There are two cases that could be improved:

1) We do not remove negations of negations. Example:

> t.drop()
> t.ensureIndex({a: 1})
> t.find({a: {$not: {$not: {$gt: 1}}}})

This query parses to the match expression below:

$not
    $not
        a $gt 1.0

Since this has a negation of something that is not bounds-generating (more precisely, another negation), this query will not use the index. If instead the CanonicalQuery::normalizeTree function rewrote this tree to simply "a $gt 1.0", then it would do an index scan over (1, Infinity] rather than a collection scan.

In 2.4.8, a double-negation is not allowed at all:

> t.find({a: {$not: {$not: {$gt: 1}}}})
error: { "$err" : "invalid use of $not", "code" : 13034 }

Another option is for canonicalization to return an error if it finds a double negation.

2) Tree normalization does not pass through $elemMatch. Example:

> t.ensureIndex({a: 1})
> t.find({a: {$elemMatch: {b: {$not: {$gt: 1}}}}})

This parses to the match expression shown below:

a $elemMatch (obj)
    $not
        $and
            b $gt 1.0

Since normalization does not pass through the $elemMatch, we do not end up removing the single-child $and as we would elsewhere. In other words, the canonicalized tree should be

a $elemMatch (obj)
    $not
         b $gt 1.0