* Pull up Rename rather than pushing it down
  * Currently a Rename applies to every tuple in a result-set, and
    doing the rename prematurely means that lots of tuples that would
    otherwise be filtered out are going to be processed. A better
    approach should be to push the rename up, dropping renames that
    are projected away. It should not distribute over Binary ops
    unless the other side of the binary op has he same aliases.

* For Binary operations, when the left or right is materialized then
  change the other relation to use a restriction to filter the records.
  * This will help optimize the fetching of the underlying records.

* More optimizations:
  * Union
    * A Union of relations with the same base, header, and restrictions should
      try to combine into a single relation with the restrictions using OR.

  * Intersection
    * An Intersection of relations with the same base, header, and restrictions
      should try to combine into a single relation with the restrictions using
      AND.
    * Use the Join::RightMaterializedOperand and Join::LeftMaterializedOperand
      optimizers to simplify Intersection operations

  * Difference
    * A Difference of relations with the same base and restrictions should
      try to combine into a single relation with the restrictions using NOT.

  * Summarization
    * Add OrderSummarizePer for factoring out Order objects inside a Summarization
    * When there are no aggregate functions, drop the Summarization and
      return the summarize_per (?)
      * Use the UnchangedHeader optimizer as a base class
    * When summarize_per is an Order, the Order can be dropped.

  * Projection
    * When it contains a Restriction, if the removed attributes are *not*
      used in the predicate, then move the Restriction to contain the
      Projection.
    * When a Projection contains a Restriction, wrap the Projection
      in the Restriction, projecting away any attributes not used in
      the restriction. If there are any remaining attributes, then
      wrap the operation in a Projection removing those attributes.
      * If all attributes are being used in the Restriction do nothing
    * When renames or extensions or summarizations are projected away and
      not used in any intermediary operation, then they can be dropped
      altogether. There's no point in going through all that work to
      not bother using an attribute at all. It would be better to simplify
      the renames/extensions/summarizations to not add the attribute, and
      then call optimize again on the op to potentially remove the op altogether
      (like in the case of an extension adding one attribute that is removed).
    * It does not distribute over Intersection or Difference, but see if
      perhaps an exception can be made if there is a functional dependency
      between the columns projected away and the one remaining. Then I *think*
      it might still work, but more research will be needed.
    * When a Projection contains a Join, wrap the Join with a Projection
      of all the headers, minus those used in the Join. If there were
      any used, then wrap the whole operation in a Projection with
      the remaining attributes.
      * If all the attributes are used in the Join, do nothing
      * Try to use the same approach for Product
      * Test if it's possible to fully distribute projections over
        joins rather than splitting it up like this.

  * Rename
    * When wrapping a Summarization or Extension, and renaming the new attribute,
      it should change the new attribute name, and remove it from the rename.

  * Restriction
    * Figure out how to reorganize the Restriction predicates so that all
      similar operations are closer together to allow more efficient
      optimizations. This would allow optimizations of stuff like this:

        "attr1 = ? OR attr2 = ? OR attr1 = ?"

      Into:

        "attr1 IN(..) OR attr2 = ?"

    * When it has an equality on a unique attribute:
      * Limit with a limit >= 1 can be factored out
      * Offset with an offset > 0 can be transformed into an empty
        relation, since at most there can be only one match.

   * When wrapping a Product and the predicate only contains
     equality/conjunction between attributes from the left and right
     operands, then transform into a Join.

  * Connective
    * "attr > ? OR attr > ?" -> "attr > ?", with the least restrictive value
      * Do the same for >=, <, <=
    * "attr > ? AND attr > ?" -> "attr > ?", with the most restrictive value
      * Do the same for >=, <, <=
    * "attr > 5 OR attr == 5" -> "attr >= 5"
    * "attr < 5 OR attr == 5" -> "attr <= 5"
    * "attr" = "string" AND "attr" =~ /string/ -> "attr" = "string"
      * If the regexp matches the constant, then it should be
        optimized down to a constant match. If it does not match
        then it should be optimized to a Contradiction.
    * Constant folding, eg:
      "attr1 > attr2 AND attr1 = 5" -> "5 > attr2 AND attr1 = 5"
      * This will probably only work across Conjunctions.
    * "attr > 5 AND attr = 6" -> "attr = 6", because attr must be
      equal to 6. this will probably be related to constant folding;
      the first expression will become 6 > 5, which evaluates to a
      Tautology, then the expression is a Tautology AND attr = 6,
      which simplifies down to attr = 6.
    * "attr < 5 AND attr = 6" -> "Contradiction", because attr must be equal to
      6, and 6 < 5 evaluates to a Contradiction.  A Contradiction AND attr = 6
      simplifies down to a Contradiction.

  * Inclusion/Exclusion
    * When the enumerable is a contiguous sequence transform it into a Range