opt: create library that determines how joins affect input rows

Previously, there was no simple way to determine whether all rows from
a join input will be included in its output, nor whether input rows will
be duplicated by the join.

This patch adds a library that constructs a Multiplicity struct for join
operators. The Multiplicity can be queried for information about how a
join will affect its input rows (e.g. duplicated, filtered and/or
null-extended). The existing SimplifyLeftJoinWithFilters rule has been
refactored to use this library. The Multiplicity library will also be
useful for future join elimination and limit pushdown rules.

Release note: None

pkg/sql/logictest/testdata/logic_test/fk

@@ -3198,3 +3198,24 @@ ALTER TABLE t2 DROP CONSTRAINT fk1; ALTER TABLE t2 DROP CONSTRAINT fk2; TRUNCATE
 
 statement ok
 DROP TABLE t2 CASCADE; DROP TABLE t1 CASCADE
+
+# Regression test for #49628.
+statement ok
+CREATE TABLE xyz (x INT, y INT, z INT, PRIMARY KEY (x, y, z));
+CREATE TABLE fk_ref
+(
+    a INT NOT NULL,
+    b INT,
+    c INT NOT NULL,
+    FOREIGN KEY (a, b, c) REFERENCES xyz (x, y, z)
+);
+INSERT INTO fk_ref (VALUES (1, NULL, 1));
+
+query IIIIII
+SELECT * FROM fk_ref LEFT JOIN xyz ON a = x
+----
+1  NULL  1  NULL  NULL  NULL
+
+statement ok
+DROP TABLE fk_ref;
+DROP TABLE xyz;

pkg/sql/logictest/testdata/logic_test/join

@@ -1093,3 +1093,22 @@ CREATE TABLE t44746_1(c1 INT)
 # Note: an "error parsing regexp" would also be acceptable here.
 statement ok
 SELECT * FROM t44746_0 FULL JOIN t44746_1 ON (SUBSTRING('', ')') = '') = (c1 > 0)
+
+# Regression test for #49630.
+statement ok
+DROP TABLE empty;
+CREATE TABLE xy (x INT PRIMARY KEY, y INT);
+CREATE TABLE fk_ref (r INT NOT NULL REFERENCES xy (x));
+CREATE TABLE empty (v INT);
+INSERT INTO xy (VALUES (1, 1));
+INSERT INTO fk_ref (VALUES (1));
+
+query IIII
+SELECT * FROM fk_ref LEFT JOIN (SELECT * FROM xy INNER JOIN empty ON True) ON r = x
+----
+1  NULL  NULL  NULL
+
+statement ok
+DROP TABLE empty;
+DROP TABLE fk_ref;
+DROP TABLE xy;

pkg/sql/opt/exec/execbuilder/testdata/enums

@@ -53,4 +53,3 @@ scan t
  └── constraint: /1
       ├── [/'hello' - /'hello']
       └── [/'hi' - /'hi']
-

pkg/sql/opt/memo/expr_format.go

@@ -686,6 +686,12 @@ func (f *ExprFmtCtx) formatRelational(e RelExpr, tp treeprinter.Node) {
 		if r.JoinSize > 1 {
 			tp.Childf("join-size: %d", r.JoinSize)
 		}
+		switch e.Op() {
+		case opt.InnerJoinOp, opt.LeftJoinOp, opt.FullJoinOp:
+			if s := r.MultiplicityProps.String(); (r.Available&props.MultiplicityProps) != 0 && s != "" {
+				tp.Childf("multiplicity: %s", s)
+			}
+		}
 		if withUses := relational.Shared.Rule.WithUses; len(withUses) > 0 {
 			n := tp.Childf("cte-uses")
 			ids := make([]opt.WithID, 0, len(withUses))