The date issue intrigued me, so I investigated further. I ran a query against a range of dates to see which values were equal and which were different. Here is the query and its output:

WITH t AS (
  SELECT
    interval '1' month a, 
    interval '7' day c 
  FROM dual ) 
SELECT b, a+(b+c),(a+b)+c FROM t, 
  (SELECT 
    TO_DATE('2007-09-01', 'YYYY-MM-DD') + rownum b 
  FROM ( 
    SELECT null 
    FROM dual 
    CONNECT BY LEVEL <= 31 ));

B         A+(B+C)   (A+B)+C
--------- --------- ---------
02-SEP-07 09-OCT-07 09-OCT-07
03-SEP-07 10-OCT-07 10-OCT-07
04-SEP-07 11-OCT-07 11-OCT-07
05-SEP-07 12-OCT-07 12-OCT-07
06-SEP-07 13-OCT-07 13-OCT-07
07-SEP-07 14-OCT-07 14-OCT-07
08-SEP-07 15-OCT-07 15-OCT-07
09-SEP-07 16-OCT-07 16-OCT-07
10-SEP-07 17-OCT-07 17-OCT-07
11-SEP-07 18-OCT-07 18-OCT-07
12-SEP-07 19-OCT-07 19-OCT-07
13-SEP-07 20-OCT-07 20-OCT-07
14-SEP-07 21-OCT-07 21-OCT-07
15-SEP-07 22-OCT-07 22-OCT-07
16-SEP-07 23-OCT-07 23-OCT-07
17-SEP-07 24-OCT-07 24-OCT-07
18-SEP-07 25-OCT-07 25-OCT-07
19-SEP-07 26-OCT-07 26-OCT-07
20-SEP-07 27-OCT-07 27-OCT-07
21-SEP-07 28-OCT-07 28-OCT-07
22-SEP-07 29-OCT-07 29-OCT-07
23-SEP-07 30-OCT-07 30-OCT-07  <-- Until this row, values are the same
24-SEP-07 01-NOV-07 31-OCT-07  <-- From here on, values are different
25-SEP-07 02-NOV-07 01-NOV-07
26-SEP-07 03-NOV-07 02-NOV-07
27-SEP-07 04-NOV-07 03-NOV-07
28-SEP-07 05-NOV-07 04-NOV-07
29-SEP-07 06-NOV-07 05-NOV-07
30-SEP-07 07-NOV-07 06-NOV-07
01-OCT-07 08-NOV-07 08-NOV-07  <-- From here on, values are the same again
02-OCT-07 09-NOV-07 09-NOV-07

31 rows selected.

What I noticed here is that the difference between the two occurred when one of the values was on the border of a month (eg., last day or first day).

I modified the query to show the value of the INTERVAL by modifying the SELECT clause to add in "b+a-b" as a column:

WITH t AS ( 
  SELECT interval '1' month a, 
    interval '7' day c FROM dual ) 
SELECT b, b+a-b 
FROM t, 
  (SELECT 
    TO_DATE('2007-09-01', 'YYYY-MM-DD') + rownum b 
  FROM ( 
    SELECT null FROM dual CONNECT BY LEVEL <= 31 ));

B              B+A-B
--------- ----------
02-SEP-07         30
03-SEP-07         30
04-SEP-07         30
05-SEP-07         30
06-SEP-07         30
07-SEP-07         30
08-SEP-07         30
09-SEP-07         30
10-SEP-07         30
11-SEP-07         30
12-SEP-07         30
13-SEP-07         30
14-SEP-07         30
15-SEP-07         30
16-SEP-07         30
17-SEP-07         30
18-SEP-07         30
19-SEP-07         30
20-SEP-07         30
21-SEP-07         30
22-SEP-07         30
23-SEP-07         30
24-SEP-07         30
25-SEP-07         30
26-SEP-07         30
27-SEP-07         30
28-SEP-07         30
29-SEP-07         30
30-SEP-07         30
01-OCT-07         31
02-OCT-07         31

31 rows selected.

What is obvious here is that the value of A changes from 30 for all September dates to 31 for the October dates. This coincides with the number of days in the respected months. Another query to demonstrate this difference in the value of INTERVAL:

The + operator is associative over real numbers (complex ones too, come to that) but there’s nothing to say that it has to be associative in all cases. Consider languages where string concatenation is indicated by +

stringvar := ‘Start ‘+ ‘Finish’;

No one reading that would expect A + B equivalent to B + A, would they?

It all comes down to defining your universe.

Regards Nigel

If you allow to add months to a date with a function, it is fine, you can define how it works. But if you use the + operator, the + does lose its intrinsic properties

your reflexivity example should be

with t as (select null a from dual)
select case when a=a then ‘YES’ else ‘NO or undefined’ end “A=A”
from t;

A=A
—————
NO or undefined

because you know quite well SQL is using a three-valued logic
(not ‘YES’ does NOT imply ‘NO’)

month / day - arithmetic
NEVER WAS ASSOCIATIVE IN REAL LIFE
(where did you hear that ?)

Thanks Hector, of course there is an explanation! but it breaks the associativity of the addition.

This example have a logical explication

with t as (
select interval ‘1′ month a,
date ‘2007-09-26′ b,
interval ‘7′ day c
from dual)
select a+(b+c),(a+b)+c
from t
/

A+(B+C) (A+B)+C
——————- ——————-
30-10-2007 00:00:00 30-10-2007 00:00:00

Brief….

A + B is=2007-10-26 + seven days => 27 –> 28 –> 29 –> 30 –> 31 –> 01 –> 02 of October 2007

other way

B + C is=2007-10-03 because 2007-09-26 more(+) seven days –> 27 –> 28 –> 29 –> 30 –> 01 –> 02 –> 03 of September 2007 more(+) one month is 03 October 2007

Another date

SQL> with t as (
2 select interval ‘1′ month a,
3 date ‘2007-07-26′ b,
4 interval ‘7′ day c
5 from dual)
6 select a+(b+c),(a+b)+c
7 from t
8 /

A+(B+C) (A+B)+C
——————- ——————-
02-09-2007 00:00:00 02-09-2007 00:00:00

is the same!

Regards
http://ligarius.wordpress.com

Oh. How stupid do I feel?

>> note that with interval, it is a dangerous mission to deal with months

Fortunately, having worked through the business rules I only need to work with intervals of years. But I still need to worry about leap years. Sigh.

Cheers, APC

That is why in oracle a=b and b=c does not imply a=c, so the equal operator is not absolutely transitive. I almost included this one about neutral element, but I thought it is too special

In addition the neutral element is supposed to be 0

with t as (select time '12:34:56.789' t, interval '999999999' day(9) i from dual) 
select case when t+i=t and i!=interval '0' second then 'YES           ' else 'NO ' end 
  "T+I=T AND I!=0" 
from t;
T+I=T AND I!=0
--------------
YES