What is the correct result for this query?
Per the standard:

SELECT 1 FROM r HAVING 1=1


means

SELECT 1 FROM r GROUP BY () HAVING 1=1


Citation ISO/IEC 9075-2:2011 7.10 Syntax Rule 1  (Part of the definition of the HAVING clause):


  Let HC be the &lt;having clause&gt;. Let TE be the &lt;table expression&gt; that
  immediately contains HC. If TE does not immediately contain a
  &lt;group by clause&gt;, then “GROUP BY ()” is implicit. Let T be the
  descriptor of the table defined by the &lt;group by clause&gt; GBC immediately
  contained in TE and let R be the result of GBC.


Ok so that much is pretty clear.



Assertion: 1=1 is true search condition. I will provide no citation for this.



Now

SELECT 1 FROM r GROUP BY () HAVING 1=1


is equivlent to 

SELECT 1 FROM r GROUP BY ()


Citation ISO/IEC 9075-2:2011 7.10 General Rule 1:


  The &lt;search condition&gt; is evaluated for each group 
  of R. The result of the &lt;having clause&gt; is a grouped
  table of those groups of R for which the result of the
  &lt;search condition&gt; is True.


Logic: Since the search condition is always true, the result is R, which is the result of the group by expression. 



The following is an excerpt from the General Rules of 7.9 (the definition of the GROUP BY CLAUSE)


  1) If no &lt;where clause&gt; is specified, then let T be the result of the preceding &lt;from clause&gt;; otherwise, let T be the result of the preceding &lt;where clause&gt;.
  
  2) Case:
  
  a) If there are no grouping columns, then the result of
  the &lt;group by clause&gt; is the grouped table consisting of T as its only group.


Thus we can conclude that 

FROM r GROUP BY ()


results in a grouped table, consisting of one group, with zero rows (since R is empty).



An excerpt from the General Rules of 7.12, which defines a Query Specification (a.k.a a SELECT statement):


  1) Case:
  
  a) If T is not a grouped table, then [...]
  
  b) If T is a grouped table, then
  
  Case:
  
  i) If T has 0 (zero) groups, then let TEMP be an empty table.
  
  ii) If T has one or more groups, then each &lt;value expression&gt; is applied
  to each group of T yielding a table TEMP of M rows, where M is the
  number of groups in T. The i-th column of TEMP contains the values
  derived by the evaluation of the i-th &lt;value expression&gt;. [...]
  
  2) Case:
  
  a) If the &lt;set quantifier&gt; DISTINCT is not specified, then the
  result of the &lt;query specification&gt; is TEMP.


Therefore since the table has one group, it must have one result row.

Thus 

SELECT 1 FROM r HAVING 1=1


should return a 1 row result set.

Q.E.D.