src/backend/optimizer/README

Optimizer
=========

These directories take the Query structure returned by the parser, and
generate a plan used by the executor.  The /plan directory generates the
actual output plan, the /path code generates all possible ways to join the
tables, and /prep handles various preprocessing steps for special cases.
/util is utility stuff.  /geqo is the separate "genetic optimization" planner
--- it does a semi-random search through the join tree space, rather than
exhaustively considering all possible join trees.  (But each join considered
by /geqo is given to /path to create paths for, so we consider all possible
implementation paths for each specific join pair even in GEQO mode.)


Paths and Join Pairs
--------------------

During the planning/optimizing process, we build "Path" trees representing
the different ways of doing a query.  We select the cheapest Path that
generates the desired relation and turn it into a Plan to pass to the
executor.  (There is pretty much a one-to-one correspondence between the
Path and Plan trees, but Path nodes omit info that won't be needed during
planning, and include info needed for planning that won't be needed by the
executor.)

The optimizer builds a RelOptInfo structure for each base relation used in
the query.  Base rels are either primitive tables, or subquery subselects
that are planned via a separate recursive invocation of the planner.  A
RelOptInfo is also built for each join relation that is considered during
planning.  A join rel is simply a combination of base rels.  There is only
one join RelOptInfo for any given set of baserels --- for example, the join
{A B C} is represented by the same RelOptInfo no matter whether we build it
by joining A and B first and then adding C, or joining B and C first and
then adding A, etc.  These different means of building the joinrel are
represented as Paths.  For each RelOptInfo we build a list of Paths that
represent plausible ways to implement the scan or join of that relation.
Once we've considered all the plausible Paths for a rel, we select the one
that is cheapest according to the planner's cost estimates.  The final plan
is derived from the cheapest Path for the RelOptInfo that includes all the
base rels of the query.

Possible Paths for a primitive table relation include plain old sequential
scan, plus index scans for any indexes that exist on the table, plus bitmap
index scans using one or more indexes.  A subquery base relation just has
one Path, a "SubqueryScan" path (which links to the subplan that was built
by a recursive invocation of the planner).  Likewise a function-RTE base
relation has only one possible Path.

Joins always occur using two RelOptInfos.  One is outer, the other inner.
Outers drive lookups of values in the inner.  In a nested loop, lookups of
values in the inner occur by scanning the inner path once per outer tuple
to find each matching inner row.  In a mergejoin, inner and outer rows are
ordered, and are accessed in order, so only one scan is required to perform
the entire join: both inner and outer paths are scanned in-sync.  (There's
not a lot of difference between inner and outer in a mergejoin...)  In a
hashjoin, the inner is scanned first and all its rows are entered in a
hashtable, then the outer is scanned and for each row we lookup the join
key in the hashtable.

A Path for a join relation is actually a tree structure, with the top
Path node representing the join method.  It has left and right subpaths
that represent the scan or join methods used for the two input relations.


Join Tree Construction
----------------------

The optimizer generates optimal query plans by doing a more-or-less
exhaustive search through the ways of executing the query.  The best Path
tree is found by a recursive process:

1) Take each base relation in the query, and make a RelOptInfo structure
for it.  Find each potentially useful way of accessing the relation,
including sequential and index scans, and make Paths representing those
ways.  All the Paths made for a given relation are placed in its
RelOptInfo.pathlist.  (Actually, we discard Paths that are obviously
inferior alternatives before they ever get into the pathlist --- what
ends up in the pathlist is the cheapest way of generating each potentially
useful sort ordering of the relation.)  Also create a RelOptInfo.joininfo
list including all the join clauses that involve this relation.  For
example, the WHERE clause "tab1.col1 = tab2.col1" generates entries in
both tab1 and tab2's joininfo lists.

If we have only a single base relation in the query, we are done.
Otherwise we have to figure out how to join the base relations into a
single join relation.

2) Normally, any explicit JOIN clauses are "flattened" so that we just
have a list of relations to join.  However, FULL OUTER JOIN clauses are
never flattened, and other kinds of JOIN might not be either, if the
flattening process is stopped by join_collapse_limit or from_collapse_limit
restrictions.  Therefore, we end up with a planning problem that contains
lists of relations to be joined in any order, where any individual item
might be a sub-list that has to be joined together before we can consider
joining it to its siblings.  We process these sub-problems recursively,
bottom up.  Note that the join list structure constrains the possible join
orders, but it doesn't constrain the join implementation method at each
join (nestloop, merge, hash), nor does it say which rel is considered outer
or inner at each join.  We consider all these possibilities in building
Paths. We generate a Path for each feasible join method, and select the
cheapest Path.

For each planning problem, therefore, we will have a list of relations
that are either base rels or joinrels constructed per sub-join-lists.
We can join these rels together in any order the planner sees fit.
The standard (non-GEQO) planner does this as follows:

Consider joining each RelOptInfo to each other RelOptInfo for which there
is a usable joinclause, and generate a Path for each possible join method
for each such pair.  (If we have a RelOptInfo with no join clauses, we have
no choice but to generate a clauseless Cartesian-product join; so we
consider joining that rel to each other available rel.  But in the presence
of join clauses we will only consider joins that use available join
clauses.  Note that join-order restrictions induced by outer joins and
IN/EXISTS clauses are also checked, to ensure that we find a workable join
order in cases where those restrictions force a clauseless join to be done.)

If we only had two relations in the list, we are done: we just pick
the cheapest path for the join RelOptInfo.  If we had more than two, we now
need to consider ways of joining join RelOptInfos to each other to make
join RelOptInfos that represent more than two list items.

The join tree is constructed using a "dynamic programming" algorithm:
in the first pass (already described) we consider ways to create join rels
representing exactly two list items.  The second pass considers ways
to make join rels that represent exactly three list items; the next pass,
four items, etc.  The last pass considers how to make the final join
relation that includes all list items --- obviously there can be only one
join rel at this top level, whereas there can be more than one join rel
at lower levels.  At each level we use joins that follow available join
clauses, if possible, just as described for the first level.

For example:

    SELECT  *
    FROM    tab1, tab2, tab3, tab4
    WHERE   tab1.col = tab2.col AND
        tab2.col = tab3.col AND
        tab3.col = tab4.col

    Tables 1, 2, 3, and 4 are joined as:
    {1 2},{2 3},{3 4}
    {1 2 3},{2 3 4}
    {1 2 3 4}
    (other possibilities will be excluded for lack of join clauses)

    SELECT  *
    FROM    tab1, tab2, tab3, tab4
    WHERE   tab1.col = tab2.col AND
        tab1.col = tab3.col AND
        tab1.col = tab4.col

    Tables 1, 2, 3, and 4 are joined as:
    {1 2},{1 3},{1 4}
    {1 2 3},{1 3 4},{1 2 4}
    {1 2 3 4}

We consider left-handed plans (the outer rel of an upper join is a joinrel,
but the inner is always a single list item); right-handed plans (outer rel
is always a single item); and bushy plans (both inner and outer can be
joins themselves).  For example, when building {1 2 3 4} we consider
joining {1 2 3} to {4} (left-handed), {4} to {1 2 3} (right-handed), and
{1 2} to {3 4} (bushy), among other choices.  Although the jointree
scanning code produces these potential join combinations one at a time,
all the ways to produce the same set of joined base rels will share the
same RelOptInfo, so the paths produced from different join combinations
that produce equivalent joinrels will compete in add_path().

Once we have built the final join rel, we use either the cheapest path
for it or the cheapest path with the desired ordering (if that's cheaper
than applying a sort to the cheapest other path).

If the query contains one-sided outer joins (LEFT or RIGHT joins), or
IN or EXISTS WHERE clauses that were converted to joins, then some of
the possible join orders may be illegal.  These are excluded by having
join_is_legal consult a side list of such "special" joins to see
whether a proposed join is illegal.  (The same consultation allows it
to see which join style should be applied for a valid join, ie,
JOIN_INNER, JOIN_LEFT, etc.)


Valid OUTER JOIN Optimizations
------------------------------

The planner's treatment of outer join reordering is based on the following
identities:

1.	(A leftjoin B on (Pab)) innerjoin C on (Pac)
	= (A innerjoin C on (Pac)) leftjoin B on (Pab)

where Pac is a predicate referencing A and C, etc (in this case, clearly
Pac cannot reference B, or the transformation is nonsensical).

2.	(A leftjoin B on (Pab)) leftjoin C on (Pac)
	= (A leftjoin C on (Pac)) leftjoin B on (Pab)

3.	(A leftjoin B on (Pab)) leftjoin C on (Pbc)
	= A leftjoin (B leftjoin C on (Pbc)) on (Pab)

Identity 3 only holds if predicate Pbc must fail for all-null B rows
(that is, Pbc is strict for at least one column of B).  If Pbc is not
strict, the first form might produce some rows with nonnull C columns
where the second form would make those entries null.

RIGHT JOIN is equivalent to LEFT JOIN after switching the two input
tables, so the same identities work for right joins.

An example of a case that does *not* work is moving an innerjoin into or
out of the nullable side of an outer join:

	A leftjoin (B join C on (Pbc)) on (Pab)
	!= (A leftjoin B on (Pab)) join C on (Pbc)

SEMI joins work a little bit differently.  A semijoin can be reassociated
into or out of the lefthand side of another semijoin, left join, or
antijoin, but not into or out of the righthand side.  Likewise, an inner
join, left join, or antijoin can be reassociated into or out of the
lefthand side of a semijoin, but not into or out of the righthand side.

ANTI joins work approximately like LEFT joins, except that identity 3
fails if the join to C is an antijoin (even if Pbc is strict, and in
both the cases where the other join is a leftjoin and where it is an
antijoin).  So we can't reorder antijoins into or out of the RHS of a
leftjoin or antijoin, even if the relevant clause is strict.

The current code does not attempt to re-order FULL JOINs at all.
FULL JOIN ordering is enforced by not collapsing FULL JOIN nodes when
translating the jointree to "joinlist" representation.  Other types of
JOIN nodes are normally collapsed so that they participate fully in the
join order search.  To avoid generating illegal join orders, the planner
creates a SpecialJoinInfo node for each non-inner join, and join_is_legal
checks this list to decide if a proposed join is legal.

What we store in SpecialJoinInfo nodes are the minimum sets of Relids
required on each side of the join to form the outer join.  Note that
these are minimums; there's no explicit maximum, since joining other
rels to the OJ's syntactic rels may be legal.  Per identities 1 and 2,
non-FULL joins can be freely associated into the lefthand side of an
OJ, but in some cases they can't be associated into the righthand side.
So the restriction enforced by join_is_legal is that a proposed join
can't join a rel within or partly within an RHS boundary to one outside
the boundary, unless the join validly implements some outer join.
(To support use of identity 3, we have to allow cases where an apparent
violation of a lower OJ's RHS is committed while forming an upper OJ.
If this wouldn't in fact be legal, the upper OJ's minimum LHS or RHS
set must be expanded to include the whole of the lower OJ, thereby
preventing it from being formed before the lower OJ is.)


Pulling Up Subqueries
---------------------

As we described above, a subquery appearing in the range table is planned
independently and treated as a "black box" during planning of the outer
query.  This is necessary when the subquery uses features such as
aggregates, GROUP, or DISTINCT.  But if the subquery is just a simple
scan or join, treating the subquery as a black box may produce a poor plan
compared to considering it as part of the entire plan search space.
Therefore, at the start of the planning process the planner looks for
simple subqueries and pulls them up into the main query's jointree.

Pulling up a subquery may result in FROM-list joins appearing below the top
of the join tree.  Each FROM-list is planned using the dynamic-programming
search method described above.

If pulling up a subquery produces a FROM-list as a direct child of another
FROM-list, then we can merge the two FROM-lists together.  Once that's
done, the subquery is an absolutely integral part of the outer query and
will not constrain the join tree search space at all.  However, that could
result in unpleasant growth of planning time, since the dynamic-programming
search has runtime exponential in the number of FROM-items considered.
Therefore, we don't merge FROM-lists if the result would have too many
FROM-items in one list.


Optimizer Functions
-------------------

The primary entry point is planner().

planner()
 set up for recursive handling of subqueries
 do final cleanup after planning
-subquery_planner()
 pull up sublinks and subqueries from rangetable, if possible
 canonicalize qual
     Attempt to simplify WHERE clause to the most useful form; this includes
     flattening nested AND/ORs and detecting clauses that are duplicated in
     different branches of an OR.
 simplify constant expressions
 process sublinks
 convert Vars of outer query levels into Params
--grouping_planner()
  preprocess target list for non-SELECT queries
  handle UNION/INTERSECT/EXCEPT, GROUP BY, HAVING, aggregates,
	ORDER BY, DISTINCT, LIMIT
--query_planner()
   pull out constant quals, which can be used to gate execution of the
	whole plan (if any are found, we make a top-level Result node
	to do the gating)
   make list of base relations used in query
   split up the qual into restrictions (a=1) and joins (b=c)
   find qual clauses that enable merge and hash joins
----make_one_rel()
     set_base_rel_pathlist()
      find seqscan and all index paths for each base relation
      find selectivity of columns used in joins
     make_rel_from_joinlist()
      hand off join subproblems to a plugin, GEQO, or standard_join_search()
-----standard_join_search()
      call join_search_one_level() for each level of join tree needed
      join_search_one_level():
        For each joinrel of the prior level, do make_rels_by_clause_joins()
        if it has join clauses, or make_rels_by_clauseless_joins() if not.
        Also generate "bushy plan" joins between joinrels of lower levels.
      Back at standard_join_search(), apply set_cheapest() to extract the
      cheapest path for each newly constructed joinrel.
      Loop back if this wasn't the top join level.
   Back at query_planner:
    put back any constant quals by adding a Result node
 Back at grouping_planner:
 do grouping(GROUP)
 do aggregates
 make unique(DISTINCT)
 make sort(ORDER BY)
 make limit(LIMIT/OFFSET)


Optimizer Data Structures
-------------------------

PlannerGlobal   - global information for a single planner invocation

PlannerInfo     - information for planning a particular Query (we make
                  a separate PlannerInfo node for each sub-Query)

RelOptInfo      - a relation or joined relations

 RestrictInfo   - WHERE clauses, like "x = 3" or "y = z"
                  (note the same structure is used for restriction and
                   join clauses)

 Path           - every way to generate a RelOptInfo(sequential,index,joins)
  SeqScan       - represents a sequential scan plan
  IndexPath     - index scan
  BitmapHeapPath - top of a bitmapped index scan
  TidPath       - scan by CTID
  AppendPath    - append multiple subpaths together
  MergeAppendPath - merge multiple subpaths, preserving their common sort order
  ResultPath    - a Result plan node (used for FROM-less SELECT)
  MaterialPath  - a Material plan node
  UniquePath    - remove duplicate rows
  NestPath      - nested-loop joins
  MergePath     - merge joins
  HashPath      - hash joins

 EquivalenceClass - a data structure representing a set of values known equal

 PathKey        - a data structure representing the sort ordering of a path

The optimizer spends a good deal of its time worrying about the ordering
of the tuples returned by a path.  The reason this is useful is that by
knowing the sort ordering of a path, we may be able to use that path as
the left or right input of a mergejoin and avoid an explicit sort step.
Nestloops and hash joins don't really care what the order of their inputs
is, but mergejoin needs suitably ordered inputs.  Therefore, all paths
generated during the optimization process are marked with their sort order
(to the extent that it is known) for possible use by a higher-level merge.

It is also possible to avoid an explicit sort step to implement a user's
ORDER BY clause if the final path has the right ordering already, so the
sort ordering is of interest even at the top level.  query_planner() will
look for the cheapest path with a sort order matching the desired order,
and grouping_planner() will compare its cost to the cost of using the
cheapest-overall path and doing an explicit sort.

When we are generating paths for a particular RelOptInfo, we discard a path
if it is more expensive than another known path that has the same or better
sort order.  We will never discard a path that is the only known way to
achieve a given sort order (without an explicit sort, that is).  In this
way, the next level up will have the maximum freedom to build mergejoins
without sorting, since it can pick from any of the paths retained for its
inputs.


EquivalenceClasses
------------------

During the deconstruct_jointree() scan of the query's qual clauses, we look
for mergejoinable equality clauses A = B whose applicability is not delayed
by an outer join; these are called "equivalence clauses".  When we find
one, we create an EquivalenceClass containing the expressions A and B to
record this knowledge.  If we later find another equivalence clause B = C,
we add C to the existing EquivalenceClass for {A B}; this may require
merging two existing EquivalenceClasses.  At the end of the scan, we have
sets of values that are known all transitively equal to each other.  We can
therefore use a comparison of any pair of the values as a restriction or
join clause (when these values are available at the scan or join, of
course); furthermore, we need test only one such comparison, not all of
them.  Therefore, equivalence clauses are removed from the standard qual
distribution process.  Instead, when preparing a restriction or join clause
list, we examine each EquivalenceClass to see if it can contribute a
clause, and if so we select an appropriate pair of values to compare.  For
example, if we are trying to join A's relation to C's, we can generate the
clause A = C, even though this appeared nowhere explicitly in the original
query.  This may allow us to explore join paths that otherwise would have
been rejected as requiring Cartesian-product joins.

Sometimes an EquivalenceClass may contain a pseudo-constant expression
(i.e., one not containing Vars or Aggs of the current query level, nor
volatile functions).  In this case we do not follow the policy of
dynamically generating join clauses: instead, we dynamically generate
restriction clauses "var = const" wherever one of the variable members of
the class can first be computed.  For example, if we have A = B and B = 42,
we effectively generate the restriction clauses A = 42 and B = 42, and then
we need not bother with explicitly testing the join clause A = B when the
relations are joined.  In effect, all the class members can be tested at
relation-scan level and there's never a need for join tests.

The precise technical interpretation of an EquivalenceClass is that it
asserts that at any plan node where more than one of its member values
can be computed, output rows in which the values are not all equal may
be discarded without affecting the query result.  (We require all levels
of the plan to enforce EquivalenceClasses, hence a join need not recheck
equality of values that were computable by one of its children.)  For an
ordinary EquivalenceClass that is "valid everywhere", we can further infer
that the values are all non-null, because all mergejoinable operators are
strict.  However, we also allow equivalence clauses that appear below the
nullable side of an outer join to form EquivalenceClasses; for these
classes, the interpretation is that either all the values are equal, or
all (except pseudo-constants) have gone to null.  (This requires a
limitation that non-constant members be strict, else they might not go
to null when the other members do.)  Consider for example

	SELECT *
	  FROM a LEFT JOIN
	       (SELECT * FROM b JOIN c ON b.y = c.z WHERE b.y = 10) ss
	       ON a.x = ss.y
	  WHERE a.x = 42;

We can form the below-outer-join EquivalenceClass {b.y c.z 10} and thereby
apply c.z = 10 while scanning c.  (The reason we disallow outerjoin-delayed
clauses from forming EquivalenceClasses is exactly that we want to be able
to push any derived clauses as far down as possible.)  But once above the
outer join it's no longer necessarily the case that b.y = 10, and thus we
cannot use such EquivalenceClasses to conclude that sorting is unnecessary
(see discussion of PathKeys below).

In this example, notice also that a.x = ss.y (really a.x = b.y) is not an
equivalence clause because its applicability to b is delayed by the outer
join; thus we do not try to insert b.y into the equivalence class {a.x 42}.
But since we see that a.x has been equated to 42 above the outer join, we
are able to form a below-outer-join class {b.y 42}; this restriction can be
added because no b/c row not having b.y = 42 can contribute to the result
of the outer join, and so we need not compute such rows.  Now this class
will get merged with {b.y c.z 10}, leading to the contradiction 10 = 42,
which lets the planner deduce that the b/c join need not be computed at all
because none of its rows can contribute to the outer join.  (This gets
implemented as a gating Result filter, since more usually the potential
contradiction involves Param values rather than just Consts, and thus has
to be checked at runtime.)

To aid in determining the sort ordering(s) that can work with a mergejoin,
we mark each mergejoinable clause with the EquivalenceClasses of its left
and right inputs.  For an equivalence clause, these are of course the same
EquivalenceClass.  For a non-equivalence mergejoinable clause (such as an
outer-join qualification), we generate two separate EquivalenceClasses for
the left and right inputs.  This may result in creating single-item
equivalence "classes", though of course these are still subject to merging
if other equivalence clauses are later found to bear on the same
expressions.

Another way that we may form a single-item EquivalenceClass is in creation
of a PathKey to represent a desired sort order (see below).  This is a bit
different from the above cases because such an EquivalenceClass might
contain an aggregate function or volatile expression.  (A clause containing
a volatile function will never be considered mergejoinable, even if its top
operator is mergejoinable, so there is no way for a volatile expression to
get into EquivalenceClasses otherwise.  Aggregates are disallowed in WHERE
altogether, so will never be found in a mergejoinable clause.)  This is just
a convenience to maintain a uniform PathKey representation: such an
EquivalenceClass will never be merged with any other.  Note in particular
that a single-item EquivalenceClass {a.x} is *not* meant to imply an
assertion that a.x = a.x; the practical effect of this is that a.x could
be NULL.

An EquivalenceClass also contains a list of btree opfamily OIDs, which
determines what the equalities it represents actually "mean".  All the
equivalence clauses that contribute to an EquivalenceClass must have
equality operators that belong to the same set of opfamilies.  (Note: most
of the time, a particular equality operator belongs to only one family, but
it's possible that it belongs to more than one.  We keep track of all the
families to ensure that we can make use of an index belonging to any one of
the families for mergejoin purposes.)


PathKeys
--------

The PathKeys data structure represents what is known about the sort order
of the tuples generated by a particular Path.  A path's pathkeys field is a
list of PathKey nodes, where the n'th item represents the n'th sort key of
the result.  Each PathKey contains these fields:

	* a reference to an EquivalenceClass
	* a btree opfamily OID (must match one of those in the EC)
	* a sort direction (ascending or descending)
	* a nulls-first-or-last flag

The EquivalenceClass represents the value being sorted on.  Since the
various members of an EquivalenceClass are known equal according to the
opfamily, we can consider a path sorted by any one of them to be sorted by
any other too; this is what justifies referencing the whole
EquivalenceClass rather than just one member of it.

In single/base relation RelOptInfo's, the Paths represent various ways
of scanning the relation and the resulting ordering of the tuples.
Sequential scan Paths have NIL pathkeys, indicating no known ordering.
Index scans have Path.pathkeys that represent the chosen index's ordering,
if any.  A single-key index would create a single-PathKey list, while a
multi-column index generates a list with one element per index column.
(Actually, since an index can be scanned either forward or backward, there
are two possible sort orders and two possible PathKey lists it can
generate.)

Note that a bitmap scan or multi-pass indexscan (OR clause scan) has NIL
pathkeys since we can say nothing about the overall order of its result.
Also, an indexscan on an unordered type of index generates NIL pathkeys.
However, we can always create a pathkey by doing an explicit sort.  The
pathkeys for a Sort plan's output just represent the sort key fields and
the ordering operators used.

Things get more interesting when we consider joins.  Suppose we do a
mergejoin between A and B using the mergeclause A.X = B.Y.  The output
of the mergejoin is sorted by X --- but it is also sorted by Y.  Again,
this can be represented by a PathKey referencing an EquivalenceClass
containing both X and Y.

With a little further thought, it becomes apparent that nestloop joins
can also produce sorted output.  For example, if we do a nestloop join
between outer relation A and inner relation B, then any pathkeys relevant
to A are still valid for the join result: we have not altered the order of
the tuples from A.  Even more interesting, if there was an equivalence clause
A.X=B.Y, and A.X was a pathkey for the outer relation A, then we can assert
that B.Y is a pathkey for the join result; X was ordered before and still
is, and the joined values of Y are equal to the joined values of X, so Y
must now be ordered too.  This is true even though we used neither an
explicit sort nor a mergejoin on Y.  (Note: hash joins cannot be counted
on to preserve the order of their outer relation, because the executor
might decide to "batch" the join, so we always set pathkeys to NIL for
a hashjoin path.)  Exception: a RIGHT or FULL join doesn't preserve the
ordering of its outer relation, because it might insert nulls at random
points in the ordering.

In general, we can justify using EquivalenceClasses as the basis for
pathkeys because, whenever we scan a relation containing multiple
EquivalenceClass members or join two relations each containing
EquivalenceClass members, we apply restriction or join clauses derived from
the EquivalenceClass.  This guarantees that any two values listed in the
EquivalenceClass are in fact equal in all tuples emitted by the scan or
join, and therefore that if the tuples are sorted by one of the values,
they can be considered sorted by any other as well.  It does not matter
whether the test clause is used as a mergeclause, or merely enforced
after-the-fact as a qpqual filter.

Note that there is no particular difficulty in labeling a path's sort
order with a PathKey referencing an EquivalenceClass that contains
variables not yet joined into the path's output.  We can simply ignore
such entries as not being relevant (yet).  This makes it possible to
use the same EquivalenceClasses throughout the join planning process.
In fact, by being careful not to generate multiple identical PathKey
objects, we can reduce comparison of EquivalenceClasses and PathKeys
to simple pointer comparison, which is a huge savings because add_path
has to make a large number of PathKey comparisons in deciding whether
competing Paths are equivalently sorted.

Pathkeys are also useful to represent an ordering that we wish to achieve,
since they are easily compared to the pathkeys of a potential candidate
path.  So, SortGroupClause lists are turned into pathkeys lists for use
inside the optimizer.

Because we have to generate pathkeys lists from the sort clauses before
we've finished EquivalenceClass merging, we cannot use the pointer-equality
method of comparing PathKeys in the earliest stages of the planning
process.  Instead, we generate "non canonical" PathKeys that reference
single-element EquivalenceClasses that might get merged later.  After we
complete EquivalenceClass merging, we replace these with "canonical"
PathKeys that reference only fully-merged classes, and after that we make
sure we don't generate more than one copy of each "canonical" PathKey.
Then it is safe to use pointer comparison on canonical PathKeys.

An additional refinement we can make is to insist that canonical pathkey
lists (sort orderings) do not mention the same EquivalenceClass more than
once.  For example, in all these cases the second sort column is redundant,
because it cannot distinguish values that are the same according to the
first sort column:
	SELECT ... ORDER BY x, x
	SELECT ... ORDER BY x, x DESC
	SELECT ... WHERE x = y ORDER BY x, y
Although a user probably wouldn't write "ORDER BY x,x" directly, such
redundancies are more probable once equivalence classes have been
considered.  Also, the system may generate redundant pathkey lists when
computing the sort ordering needed for a mergejoin.  By eliminating the
redundancy, we save time and improve planning, since the planner will more
easily recognize equivalent orderings as being equivalent.

Another interesting property is that if the underlying EquivalenceClass
contains a constant and is not below an outer join, then the pathkey is
completely redundant and need not be sorted by at all!  Every row must
contain the same constant value, so there's no need to sort.  (If the EC is
below an outer join, we still have to sort, since some of the rows might
have gone to null and others not.  In this case we must be careful to pick
a non-const member to sort by.  The assumption that all the non-const
members go to null at the same plan level is critical here, else they might
not produce the same sort order.)  This might seem pointless because users
are unlikely to write "... WHERE x = 42 ORDER BY x", but it allows us to
recognize when particular index columns are irrelevant to the sort order:
if we have "... WHERE x = 42 ORDER BY y", scanning an index on (x,y)
produces correctly ordered data without a sort step.  We used to have very
ugly ad-hoc code to recognize that in limited contexts, but discarding
constant ECs from pathkeys makes it happen cleanly and automatically.

You might object that a below-outer-join EquivalenceClass doesn't always
represent the same values at every level of the join tree, and so using
it to uniquely identify a sort order is dubious.  This is true, but we
can avoid dealing with the fact explicitly because we always consider that
an outer join destroys any ordering of its nullable inputs.  Thus, even
if a path was sorted by {a.x} below an outer join, we'll re-sort if that
sort ordering was important; and so using the same PathKey for both sort
orderings doesn't create any real problem.



Though Bob Devine <bob.devine@worldnet.att.net> was not involved in the 
coding of our optimizer, he is available to field questions about
optimizer topics.

-- bjm & tgl
