Compare words in a string without considering their positions?
I suggest a single SELECT in a plain SQL function:

CREATE OR REPLACE FUNCTION strings_equivalent(a text, b text)
  RETURNS bool AS
$func$
   SELECT a1 = b1
   FROM  (
      SELECT string_agg(w, ' ') AS a1
      FROM  (
         SELECT w
         FROM   unnest(string_to_array(a, ' ')) w
         ORDER  BY w
         ) a1
      ) a2
   , (
      SELECT string_agg(w, ' ') AS b1
      FROM  (
         SELECT w
         FROM   unnest(string_to_array(b, ' ')) w
         ORDER  BY w
         ) b1
      ) b2
   WHERE  length(a) = length(b)
   UNION ALL
   SELECT FALSE
   LIMIT 1;  -- for clarity, not needed
$func$ LANGUAGE sql IMMUTABLE;


Call:

SELECT strings_equivalent('this is a test number 01', 'number this is 01 a test');


This is assuming:


Duplicate words count like any other words
Separator is a single space 
No leading or trailing spaces


The function returns NULL for any empty string or NULL input.

The UNION ALL construct is a shortcut to return FALSE immediately if the input strings don't have the same length and avoid more expensive processing. Related:


Return a value if no record is found
SQL order by query results in any arbitrary (but reproducible) manner


LIMIT 1 is not needed because the function only returns the first column of the first row anyway and ignores the rest if there are more rows.

IMMUTABLE (since the result never changes for the same input) helps performance with repeated evaluation and allows indexes on functional expressions.

You could use regexp_split_to_table(a, ' ') instead of unnest(string_to_array(a, ' ')), but regular expression functions are typically more expensive. (You can cover more sophisticated separator characters with the regex, though, like '\s+' for any white space). Related:


How to preserve the original order of elements in an unnested array?




BTW, your simple function sort_text() looks good. But use string_agg() instead of array_to_string(ARRAY(...)) in a simple SQL function. No variable assignment needed:

CREATE OR REPLACE FUNCTION sort_text(a text)
  RETURNS text AS
$$
   SELECT string_agg(w, ' ')   
   FROM  (
      SELECT w
      FROM   unnest(string_to_array(a, ' ')) w
      ORDER  BY 1
      ) sub
$$ LANGUAGE sql IMMUTABLE;