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Here is the spec I have been noodling with feel free to tell me
what is 
missing or what I haven't thought of. Algebra is but a
distant memory 
to me at this point.

'I' stands for interval 'N' stands for number (real 
or integer),
'D' stands for date. -> is read as creates. The number is 
just
an instance specifier I1 - I2 interval 1 minus interval 2 
etc.

The interval package should support the following 
operations
and use cases:

   I1 + I2 -> I3  - add two intervals

   
I1 - I2  -> I3  - subtract two intervals if I1 > I2 the result is
                       a positive interval 
that will result in a future
                       time when added to a date. Otherwise the
                       
result is a negative interval that will result
                       in a time in the past when 
added to a date.
                       Also,  (I1 - I2) + (I2 - I1) = 0 should be true.

   I * N -> I    - 
multiple an interval by a number. I expect this
                 to take 14 hours and 10 
minutes. so I can do
                 4 of them in 4*(14:10)

   I / N -> I   - divide an 
interval by a number. The average
                    time it took to do this was 
(I1+I2+i3+I4)/4.

  I1/I2 -> N  - Division of two intervals. Used for 
calculating
                   percentage of time in a given state. E.G. I1 is
                   the 
amount of time in the open state. I2 is
                   the amount of time it was in the 
open and
                   testing states. The ratio gives us the amount of
                   time 
spend working compared to time to close.

  D + I -> D  what date time 
is it in 1 day 4 hours

  D - I -> D    what date was it 1 day and 4 hours ago
                   
Also D + (-I) = D - I. where -I is a negative
                   interval.

I claim that only 
I+I should be supported for intervals that
include months since there 
is a fixed number of months per
year and we can round up. If we can use 
some heuristic to
allow carrying from a month into days, then I -I and 
other
operations are allowed.

If we can live with this 
restriction, then the date math needs
to be able to produce the 
difference of two dates without the
months component using days 
instead, which should be
doable since there is a fixed number of days 
between any
two dates.

-- rouilj