULL result for the same inputs. Then, for the proof types
1741 : * where we start with an assumption of truth of the clause, the predicate
1742 : * operator could not return NULL either, so it doesn't matter whether we are
1743 : * trying to make a strong or weak proof. For weak implication, it could be
1744 : * that the clause operator returned NULL, but then the predicate operator
1745 : * would as well, so that the weak implication still holds. This argument
1746 : * doesn't apply in the case where we are considering two different constant
1747 : * values, since then the operators aren't being given identical inputs. But
1748 : * we only support that for btree operators, for which we can assume that all
1749 : * non-null inputs result in non-null outputs, so that it doesn't matter which
1750 : * two non-null constants we consider. If either constant is NULL, we have
1751 : * to think harder, but sometimes the proof still works, as explained below.
1752 : *
1753 : * We can make proofs involving several expression forms (here "foo" and "bar"
1754 : * represent subexpressions that are identical according to equal()):
1755 : * "foo op1 bar" refutes "foo op2 bar" if op1 is op2's negator
1756 : * "foo op1 bar" implies "bar op2 foo" if op1 is op2's commutator
1757 : * "foo op1 bar" refutes "bar op2 foo" if op1 is negator of op2's commutator
1758 : * "foo op1 bar" can imply/refute "foo op2 bar" based on btree semantics
1759 : * "foo op1 bar" can imply/refute "bar op2 foo" based on btree semantics
1760 : * "foo op1 const1" can imply/refute "foo op2 const2" based on btree semantics
1761 : *
1762 : * For the last three cases, op1 and op2 have to be members of the same btree
1763 : * operator family. When both subexpressions are identical, the idea is that,
1764 : * for instance, x < y implies x <= y, independently of exactly what x and y
1765 : * are. If we have two different constants compared to the same expression
1766 : * foo, we have to execute a comparison between the two constant values
1767 : * in order to determine the result; for instance, foo < c1 implies foo < c2
1768 : * if c1 <= c2. We assume it's safe to compare the constants at plan time
1769 : * if the comparison operator is immutable.
1770 : *
1771 : * Note: all the operators and subexpressions have to be immutable for the
1772 : * proof to be safe. We assume the predicate expression is entirely immutable,
1773 : * so no explicit check on the subexpressions is needed here, but in some
1774 : * cases we need an extra check of operator immutability. In particular,
1775 : * btree opfamilies can contain cross-type operators that are merely stable,
1776 : * and we dare not make deductions with those.
1777 : */
1778 : static bool
1779 181896 : operator_predicate_proof(Expr *predicate, Node *clause,
1780 : bool refute_it, bool weak)
1781 : {
1782 : OpExpr *pred_opexpr,
1783 : *clause_opexpr;
1784 : Oid pred_collation,
1785 : clause_collation;
1786 : Oid pred_op,
1787 : clause_op,
1788 : test_op;
1789 : Node *pred_leftop,
1790 : *pred_rightop,
1791 : *clause_leftop,
1792 : *clause_rightop;
1793 : Const *pred_const,
1794 : *clause_const;
1795 : Expr *test_expr;
1796 : ExprState *test_exprstate;
1797 : Datum test_result;
1798 : bool isNull;
1799 : EState *estate;
1800 : MemoryContext oldcontext;
1801 :
1802 : /*
1803 : * Both expressions must be binary opclauses, else we can't do anything.
1804 : *
1805 : * Note: in future we might extend this logic to other operator-based
1806 : * constructs such as DistinctExpr. But the planner isn't very smart
1807 : * about DistinctExpr in general, and this probably isn't the first place
1808 : * to fix if you want to improve that.
1809 : */
1810 181896 : if (!is_opclause(predicate))
1811 34804 : return false;
1812 147092 : pred_opexpr = (OpExpr *) predicate;
1813 147092 : if (list_length(pred_opexpr->args) != 2)
1814 0 : return false;
1815 147092 : if (!is_opclause(clause))
1816 5926 : return false;
1817 141166 : clause_opexpr = (OpExpr *) clause;
1818 141166 : if (list_length(clause_opexpr->args) != 2)
1819 0 : return false;
1820 :
1821 : /*
1822 : * If they're marked with different collations then we can't do anything.
1823 : * This is a cheap test so let's get it out of the way early.
1824 : */
1825 141166 : pred_collation = pred_opexpr->inputcollid;
1826 141166 : clause_collation = clause_opexpr->inputcollid;
1827 141166 : if (pred_collation != clause_collation)
1828 21028 : return false;
1829 :
1830 : /* Grab the operator OIDs now too. We may commute these below. */
1831 120138 : pred_op = pred_opexpr->opno;
1832 120138 : clause_op = clause_opexpr->opno;
1833 :
1834 : /*
1835 : * We have to match up at least one pair of input expressions.
1836 : */
1837 120138 : pred_leftop = (Node *) linitial(pred_opexpr->args);
1838 120138 : pred_rightop = (Node *) lsecond(pred_opexpr->args);
1839 120138 : clause_leftop = (Node *) linitial(clause_opexpr->args);
1840 120138 : clause_rightop = (Node *) lsecond(clause_opexpr->args);
1841 :
1842 120138 : if (equal(pred_leftop, clause_leftop))
1843 : {
1844 41266 : if (equal(pred_rightop, clause_rightop))
1845 : {
1846 : /* We have x op1 y and x op2 y */
1847 4672 : return operator_same_subexprs_proof(pred_op, clause_op, refute_it);
1848 : }
1849 : else
1850 : {
1851 : /* Fail unless rightops are both Consts */
1852 36594 : if (pred_rightop == NULL || !IsA(pred_rightop, Const))
1853 1632 : return false;
1854 34962 : pred_const = (Const *) pred_rightop;
1855 34962 : if (clause_rightop == NULL || !IsA(clause_rightop, Const))
1856 62 : return false;
1857 34900 : clause_const = (Const *) clause_rightop;
1858 : }
1859 : }
1860 78872 : else if (equal(pred_rightop, clause_rightop))
1861 : {
1862 : /* Fail unless leftops are both Consts */
1863 3266 : if (pred_leftop == NULL || !IsA(pred_leftop, Const))
1864 3258 : return false;
1865 8 : pred_const = (Const *) pred_leftop;
1866 8 : if (clause_leftop == NULL || !IsA(clause_leftop, Const))
1867 0 : return false;
1868 8 : clause_const = (Const *) clause_leftop;
1869 : /* Commute both operators so we can assume Consts are on the right */
1870 8 : pred_op = get_commutator(pred_op);
1871 8 : if (!OidIsValid(pred_op))
1872 0 : return false;
1873 8 : clause_op = get_commutator(clause_op);
1874 8 : if (!OidIsValid(clause_op))
1875 0 : return false;
1876 : }
1877 75606 : else if (equal(pred_leftop, clause_rightop))
1878 : {
1879 916 : if (equal(pred_rightop, clause_leftop))
1880 : {
1881 : /* We have x op1 y and y op2 x */
1882 : /* Commute pred_op that we can treat this like a straight match */
1883 812 : pred_op = get_commutator(pred_op);
1884 812 : if (!OidIsValid(pred_op))
1885 0 : return false;
1886 812 : return operator_same_subexprs_proof(pred_op, clause_op, refute_it);
1887 : }
1888 : else
1889 : {
1890 : /* Fail unless pred_rightop/clause_leftop are both Consts */
1891 104 : if (pred_rightop == NULL || !IsA(pred_rightop, Const))
1892 96 : return false;
1893 8 : pred_const = (Const *) pred_rightop;
1894 8 : if (clause_leftop == NULL || !IsA(clause_leftop, Const))
1895 0 : return false;
1896 8 : clause_const = (Const *) clause_leftop;
1897 : /* Commute clause_op so we can assume Consts are on the right */
1898 8 : clause_op = get_commutator(clause_op);
1899 8 : if (!OidIsValid(clause_op))
1900 0 : return false;
1901 : }
1902 : }
1903 74690 : else if (equal(pred_rightop, clause_leftop))
1904 : {
1905 : /* Fail unless pred_leftop/clause_rightop are both Consts */
1906 146 : if (pred_leftop == NULL || !IsA(pred_leftop, Const))
1907 106 : return false;
1908 40 : pred_const = (Const *) pred_leftop;
1909 40 : if (clause_rightop == NULL || !IsA(clause_rightop, Const))
1910 0 : return false;
1911 40 : clause_const = (Const *) clause_rightop;
1912 : /* Commute pred_op so we can assume Consts are on the right */
1913 40 : pred_op = get_commutator(pred_op);
1914 40 : if (!OidIsValid(pred_op))
1915 0 : return false;
1916 : }
1917 : else
1918 : {
1919 : /* Failed to match up any of the subexpressions, so we lose */
1920 74544 : return false;
1921 : }
1922 :
1923 : /*
1924 : * We have two identical subexpressions, and two other subexpressions that
1925 : * are not identical but are both Consts; and we have commuted the
1926 : * operators if necessary so that the Consts are on the right. We'll need
1927 : * to compare the Consts' values. If either is NULL, we can't do that, so
1928 : * usually the proof fails ... but in some cases we can claim success.
1929 : */
1930 34956 : if (clause_const->constisnull)
1931 : {
1932 : /* If clause_op isn't strict, we can't prove anything */
1933 4 : if (!op_strict(clause_op))
1934 0 : return false;
1935 :
1936 : /*
1937 : * At this point we know that the clause returns NULL. For proof
1938 : * types that assume truth of the clause, this means the proof is
1939 : * vacuously true (a/k/a "false implies anything"). That's all proof
1940 : * types except weak implication.
1941 : */
1942 4 : if (!(weak && !refute_it))
1943 2 : return true;
1944 :
1945 : /*
1946 : * For weak implication, it's still possible for the proof to succeed,
1947 : * if the predicate can also be proven NULL. In that case we've got
1948 : * NULL => NULL which is valid for this proof type.
1949 : */
1950 2 : if (pred_const->constisnull && op_strict(pred_op))
1951 0 : return true;
1952 : /* Else the proof fails */
1953 2 : return false;
1954 : }
1955 34952 : if (pred_const->constisnull)
1956 : {
1957 : /*
1958 : * If the pred_op is strict, we know the predicate yields NULL, which
1959 : * means the proof succeeds for either weak implication or weak
1960 : * refutation.
1961 : */
1962 20 : if (weak && op_strict(pred_op))
1963 12 : return true;
1964 : /* Else the proof fails */
1965 8 : return false;
1966 : }
1967 :
1968 : /*
1969 : * Lookup the constant-comparison operator using the system catalogs and
1970 : * the operator implication tables.
1971 : */
1972 34932 : test_op = get_btree_test_op(pred_op, clause_op, refute_it);
1973 :
1974 34932 : if (!OidIsValid(test_op))
1975 : {
1976 : /* couldn't find a suitable comparison operator */
1977 15996 : return false;
1978 : }
1979 :
1980 : /*
1981 : * Evaluate the test. For this we need an EState.
1982 : */
1983 18936 : estate = CreateExecutorState();
1984 :
1985 : /* We can use the estate's working context to avoid memory leaks. */
1986 18936 : oldcontext = MemoryContextSwitchTo(estate->es_query_cxt);
1987 :
1988 : /* Build expression tree */
1989 18936 : test_expr = make_opclause(test_op,
1990 : BOOLOID,
1991 : false,
1992 : (Expr *) pred_const,
1993 : (Expr *) clause_const,
1994 : InvalidOid,
1995 : pred_collation);
1996 :
1997 : /* Fill in opfuncids */
1998 18936 : fix_opfuncids((Node *) test_expr);
1999 :
2000 : /* Prepare it for execution */
2001 18936 : test_exprstate = ExecInitExpr(test_expr, NULL);
2002 :
2003 : /* And execute it. */
2004 18936 : test_result = ExecEvalExprSwitchContext(test_exprstate,
2005 18936 : GetPerTupleExprContext(estate),
2006 : &isNull);
2007 :
2008 : /* Get back to outer memory context */
2009 18936 : MemoryContextSwitchTo(oldcontext);
2010 :
2011 : /* Release all the junk we just created */
2012 18936 : FreeExecutorState(estate);
2013 :
2014 18936 : if (isNull)
2015 : {
2016 : /* Treat a null result as non-proof ... but it's a tad fishy ... */
2017 0 : elog(DEBUG2, "null predicate test result");
2018 0 : return false;
2019 : }
2020 18936 : return DatumGetBool(test_result);
2021 : }
2022 :
2023 :
2024 : /*
2025 : * operator_same_subexprs_proof
2026 : * Assuming that EXPR1 clause_op EXPR2 is true, try to prove or refute
2027 : * EXPR1 pred_op EXPR2.
2028 : *
2029 : * Return true if able to make the proof, false if not able to prove it.
2030 : */
2031 : static bool
2032 5484 : operator_same_subexprs_proof(Oid pred_op, Oid clause_op, bool refute_it)
2033 : {
2034 : /*
2035 : * A simple and general rule is that the predicate is proven if clause_op
2036 : * and pred_op are the same, or refuted if they are each other's negators.
2037 : * We need not check immutability since the pred_op is already known
2038 : * immutable. (Actually, by this point we may have the commutator of a
2039 : * known-immutable pred_op, but that should certainly be immutable too.
2040 : * Likewise we don't worry whether the pred_op's negator is immutable.)
2041 : *
2042 : * Note: the "same" case won't get here if we actually had EXPR1 clause_op
2043 : * EXPR2 and EXPR1 pred_op EXPR2, because the overall-expression-equality
2044 : * test in predicate_implied_by_simple_clause would have caught it. But
2045 : * we can see the same operator after having commuted the pred_op.
2046 : */
2047 5484 : if (refute_it)
2048 : {
2049 4526 : if (get_negator(pred_op) == clause_op)
2050 1846 : return true;
2051 : }
2052 : else
2053 : {
2054 958 : if (pred_op == clause_op)
2055 776 : return true;
2056 : }
2057 :
2058 : /*
2059 : * Otherwise, see if we can determine the implication by finding the
2060 : * operators' relationship via some btree opfamily.
2061 : */
2062 2862 : return operator_same_subexprs_lookup(pred_op, clause_op, refute_it);
2063 : }
2064 :
2065 :
2066 : /*
2067 : * We use a lookaside table to cache the result of btree proof operator
2068 : * lookups, since the actual lookup is pretty expensive and doesn't change
2069 : * for any given pair of operators (at least as long as pg_amop doesn't
2070 : * change). A single hash entry stores both implication and refutation
2071 : * results for a given pair of operators; but note we may have determined
2072 : * only one of those sets of results as yet.
2073 : */
2074 : typedef struct OprProofCacheKey
2075 : {
2076 : Oid pred_op; /* predicate operator */
2077 : Oid clause_op; /* clause operator */
2078 : } OprProofCacheKey;
2079 :
2080 : typedef struct OprProofCacheEntry
2081 : {
2082 : /* the hash lookup key MUST BE FIRST */
2083 : OprProofCacheKey key;
2084 :
2085 : bool have_implic; /* do we know the implication result? */
2086 : bool have_refute; /* do we know the refutation result? */
2087 : bool same_subexprs_implies; /* X clause_op Y implies X pred_op Y? */
2088 : bool same_subexprs_refutes; /* X clause_op Y refutes X pred_op Y? */
2089 : Oid implic_test_op; /* OID of the test operator, or 0 if none */
2090 : Oid refute_test_op; /* OID of the test operator, or 0 if none */
2091 : } OprProofCacheEntry;
2092 :
2093 : static HTAB *OprProofCacheHash = NULL;
2094 :
2095 :
2096 : /*
2097 : * lookup_proof_cache
2098 : * Get, and fill in if necessary, the appropriate cache entry.
2099 : */
2100 : static OprProofCacheEntry *
2101 37794 : lookup_proof_cache(Oid pred_op, Oid clause_op, bool refute_it)
2102 : {
2103 : OprProofCacheKey key;
2104 : OprProofCacheEntry *cache_entry;
2105 : bool cfound;
2106 37794 : bool same_subexprs = false;
2107 37794 : Oid test_op = InvalidOid;
2108 37794 : bool found = false;
2109 : List *pred_op_infos,
2110 : *clause_op_infos;
2111 : ListCell *lcp,
2112 : *lcc;
2113 :
2114 : /*
2115 : * Find or make a cache entry for this pair of operators.
2116 : */
2117 37794 : if (OprProofCacheHash == NULL)
2118 : {
2119 : /* First time through: initialize the hash table */
2120 : HASHCTL ctl;
2121 :
2122 324 : ctl.keysize = sizeof(OprProofCacheKey);
2123 324 : ctl.entrysize = sizeof(OprProofCacheEntry);
2124 324 : OprProofCacheHash = hash_create("Btree proof lookup cache", 256,
2125 : &ctl, HASH_ELEM | HASH_BLOBS);
2126 :
2127 : /* Arrange to flush cache on pg_amop changes */
2128 324 : CacheRegisterSyscacheCallback(AMOPOPID,
2129 : InvalidateOprProofCacheCallBack,
2130 : (Datum) 0);
2131 : }
2132 :
2133 37794 : key.pred_op = pred_op;
2134 37794 : key.clause_op = clause_op;
2135 37794 : cache_entry = (OprProofCacheEntry *) hash_search(OprProofCacheHash,
2136 : &key,
2137 : HASH_ENTER, &cfound);
2138 37794 : if (!cfound)
2139 : {
2140 : /* new cache entry, set it invalid */
2141 1168 : cache_entry->have_implic = false;
2142 1168 : cache_entry->have_refute = false;
2143 : }
2144 : else
2145 : {
2146 : /* pre-existing cache entry, see if we know the answer yet */
2147 36626 : if (refute_it ? cache_entry->have_refute : cache_entry->have_implic)
2148 36550 : return cache_entry;
2149 : }
2150 :
2151 : /*
2152 : * Try to find a btree opfamily containing the given operators.
2153 : *
2154 : * We must find a btree opfamily that contains both operators, else the
2155 : * implication can't be determined. Also, the opfamily must contain a
2156 : * suitable test operator taking the operators' righthand datatypes.
2157 : *
2158 : * If there are multiple matching opfamilies, assume we can use any one to
2159 : * determine the logical relationship of the two operators and the correct
2160 : * corresponding test operator. This should work for any logically
2161 : * consistent opfamilies.
2162 : *
2163 : * Note that we can determine the operators' relationship for
2164 : * same-subexprs cases even from an opfamily that lacks a usable test
2165 : * operator. This can happen in cases with incomplete sets of cross-type
2166 : * comparison operators.
2167 : */
2168 1244 : clause_op_infos = get_op_btree_interpretation(clause_op);
2169 1244 : if (clause_op_infos)
2170 1232 : pred_op_infos = get_op_btree_interpretation(pred_op);
2171 : else /* no point in looking */
2172 12 : pred_op_infos = NIL;
2173 :
2174 1470 : foreach(lcp, pred_op_infos)
2175 : {
2176 840 : OpBtreeInterpretation *pred_op_info = lfirst(lcp);
2177 840 : Oid opfamily_id = pred_op_info->opfamily_id;
2178 :
2179 1090 : foreach(lcc, clause_op_infos)
2180 : {
2181 864 : OpBtreeInterpretation *clause_op_info = lfirst(lcc);
2182 : StrategyNumber pred_strategy,
2183 : clause_strategy,
2184 : test_strategy;
2185 :
2186 : /* Must find them in same opfamily */
2187 864 : if (opfamily_id != clause_op_info->opfamily_id)
2188 24 : continue;
2189 : /* Lefttypes should match */
2190 : Assert(clause_op_info->oplefttype == pred_op_info->oplefttype);
2191 :
2192 840 : pred_strategy = pred_op_info->strategy;
2193 840 : clause_strategy = clause_op_info->strategy;
2194 :
2195 : /*
2196 : * Check to see if we can make a proof for same-subexpressions
2197 : * cases based on the operators' relationship in this opfamily.
2198 : */
2199 840 : if (refute_it)
2200 508 : same_subexprs |= BT_refutes_table[clause_strategy - 1][pred_strategy - 1];
2201 : else
2202 332 : same_subexprs |= BT_implies_table[clause_strategy - 1][pred_strategy - 1];
2203 :
2204 : /*
2205 : * Look up the "test" strategy number in the implication table
2206 : */
2207 840 : if (refute_it)
2208 508 : test_strategy = BT_refute_table[clause_strategy - 1][pred_strategy - 1];
2209 : else
2210 332 : test_strategy = BT_implic_table[clause_strategy - 1][pred_strategy - 1];
2211 :
2212 840 : if (test_strategy == 0)
2213 : {
2214 : /* Can't determine implication using this interpretation */
2215 226 : continue;
2216 : }
2217 :
2218 : /*
2219 : * See if opfamily has an operator for the test strategy and the
2220 : * datatypes.
2221 : */
2222 614 : if (test_strategy == BTNE)
2223 : {
2224 108 : test_op = get_opfamily_member(opfamily_id,
2225 : pred_op_info->oprighttype,
2226 : clause_op_info->oprighttype,
2227 : BTEqualStrategyNumber);
2228 108 : if (OidIsValid(test_op))
2229 108 : test_op = get_negator(test_op);
2230 : }
2231 : else
2232 : {
2233 506 : test_op = get_opfamily_member(opfamily_id,
2234 : pred_op_info->oprighttype,
2235 : clause_op_info->oprighttype,
2236 : test_strategy);
2237 : }
2238 :
2239 614 : if (!OidIsValid(test_op))
2240 0 : continue;
2241 :
2242 : /*
2243 : * Last check: test_op must be immutable.
2244 : *
2245 : * Note that we require only the test_op to be immutable, not the
2246 : * original clause_op. (pred_op is assumed to have been checked
2247 : * immutable by the caller.) Essentially we are assuming that the
2248 : * opfamily is consistent even if it contains operators that are
2249 : * merely stable.
2250 : */
2251 614 : if (op_volatile(test_op) == PROVOLATILE_IMMUTABLE)
2252 : {
2253 614 : found = true;
2254 614 : break;
2255 : }
2256 : }
2257 :
2258 840 : if (found)
2259 614 : break;
2260 : }
2261 :
2262 1244 : list_free_deep(pred_op_infos);
2263 1244 : list_free_deep(clause_op_infos);
2264 :
2265 1244 : if (!found)
2266 : {
2267 : /* couldn't find a suitable comparison operator */
2268 630 : test_op = InvalidOid;
2269 : }
2270 :
2271 : /*
2272 : * If we think we were able to prove something about same-subexpressions
2273 : * cases, check to make sure the clause_op is immutable before believing
2274 : * it completely. (Usually, the clause_op would be immutable if the
2275 : * pred_op is, but it's not entirely clear that this must be true in all
2276 : * cases, so let's check.)
2277 : */
2278 1580 : if (same_subexprs &&
2279 336 : op_volatile(clause_op) != PROVOLATILE_IMMUTABLE)
2280 0 : same_subexprs = false;
2281 :
2282 : /* Cache the results, whether positive or negative */
2283 1244 : if (refute_it)
2284 : {
2285 508 : cache_entry->refute_test_op = test_op;
2286 508 : cache_entry->same_subexprs_refutes = same_subexprs;
2287 508 : cache_entry->have_refute = true;
2288 : }
2289 : else
2290 : {
2291 736 : cache_entry->implic_test_op = test_op;
2292 736 : cache_entry->same_subexprs_implies = same_subexprs;
2293 736 : cache_entry->have_implic = true;
2294 : }
2295 :
2296 1244 : return cache_entry;
2297 : }
2298 :
2299 : /*
2300 : * operator_same_subexprs_lookup
2301 : * Convenience subroutine to look up the cached answer for
2302 : * same-subexpressions cases.
2303 : */
2304 : static bool
2305 2862 : operator_same_subexprs_lookup(Oid pred_op, Oid clause_op, bool refute_it)
2306 : {
2307 : OprProofCacheEntry *cache_entry;
2308 :
2309 2862 : cache_entry = lookup_proof_cache(pred_op, clause_op, refute_it);
2310 2862 : if (refute_it)
2311 2680 : return cache_entry->same_subexprs_refutes;
2312 : else
2313 182 : return cache_entry->same_subexprs_implies;
2314 : }
2315 :
2316 : /*
2317 : * get_btree_test_op
2318 : * Identify the comparison operator needed for a btree-operator
2319 : * proof or refutation involving comparison of constants.
2320 : *
2321 : * Given the truth of a clause "var clause_op const1", we are attempting to
2322 : * prove or refute a predicate "var pred_op const2". The identities of the
2323 : * two operators are sufficient to determine the operator (if any) to compare
2324 : * const2 to const1 with.
2325 : *
2326 : * Returns the OID of the operator to use, or InvalidOid if no proof is
2327 : * possible.
2328 : */
2329 : static Oid
2330 34932 : get_btree_test_op(Oid pred_op, Oid clause_op, bool refute_it)
2331 : {
2332 : OprProofCacheEntry *cache_entry;
2333 :
2334 34932 : cache_entry = lookup_proof_cache(pred_op, clause_op, refute_it);
2335 34932 : if (refute_it)
2336 31742 : return cache_entry->refute_test_op;
2337 : else
2338 3190 : return cache_entry->implic_test_op;
2339 : }
2340 :
2341 :
2342 : /*
2343 : * Callback for pg_amop inval events
2344 : */
2345 : static void
2346 562 : InvalidateOprProofCacheCallBack(Datum arg, int cacheid, uint32 hashvalue)
2347 : {
2348 : HASH_SEQ_STATUS status;
2349 : OprProofCacheEntry *hentry;
2350 :
2351 : Assert(OprProofCacheHash != NULL);
2352 :
2353 : /* Currently we just reset all entries; hard to be smarter ... */
2354 562 : hash_seq_init(&status, OprProofCacheHash);
2355 :
2356 4964 : while ((hentry = (OprProofCacheEntry *) hash_seq_search(&status)) != NULL)
2357 : {
2358 4402 : hentry->have_implic = false;
2359 4402 : hentry->have_refute = false;
2360 : }
2361 562 : }
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